For advanced offshore engineering applications the prediction with available nautical X-band radars of phase-resolved incoming waves is very much desired. At present, such radars are already used to detect averaged characteristics of waves, such as the peak period, significant wave height, wave directions and currents. A deterministic prediction of individual waves in an area near the radar from remotely sensed spatial sea states needs a complete simulation scenario such as will be proposed here and illustrated for synthetic sea states and geometrically shadowed images as synthetic radar images. The slightly adjusted shadowed images are used in a dynamic averaging scenario as assimilation data for the ongoing dynamic simulation that evolves the waves towards the near-radar area where no information from the radar is available.The dynamic averaging and evolution scenario is rather robust, very efficient and produces qualitatively and quantitatively good results. For study cases of wind waves and multi-modal wind-swell seas, with a radar height of 5 times the significant wave height, the correlation between the simulated and the actual sea is found to be at least 90%; future waves can be predicted up to the physically * Corresponding author at : LabMath-Indonesia, Jl. Dago Giri no 99, Warung Caringin, Mekarwangi, 40391 Bandung, Indonesia. Tel : +62 22 2507476Email address: a.parama@labmath-indonesia.org (A. P. Wijaya ) May 25, 2015 maximal time horizon with an averaged correlation of more than 80%. Preprint submitted to Ocean Engineering

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A method is presented for the inversion of images of the sea surface taken by nautical radar into wave elevation that is specifically suitable for the prediction of the wave elevation outside the observation domain covered by the radar. By means of a beam-wise analysis of the image obtained by a scanning radar, the image information is translated into wave elevation. Subsequently a 2D FFT is applied in order to obtain the directional wave components required for a linear propagation of the wave field. Assuming knowledge of the significant wave height, a method to obtain the correct scaling of the wave prediction is proposed. The proposed method is verified using synthetic radar images which are modelled by applying shadowing and tilt effect to synthesised short crested linear waves.

The use of remotely wave sensing by a marine radar is increasingly needed to provide wave information for the sake of safety and operational effectiveness in many offshore activities. Reconstruction of radar images needs to be carried out since radar images are a poor representation of the sea surface elevation: effects like shadowing and tilt determine the backscattered intensity of the images. In [1], the sea state reconstruction and wave propagation to the radar has been tackled successfully for synthetic radar images of linear seas, except for a scaling in the vertical direction. The determination of the significant wave height from the shadowed images only has been described in [2]. This paper will summarize these methods, and provides the first results for the extension to nonlinear seas.

In Part 1, Van Groesen et al. (J Ocean Eng Mar Energy, 2017), a numerical study of extreme waves in socalled Draupner seas showed that extreme crest heights of 18 m, one-and-a-half times the significant wave height, occur in a time span of 20 min on average in every area less than 1 km 2 . Such extreme, steep waves are dangerous for ships and offshore structures. In this Part 2, we demonstrate that using synthetic images of an X-band radar such high waves can be predicted around 60 s before their actual appearance. It will be shown that a recent dynamic average and evolution scenario (DAES) that has demonstrated to lead to good reconstruction of the sea from distorted shadowed radar images of synthetic seas with moderate wave heights can also be applied to the high seas using nonlinear evolution codes. Taking at one instant a reconstructed sea state to calculate the nonlinear sea in future times leads to a qualitatively good prediction that can warn ships of freak waves before their appearance.