A nonlinear weakly dispersive method for recovering the elevation of irrotational surface waves from pressure measurements

We present the derivation of a nonlinear weakly dispersive formula to reconstruct, from pressure measurements, the surface elevation of nonlinear waves propagating in shallow water. The formula is simple and easy to use as it is local in time and only involves first and second order time derivatives of the measured pressure. This novel approach is evaluated on laboratory and field data of shoaling waves near the breaking point. Unlike linear methods, the nonlinear formula is able to reproduce at the individual wave scale the peaked and skewed shape of nonlinear waves close to the breaking point. Improvements in the frequency domain are also observed as the new method is able to accurately predict surface wave elevation spectra over four harmonics. The nonlinear weakly dispersive formula derived in this paper represents an economic and easy to use alternative to direct wave elevation measurement methods (e.g. acoustic surface tracking and LiDAR scanning).