The goal of the project is to solve the scientific challenges for predicting individual waves on the ocean before they happen. The wave field will first be observed at a distance with radar. Then the propagation of the wave field will be computed forward in time and space in order to predict individual waves. The prediction should be given sufficiently early that it can be used as a tool in marine operations. We especially want to predict extreme or freak waves, i.e. waves surprisingly large in comparison to the actual sea state.
There are several challenges: The relationship between the radar image and the actual sea surface is complicated and to some extent unknown, this is partially due to the radar not providing all the information we would desire because high crests can shadow the sea surface farther away. The radar can see only a limited part of the sea surface which may not be sufficient to characterize the wave field such that a good prediction can be made, this is especially true for short-crested seas or crossing seas, i.e. sea states propagating in various directions simultaneously. The models for wave propagation should be both fast and robust such that useful predictions can be made also in cases of limited data or limit computational capacity. Finally it is also desirable to recognize characteristic properties of wave fields as precursors for enhanced probability for extreme or freak waves.
If all of these challenges are solved and integrated into a common system, then this would be useful for the maritime sector. We have worked on each of these challenges separately and achieved progress within each one. This project has made important contributions to achieving an integrated system. In the following we summarize our most important results.
The project has funded two Ph.D. students, but a third Ph.D. student also worked as an integrated part of the team, therefore we summarize in the following the most important results published by the three students Tore Magnus Taklo, Abushet Simanesew, Susanne Støle-Hentschel and their supervisors until summer 2018:
Radar inversion and reconstruction of the sea surface: Conventional nautical radars are incoherent X-band and only give amplitude signals. We have employed a more advanced coherent X-band radar also providing Doppler signals. We have shown good comparisons between the reconstruction of the sea surface between the Doppler signals and the conventional amplitude signals (Støle-Hentschel, Seemann, Nieto Borge & Trulsen 2018).
Description of the properties of wave fields: We have shown how nonlinear behavior of wave fields lead to systematic deviation from the linear dispersion relation, in a way that has not been documented so far, wave energy can be distributed in wavenumber-frequency space along the tangent to the linear dispersion relation (Taklo, Trulsen, Gramstad, Krogstad & Jensen 2015; Taklo, Trulsen, Krogstad & Nieto Borge 2017). Here the wavenumber is the inverse of the wave length, the frequency is the inverse of the wave period, and the dispersion relation gives the relationship between the wavenumber and the frequency for free waves. We have also shown how typical directional spreading and bimodality for ocean waves behave and is established surprisingly fast by nonlinear interaction (Simanesew, Krogstad, Trulsen & Nieto Borge 2016; Simanesew, Krogstad, Trulsen & Nieto Borge 2018).
Prediction of individual waves: We have shown that the region in time and space, in which it is possible to give a prediction, is limited by the group velocity of the wave field (Naaijen, Trulsen & Blondel-Couprie 2014). We have demonstrated how various methods for predicting short-crested sea work in practice (Simanesew, Trulsen, Krogstad & Nieto Borge 2017). Thereby we have generated new knowledge about the feasible time and space horizons for the prediction of individual waves.
Extreme and freak waves: We have shown how uneven bathymetry can provoke locally enhanced occurrence of freak waves, localized to a certain distance on the inside of a shoal (Gramstad, Zeng, Trulsen & Pedersen 2013). We have published simulations of the crossing sea state that occurred when the oil tanker Prestige suffered an accident off Spain in 2002, and we have argued that this crossing sea state not likely provoked enhanced probability for freak waves as a possible cause for the oil catastrophe that resulted (Trulsen, Nieto Borge, Gramstad, Aouf & Lefevre 2015). We have also shown how crossing sea states under certain circumstances can reduce the probability for extreme and freak waves (Støle-Hentschel, Trulsen, Rye & Raustøl 2018).

Weather sensitive offshore operations will benefit from the possibility of real time predictions of the local wave surface conditions over time intervals of the order of seconds to minutes. This applies to dynamic positioning of vessels and marine operat ions such as float-over-installation, lifting operations, LNG loading connection, and helicopter take-off and landing, to mention a few. Such predictions would also warn against freak waves or dangerous wave groups. Another important application is alte rnative energy, where the prediction leads to enhanced extraction of power from floating wind turbines and, in particular, some wave power installations that are critically dependent on accurate dynamic control.
The current project aims to achieve a syst em making this possible by combining real time radar remote sensing and deterministic wave prediction.
An important step towards bringing these ideas into reality have been the recent advances in the inversion of X-band nautical radar imagery into real o cean surface elevation.
Practical demonstration efforts reported so far have been limited to linear wave models as well as a linearized inversion mechanism for the radar images. However, there is strong evidence that attention to nonlinear effects can s ubstantially improve performance of both. We will focus attention on nonlinearity in the imaging mechanisms for nautical radar, the assimilation of radar data into wave prediction models, and the wave propagation model itself, with the goal of significan tly improving the quality and extending the horizon of real time wave predictions.