What a Wave Buoy Actually Measures in 3D: analysis of a Mild Sea State

Measurements of surface waves from oceanographic buoys have been regarded as the “ground truth” for validation of sea-state prediction models, providing the basis for input to the design of offshore structures. The engineering practice is to produce wave statistics of vertical surface displacements over periods of years. However, a wave buoy can provide simultaneous time histories of its motion, one vertically and the other two horizontally, giving the complete vector displacement field in time. We investigate the measured time histories of a wave buoy in three orthogonal directions and explore the relationship between them, for a relatively benign, so typical, sea state. We adopt a NewWave-type analysis to investigate the average shape of the large events across the measured time histories. In combination with a conditioning analysis, we give a reciprocity relationship between the vertical displacement of the wave buoy and those in the horizontal plane. The relationship is of value, as it allows for the prediction of wave kinematics in the horizontal plane based on the vertical measurement only. We observe significant second-order components in the measured data in the horizontal directions and smaller contributions vertically. This data-driven analysis paves the way for wave-by-wave prediction and the active control of wave energy converters and personnel transfers offshore.