Wave heights from sea surface and bottom measurements: Variations with different water depths

Wave instruments equipped with pressure sensors have long been recognized as an effective means of obtaining statistical characteristics of wave distributions in complex sea conditions. However, the commonly used theory based on pressure response functions may not accurately capture surface height signals due to the nonlinearity of wave propagation at different water depths. To address this issue, field measurements were conducted at five stations with water depths ranging from 2.4 m to 54.8 m. The validity threshold of the linear wave theory was investigated using surface buoy and bottom pressure measurements. Statistical analyses showed that the classical linear theory performed well in shallow water, but its credibility decreased with increasing depth. In addition, the measured data showed agreement with the Weibull distribution for wave pressure and the Rayleigh distribution for surface wave height. For applications in ocean and coastal engineering, we propose two empirical formulas for estimating wave heights based on seabed or sea surface measurements at intermediate water depths. These formulas take into account the ratio of wave height to water depth, which reflects the nonlinear effects in shallow water, thereby improving the accuracy of surface wave height estimation (with an accuracy of ±10%) compared to the traditional linear theory method.