A Simulator for SAR Sea Surface Waves Imaging Ferdinando Nunziata, Attilio Gambardella and Maurizio Migliaccio Università degli Studi di Napoli Parthenope Dipartimento per le Tecnologie Via Medina, 40 - 80037 Napoli Email: {ferdinando.nunziata, attilio.gambardella, maurizio.migliaccio} at uniparthenope.it Abstract—This paper describes a Synthetic Aperture Radar (SAR) sea surface waves simulator. The simulator, based on the velocity bunching (VB) theory, has been developed and impemented modularly and its use can also assist microwave remote sensing courses. The present version of the software is run in classes at National Oceanographic Centre of Southampton (NOCS), UK and at the Università di Napoli Parthenope, Italy. I. I NTRODUCTION Microwave remote sensing sensors are widely used in sea monitoring due to their all-weather day and night capability. Among these sensors the Synthetic Aperture Radar (SAR) has succesfully demonstrated its capacity to uniquely provide valuable high resolution information for marine applications [1]. However, SAR imaging of the sea surface is considerably more complex than the imaging of a stationary scene. In particular, though wave-like patterns are often discernible on sea surface SAR images obtained both from aircraft and space missions, the relationship between such patterns and the actual sea surface wave field is an intriguing and non-trivial issue [2]. Hence, simulation procedures can be very helpful to shed light in physical aspects governing the SAR sea suface waves imaging. Two main theories have been proposed: the distributed surface (DS) theory [3] and the velocity bunching (VB) one [4]. Most of the available SAR surface waves simulators [2], [5], [6], [7], are developed in programming language not user-friendly, they are time consuming and thus they are not able, for example, to be run in classes at University for educational purposes. In this paper a SAR sea surface waves simulator, based on VB theory, is presented and discussed. It is entirely developed in Matlab environment, which is probably the most popular programming environment at educational and research centres. The simulator can run on Windows, Mac OS and Linux PC systems and only a student version of Matlab is required. To facilitate users a Graphic User Interface (GUI) has been developed. The present version of the software is run in classes at National Oceanographic Centre of Southampton (NOCS), UK and at the Università di Napoli Parthenope, Italy. The paper is organized as follows. In section II the back- ground scattering theory governing the SAR sea surface waves imaging is reviewed. In section III the simulation approach is described and in section IV some meaningful experiments are presented and discussed. In section V the conclusions are drawn. II. THEORETICAL FACTS The scattering machanism governing the formation of a conventional SAR sea surface waves image can be modelled by a two-scale scattering model which includes the sea dy- namics. Since satellite and airborne SAR generally operates at incidence angles ranging between 20 ◦ and 70 ◦ , for low to moderate sea state, it is normally assumed that the small scale backscattering mechanism is the Bragg one [2], [4]. According to Bragg theory only sea waves whose wavelengths are the same order of the incidence electromagnetic one are ‘seen‘ by the SAR. Thus longer waves are imaged indirectly because of Real Apertur Radar (RAR) modulation mechanism and motion induced effects (MI). The RAR mechanism can be described by a linear function, the RAR Modulation Transfer Function (MTF), which relates the Normalized Radar Cross-Section (NRCS) to the long sea wave field. Under the hypothesis of linear modulation the RAR MTF does not depend on the long wave field an can be decomposed in three terms: tilt, R t (·), range bunching, R rb (·), and hydrodynamic modulation, R h (·) [4], [8]. Thus, according to this theory, the dynamic NRCS, σ o (·), can be written as [8]: σ o (x o )= σ o  1+ M  m=1   R RAR (K m )   z m (K m ) · cos(K m x o + ϕ m + ψ m )  . (1) Here x o =(x o ,y o ) and x =(x,y) are the ocean surface and the corresponding SAR plane, respectively. In particular x denotes the coordinate in flight (azimuthal) direction, y denotes the one in cross-track or ground range direction. The amplitudes z(K) are related to the two-dimensional ocean wave spectrum sampled by M long wave wavenumbers K. ϕ m is an uniformly distributed random variable, σ o is the NRCS evaluated according to Small Perturbation Model (SPM), R RAR (K m ) and ψ m denote modulus and phase of the RAR MTF, respectively [8]. The MI effects are SAR inherent artefacts. In fact, since SAR is a coherent system, in order to form an image, it relies on the signal phase structure derived from each elemental scatter in the observed scene. In the case of ocean surface, in presence of a longer gravity which across the scene, all the particles, including the short Bragg resonant waves, are advected giving rise their orbital velocity. Thus, a SAR 1-4244-1212-9/07/$25.00 ©2007 IEEE. 786