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 background 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. 1-4244-1212-9/07/$25.00 ©2007 IEEE. II. T HEORETICAL 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 dynamics. 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, Rt (·), range bunching, Rrb (·), and hydrodynamic modulation, Rh (·) [4], [8]. Thus, according to this theory, the dynamic NRCS, σ o (·), can be written as [8]: ( M X o o RRAR (Km ) zm (Km ) σ (xo ) = σ 1 + m=1 ) · cos(Km xo + ϕm + ψm ) (1) . Here xo = (xo , yo ) 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. ϕm is an uniformly distributed random variable, σ o is the NRCS evaluated according to Small Perturbation Model (SPM), RRAR (Km ) and ψm 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 786 coherently senses the radial component of this orbital motion. In particular the radial component of the orbital velocity gives rise to the well-known velocity bunching phenomenon [4], [2]. The radial component of the orbital acceleration is responsible for the degradation of the azimuthal resolution. Since both orbital acceleration and orbital velocity vary along the flight direction they can produce a wave-like pattern onto SAR image. Actually, in addition to this acceleration induced mechanism, the azimuthal resolution is also degraded by the sub-resolution scale variations of the orbital velocities which characterize the different backscattering elements within the SAR resolution cell. This term can be modelled by a scene coherence time [2], [8]. Once the main processes responsible for the wave-like formation onto SAR images have been described, the relationship between the SAR image intensity I(x) and the dynamic NRCS is given by [2], [8]: Z o σ (xo ) I(x) = δ(y − yo ) ρa (xo ) (  2 ) (2) R π2 x − xo − ur (xo ) · exp − . ρa (xo ) V Here R and V are slant range of the target and platform velocity, respectively. δ(·) is the Dirac delta function. ρa (·) is the degraded azimuthal resolution, which depends on the orbital acceleration, scene coherence time, sensor integration time and nominal azimuthal resolution [2]. ur (·) is the orbital velocity [8]. MI effects can make the overall SAR MTF higly non-linear. In fact, both VB and the degradation in azimuthal resolution can be, for certain radar and sea parameters, highly non-linear mechanisms [2]. According to [4], [2] VB depends on the gradient of the azimuthal component of the orbital velocity. The degree of non-linearity of VB is strongly related to the direction of the long waves. In detail, for range travelling waves, VB vanishes and the overall SAR MTF can become linear, for azimuthal travelling waves VB is highly non-linear as soon as the SAR MTF [4], [2]. III. S IMULATION FACTS The simulator has been designed and implemented modularly and the numerical code can be described according to the steps depicted in Fig.1 which are described hereafter [9]. Step I generates a realization of the sea surface displacement associated with the long sea waves. The directional wave spectrum, in the range relevant to the long sea waves, is approssimated by means of a JONSWAP spectrum with a cosine-type spreading function [2]. Step II models the NRCS according to the SPM. In particular the short wave spectrum is modelled by means of the Phillips spectrum. Step III evaluates the overall SAR MTF which consists of the RAR MTF and the MI effects. The long and the short waves are considered aligned. Step IV evaluates the SAR noise-free intensity image. 1-4244-1212-9/07/$25.00 ©2007 IEEE. Fig. 1. SAR simulator block scheme Fig. 2. SAR simulator GUI Step V generates the SAR noisy intensity image. In particular two noise sources are considered: the additive and the multiplicative one. The latter one is modelled by means of the Weibull distribution [10]. The external inputs to the simulator are grouped into three classes, i.e. sensor, sea and noise input [9]. User is allowed to set such parameters scrolling the input parameters menu through the GUI (Fig.2). Moreover, the GUI has two other menus: the Option and the File one. The first one allows, for example, reducing the image size in order to have a quicker simulation. The second one allows opening a previously simulated SAR image, to display its statistics, to print the SAR image and to exit from the SAR simulator. The simulation starts clicking the RUN button (Fig.2). Obviously the processing time depends on many factor, but the algorithm is quite fast (of the order of few minutes). Once the processing is completed the noisy and the noise-free intensity images are displayed. Then it is possible to save these images as *.dat files. Further an information *.txt file, which contains input and image parameters, is also generated in an user defined folder. These latters are the outputs of the simulator [9]. 