Abstract
Observations of waves as a time series from a fixed or moored sensor are shown to underestimate the extreme waves occurring in the vicinity. The underestimate arises because of the difference in phase and envelope propagation of surface water waves so that the highest crest, for example, is recorded only when the crest coincides with the envelope maximum at the location of the wave recorder. In addition, the dispersive nature of water waves can lead to the coalescence of groups of waves as longer waves catch up to shorter slower waves, so that the group shape changes markedly as the waves propagate. Moored accelerometer buoys introduce another error that exacerbates the underestimate of the highest crest—the quasi-Lagrangian motion of the buoy leads to flattening of the crests and sharpening of the troughs so that apparent mean water level is raised and thus the height of crests above it is reduced. An analysis approach to correct these underestimates is outlined and tested with observed data against the predictions of extreme values based on narrow-banded random wave theory.
