An Experimental Study of the Systematic Underestimation of Wave Crests Measured by Lagrangian Buoys, and a Retrospective Correction Method

Wave-following buoys are used to provide measurements of free surface elevation across the oceans. The measurements they produce are widely used to derive wave-averaged parameters such as significant wave height and peak period, alongside wave-by-wave statistics such as crest height distributions. Particularly concerning the measurement of extreme wave crests, these measurements are often perceived to be less accurate. We directly assess this through a side-by-side laboratory comparison of measurements made using Eulerian wave gauges and model wave-following buoys for directionally spread waves representative of extreme conditions on deep water. Our experimental measurements are compared to exact (Herbers and Janssen 2016, J. Phys. Oceanogr, 46, 1009-1021) and new approximate expression for Lagrangian second-order theory derived herein. We derive simple closed-form expressions for the second-order contribution to crest height representative of extreme ocean waves. Our experiments confirm that the motion a wave-following buoy should not significantly affect the measurements of wave crests or spectral parameters, and that discrepancies observed for in-situ buoy data are most likely a result of filtering. This filtering occurs when accelerations that are measured by the sensors within a buoy are converted to displacements. We present an approximate means of correcting the resulting measured crest height distributions, which is shown to be effective using our experimental data.