787 Fig. 3. SAR 250x250 pixels noisy intensity image relevant to a single 60m range travelling wave Fig. 5. SAR 250x250 pixels noisy intensity image relevant to a single 60m azimuth travelling wave Fig. 4. Plot of the 60m range travelling wave (top) and of the simulated one (down) Fig. 6. Plot of the 60m azimuth travelling wave (top) and of the simulated one (down) IV. E XPERIMENTS The last two experiments are relevant to the simulation of more complex sea wave field, which is generated by means of a fully-developed JONSWAP spectrum with a spreading factor equal to 10 (which corrspond to a broaden spreading function). Such spectrum has been approximated by means of 30 wavenumber and 20 angular directions [9]. In the first experiment a 100m peack wavelength, relavant to a range traveling wave, has been simulated. The SAR noisy intensity image is shown in Fig.7. The second experiment is similar to the former one but an azimuthal travelling wave has been considered. The SAR noisy intensity image is shown in Fig.8. Unlike the monochromatic cases formerly showed, these experiments are more complicated to analize. In particular a spectral analysis is needed to emphasize the behaviour of the SAR MTF [9]. In all subsequent experiments reference is made to ERS-1/2 SAR parameters. Speckle noise is Weibull distributed with a shape parameter equal to 1.5. The wind speed is 10m/s and standard values for sea temperature and salinity have been considered [9]. The first experiment is relevant to the simulation of a single 60m range travelling wave. The SAR noisy image is shown in Fig.3. In order to recognize the linearity of the overall SAR MTF a range transect is made in the noise free image (not shown) and referred to the corresponding long wave (Fig.4). Since a range travelling wave has been simulated it is possible to experience the linearity of the SAR imaging process [4], [9]. The second experiment is relevant to the simulation of a single 60m azimuthal travelling wave. The SAR noisy intensity image is shown in Fig.5. Similarly to the former case an azimuth transect is made on the SAR noise-free image and referred to the corresponding long wave (Fig.6). Unlike the previous case, since an azimuthal travelling wave has been simulated, the SAR MTF is strongly non-linear [4], [9]. 1-4244-1212-9/07/$25.00 ©2007 IEEE. V. C ONCLUSION A new SAR sea surface waves simulator has been developed and tested. The software has been developed in Matlab enviroment, which is probably the most popular programming environment at educational and research centres. Since the 788 R EFERENCES Fig. 7. SAR 250x250 pixels noisy intensity image relevant to 100m range travelling peack wavelength [1] C. R. Jackson and J. R. Apel, Synthetic Aperture Radar Marine Users Manual. Washington, DC: NOAA, 2004. [2] C. Brüning, W. Alpers, and K. Hasselmann, “Monte-Carlo simulation studies of the nonlinear imaging of a two dimensional surface wave field by a synthetic aperture radar,“ Int. J. Remote Sensing, vol. 11, no. 4, pp. 1695–1727, 1990. [3] R. O. Harger, “The synthetic aperture image of time-variant scenes,“ Radio Sci., vol. 15, pp. 749–756, 1980. [4] W. Alpers, D. Ross, and C. Rufenach, “On the detectability of ocean surface waves by real and synthetic aperture radar,“ J. Geophys. Res., vol. 86, no. C7, pp. 6481–6498, 1981. [5] R. O. Harger and C. E. Korman, “Comparisons of simulated and actual synthetic aperture radar gravity waves images,“ J. Geophys. Res., vol. 93, pp. 13867–13882, 1989. [6] G. Franceschetti, M. Migliaccio, and D. Riccio, “On ocean SAR raw signal simulation,“ IEEE Trans. Geosci. Remote Sensing, vol. 36, no. 1, pp. 84–100, 1998. [7] P. W. Vachon R. K. Raney, and W. Emery, “A simulation for spaceborne SAR imagery of a distributed moving scene,“ IEEE Trans. Geosci. Remote Sensing, vol. 27, no. 1, pp. 67–78, 1989. [8] M. Bao, On the imaging of a two-dimensional ocean surface wave field by an along-track interferometric synthetic aperture radar. Ph.D. Thesis, Hamburg, 1995. [9] F. Nunziata, A. Gambardella, and M. Migliaccio, “An educational SAR sea surface waves simulator,“ Int. J. Remote Sensing, submitted for pubblication. [10] M. Greco, F. Bordoni, and F. Gini, “X-band sea-clutter nonstationarity: influence of long waves,“ IEEE Trans. Geosci. Remote Sensing, vol. 29, no. 2, pp. 269–283, 2004. Fig. 8. SAR 250x250 pixels noisy intensity image relevant to 100m azimuth travelling peack wavelength software has been conceived and implemented modularly it can easily up-to-dated. The simulator can be used at Universities for educational purposes and, if tailored block are developed, for scientific purposes at research centres. 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 ESA endorsement has been required and is under evaluation. ACKNOWLEDGMENT The authors would like to thank Prof. Werner Alpers, University of Hamburg, Germany for useful discussion at ESAESRIN, Frascati, Italy and Prof. Roland Romeiser, University of Hamburg, Germany, for useful discussion at University of Hamburg. 1-4244-1212-9/07/$25.00 ©2007 IEEE. 789