An Effective Water Depth Correction for Pressure-Based Wave Statistics on Rough Bathymetry

Abstract Near-bottom pressure sensors are widely used to measure surface gravity waves. Pressure spectra are usually converted to sea surface elevation spectra with a linear-theory transfer function assuming constant depth. This methodology has been validated over smooth sandy beaches but not over complex bathymetry of coral or rocky environments. Bottom-mounted pressure sensors collocated with wave buoys in 10–13-m water depth from a 5-week rocky shoreline experiment are used to quantify the error of pressure-based surface gravity wave statistics and develop correction methods. The rough bathymetry has O (1) m vertical variability on O (1–10) m horizontal scales, much shorter than the 90–40-m wavelength of sea band (0.1–0.2 Hz). For sensor stability, pressure sensors were deployed by divers in bathymetric lows. When using the local depth measured by the pressure sensor, significant wave height squared overestimates the direct wave buoy measurements (up to 21%) in the sea band. An effective depth hypothesis is proposed where a spatially averaged water depth provides more accurate wave height statistics than the local depth at the pressure sensor. An optimal depth correction, estimated by minimizing the wave height error, varies from 0.1 to 1.6 m. A bathymetry averaging scale of 13 m is found by minimizing the median bathymetry deviation relative to the optimal. The optimal and averaged bathymetry depth corrections are similar across locations and, using linear theory, significantly reduce wave statistical errors. Therefore, pressure-based wave measurements require a correction that depends on the spatially averaged bathymetry around the instrument. The larger errors when using the local depth suggest that approximately linear surface waves are not strongly modified by abrupt depth changes over O (1) m horizontal scales. Significance Statement The measurement of surface waves by bottom-mounted pressure sensors relies on wave theory formally derived for constant depth. We show that the constant depth assumption leads to systematic errors in wave statistics from observations over a rough, rocky bottom. By considering a spatially averaged bathymetry instead of the local water depth at the pressure sensor, the accuracy of wave energy density is improved, and upper-bound biases decay from 20% to 10%.