Phase-Resolved Reconstruction Algorithm and Deterministic Prediction of Nonlinear Ocean Waves From Spatio-Temporal Optical Measurements

We investigate a nonlinear phase-resolved reconstruction algorithm and models for the deterministic prediction of ocean waves based on a large number of spatio-temporal optical measurements of surface elevations. We consider a single sensor (e.g., LIDAR, stereo-video, etc.) mounted on a fixed offshore structure and remotely measuring fields of free surface elevations. Assuming a uniform distribution of measurement points over the sensor aperture angles, the density of free surface observation points geometrically decreases with the distance from the sensor. Additionally, wave shadowing effects occur, which become more important at small viewing angles (i.e., grazing incidence on the surface). These effects result in observations of surface elevation that are sparsely distributed. Here, based on earlier work by [1], we present and discuss the characteristics of an algorithm, aimed at assimilating such sparse data and able to deterministically reconstruct and propagate ocean surface elevations for their prediction in time and space. This algorithm could assist in the automatic steering and control of a variety of surface vehicles. Specifically, we compare prediction results using linear wave theory and the weakly nonlinear Choppy Wave Model [2, 3], extended here to an “improved” second order formulation. The latter model is based on an efficient Lagrangian formulation of the free surface and was shown to be able to model wave properties that are important to the proper representation of nonlinear free surfaces, namely wave shape and celerity. Synthetic datasets from highly nonlinear High Order Spectral simulations are used as reference oceanic surfaces. Predicted results are analyzed over an area that evolves in time, using the theoretical amount of information assimilated during the reconstruction of the wave field. For typical horizons of prediction, we discuss the capabilities of our assimilation process for each wave model considered.