Deterministic models for wave and ship motion forecasting, based on measurements collected from wave radar, are becoming more and more appealing with the improvement of marine wave radar technologies. Although these devices are largely validated for the assessment of the characteristics of the sea spectrum, several improvements are still necessary to achieve an accurate deterministic reconstruction of the wave field in time and space. The common filtering techniques adopted for the analysis of the marine wave radar imaging are nowadays targeting the identification of the more prominent wave field features of the sea spectrum. This work instead investigates the feasibility of reconstructing the instantaneous wave field from radar imaging. To this end two different methodologies are compared. The first approach, referred to as LSQR, is a novel approach based on a regularised inversion of the radar tilt modulation model. The use of a linearised model for the wave radar imaging and a linear wave model for the sea elevation allows the derivation of a linear discrete inverse problem which is solved through a least-squares technique. The second approach, which is also the more common in the wave radar community, is based on the concept of Modulation Transfer Function (MTF). The adopted MTF approach is based on the idea of deriving a tuned MTF form a series of numerical simulation. The performances of two different approaches in inverting series of synthetic radar images derived from a known set of wave elevation time histories are then compared.
Marine X-band radar is a widespread technology originally employed to detect targets on the sea surface as ships or navigation obstacles. Therefore, the radar echoes arising from the sea surface have been usually considered as an undesired signal (clutter) for navigation purposes. In fact, the sea surface induced radar echoes as well as the interaction between the electromagnetic waves can strongly affect the capability to detect obstacles during the navigation, (Granström et al., 2015). Nevertheless, the last few decades of research on these devices have turned the radar echoes coming from the sea surface into a key asset for the estimation of the gravity waves features. The electromagnetic scattering of the X-band radar signal is deeply affected by the sea surface roughness due to the presence of the wind-induced ripples (Lee et al., 1995). The presence of the longer gravity waves underlying the wind induced ripples is sensed by the wave radar as a modulation of the Radar Cross Section (e.g. tilt modulation, hydrodynamic modulation and shadowing modulation) that, once correctly interpreted, makes the gravity waves visible on the radar images (Plant and Keller, 1990).
