A comparison of linear and nonlinear 3D semi-Lagrangian motion of moored Waverider and Spotter wave buoys

Wave records from oceanographic buoys remain indispensable in coastal and offshore engineering. Modern wave buoys produce semi-Lagrangian time histories of motions in three dimensions (one vertical and two horizontal) in addition to the standard statistical output. Datawell Directional Waverider (DWR) buoys have long been recognized as providing high quality measurements, while other types of wave buoys have been introduced more recently. This study analyses field data measured by two types of wave buoys: one DWR4 and three Sofar Spotter buoys, all moored on intermediate water depth offshore Western Australia. The time histories recorded by the two types of wave buoys in three orthogonal directions and the relationship between them are comprehensively examined on a wave-by-wave basis. Although focusing on mild sea states, the analysis identifies significant second-order motion components in the horizontal plane for both DWR4 and Spotter buoys. It is confirmed that both DWR and Spotters work well and consistently in the vertical direction. However, we present considerable evidence that the DWR4 buoy overestimates the displacements in the horizontal plane by a factor of approximately 1/0.85 times, while the Spotter buoys’ displacements match well with theoretical predictions in the horizontal plane. Despite this apparent calibration error, both the mean wave direction and the directional spreading match well between the two buoy types, with the DWR4 giving slightly lower spreading angles at higher frequency. These observations shed new insights into the wave buoy motions in 3D on intermediate water depth. • Measured data from DWR4 and Sofar Spotter buoys are comprehensively analysed. • Both statistical analysis and wave-by-wave analysis are conducted. • Nonlinear components are clearly identified in these semi-Lagrangian motion data. • It is striking to observe that the DWR4 buoy overestimates horizontal displacements.