A comparison of time-and space-determined wave geometry for individual non-breaking waves in unidirectional random sea states

Because high-resolution spatial wave measurements are difficult to obtain in the field, individual-wave geometry is often estimated from point-based time series, with wavelength inferred by applying the linear dispersion relation to the measured wave period. We evaluate the accuracy of this approach using time-synchronised digital cameras to record the temporal and spatial evolution of unidirectional, non-breaking waves in laboratory-generated random sea states. Individual waves are identified through zero-crossing analysis and matched between the time and space domains using the digital imagery. In total, we have analysed almost 55,000 matched waves encompassing both unforced and wind-forced conditions. For each wave, direct spatial measurements of crest height, wavelength, and steepness are compared with the corresponding values derived from point-based time-domain records. The results show that time-and space-domain crest heights agree closely, as expected, but time-derived wavelength and wave steepness estimates show larger discrepancies from their spatially measured values. A wave-type classification shows that these differences are most pronounced for waves containing additional local peaks within their spatial wavelength or temporal period, for which we use the term ”irregular”, characteristic of shorter waves superimposed on longer waves. Temporally-derived and spatially-measured wavelength and steepness are typically in good agreement for ”regular-like” waves across the sea states examined. We further introduce a paired zero-crossing wave-combination scheme that identifies waves with more reliable time-derived geometric estimates while retaining approximately 80% of the observations. These findings provide a practical approach for improving estimates of individual-wave geometry when only point-based temporal measurements are available. Plain Language Summary Ocean waves are usually measured at a fixed point using buoys or gauges. To estimate wavelength and wave steepness that describe the wave shape in space, the linear dispersion relation is used. However, this conversion relies on assumptions that may not hold for unsteady waves. We used high-resolution cameras in a laboratory wave channel to measure nearly 55,000 individual waves in both time and space, allowing us to directly compare wave properties measured in space with those estimated from time records. While wave crest heights match very well, wavelength and steepness can differ significantly, especially when wind is present. We therefore developed a scheme that combines two standard methods of separating waves in time to identify a large subset of waves with more reliable geometric estimates. These findings can improve the interpretation of point-based wave records used in ocean science and engineering.