

Numerical PseudoRandom Simulation of SAR Sea and Wind Response
Eugenio Pugliese Carratelli^{(1)} , Fabio Dentale^{(1)} , and Ferdinando Reale^{(2)}
^{(1)}
University of Salerno,
Via Ponte Don Melillo,
84084 Fisciano,
Italy
^{(2)} CUGRI, Piazza V: Emanuele  Penta, 84084 Fisciano, Italy
Abstract
Wind and wave data from SAR imagery over the oceans has been routinely employed for many years, and the techniques to extract such data are a well established field of research. The use of SAR over enclosed seas and along coastal areas, however, is severely limited: on the one hand the present resolution of satellite SAR is too low to be of any use with the relatively short wavelengths which are usually encountered under short fetch conditions; on the other hand, the complex morphology of coastal bathymetry and topography often causes sharp variations of the sea surface conditions which can be very hard to interpret; research in this field is therefore still very active.
Most if not all the techniques used for measuring the sea parameters with active sensors are based upon analytical forms of the sea wave spectrum. This has the obvious advantage of providing a closed form for the function which relates the sensor response to the physical parameters of interest, but it also poses a strong constraint on the complexity of physical effects which can be taken into account.
In order to provide some insight on the image formation mechanism, an alternative approach is proposed here, whereby numerical simulation of the sea state is carried out by pseudo random generating the water surface according to any given spectrum. Just like any two (or three) wavelength model this supplies all the information about surface tilt, while backscattering characteristics – which depend on shorter wavelengths – can be separately specified; the difference being that there is no limit to the shape of the spectrum which can be generated by the numerical simulation techniques and a much greater freedom to specify and to test different hypotheses on the local scattering function. This latter possibility appears to be particularly relevant since new results are now available on the spatial distribution of small scale roughness over sea waves, mostly due to the work by Malin et al.(1999,2001)
The basic idea  i.e. to simulate a great number of sea surface realisations and to evaluate the scattering coefficient by ensemble averaging the statistics of surface tilt an other parameters is of course not new in principle: deriving from the large experience of numerical wave synthesis techniques developed in the past in different contexts, it dates back to 1990 (Bruening et al.) and was used again to investigate into wave radio altimeter data (Della Rocca and Pugliese Carratelli, 2001). Unlike Bruening’s classical work, however, the simulations shown in this work were carried out down to wave lengths of the order of one meter, well under SAR pixel size, thus allowing a numerical rather than parametric representation of sub resolution phenomena.
Each realisation is based on a particular wave field generated by pseudorandomly setting the phase parameters in a discrete spectrum; the most obvious case would be a JONSWAP spectrum with a cosine spreading function, but of course any shape can be easily taken into account.
Radar RAR and SAR cross section for various values of parameters such as wave height, spectral period and spreading function and for both horizontal and vertical polarization backscattering can thus be computed just like in any analytical model, but nonspectral information such as different distribution of the capillary – Bragg resonant water waves on the two sides (windward and leeward) of the long waves can easily be added.
The effects of macroscopic effetcts such as shoaling and current interaction can thus be taken into account by separately evaluating wave height and period changes with any state of the art model such as WAM or SWAN, and then making use of the results describe above to calculate the radar sections.
Work carried out within ESAESRIN Project CAT1 No 1172: “Remote sensing of wave transformation”, PI Eugenio Pugliese Carratelli.
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