Measuring free surface elevation of shoaling waves with pressure transducers

An assessment of formulas to recover wave surface elevation from pressure measurements was carried out in the present study. The investigation focused on the formulas’ performance in the shoaling region, i.e. where the wave nonlinearity gradually increases as the wave travels towards shallower waters. Formulas based on linear wave theory alongside nonlinear reconstructions were considered. Experiments in a large-scale wave flume provided with a concrete beach profile were performed, in which regular waves were generated and surface elevation was measured with acoustic, resistive and pressure gauges. The considered formulas require the application of a cutoff frequency to the wave signal in order to avoid high frequencies amplification that progressively arise as wave shoaling occur. A simple but effective method to obtain a reference cutoff frequency is proposed in the present work; the method is based on a polynomial fitting of the unfiltered wave energy spectrum. A sensitivity analysis of each formula to the variation of this cutoff frequency was carried out. Results showed that all the investigated formulas recover wave elevation fairly well for low-nonlinearity waves, whereas overestimating wave crest height as nonlinearity increases. Wave reconstruction of the linear formulation performance was comparable to nonlinear formulations in terms of wave crest height reconstruction, although tending to amplify frequencies in the wave trough. Moreover, the performance of the formulas to correctly recover the asymmetry and flatness of the surface elevation distribution was assessed by analysing third- and fourth-order moment statistics. In this sense, nonlinear reconstruction formulas performed better in recovering the asymmetric distribution of the wave elevation, with the formula based on linear wave theory underestimating skewness and kurtosis for large nonlinearity waves.