A method for the reconstruction of nonlinear ocean surfaces is presented and applied to regular waves. From random samples of surface elevation, the method reconstructs the nonlinear features of the observed waves by means of the High-Order Spectral approach. The reconstructed surface is then propagated to provide a prediction at a later time. The agreement of the reconstructed and predicted surfaces with the reference one is quantified for a wide range of wave steepness. In each case, the accuracy of the surface elevation and surface velocity potential is evaluated for the first-, second- and third-orders of nonlinearity, while the reference surface corresponds to a fourth-order solution. This way, the improvement of the solution pertaining to each order of nonlinearity can be easily identified. The results show that the grid-based method is able to correctly reconstruct highly nonlinear regular waves, providing an accurate initial solution for the surface propagation. Due to the effect of the nonlinear dispersion, it is further shown that the third order of nonlinearity is necessary to obtain an accurate reconstruction/prediction of steep waves.
