ω, would be a JONSWAP

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1 NUMERICAL PSEUDO RANDOM SIMULATION OF SAR SEA AND WIND RESPONSE Eugeno Puglese Carratell (1,), Fabo Dentale (1), and Ferdnando Reale () (1) Unversty of Salerno, Va Ponte Don Melllo, 8484 Fscano, Italy () CUGRI, Pazza V. Emanuele - Penta, 8484 Fscano, Italy ABSTRACT Wnd and wave data from SAR magery over the oceans have been routnely employed for many years, and the technques to extract such data are a well establshed feld of research. The paper presents a dfferent method, based the well establshed two wavelength models, whereby the surface slope s smulated by numercally generatng the nstantaneous water heght. The numercal approach seems to offer a greater flexblty grantng a much greater freedom to ntroduce fully non lnear and non spectral effects n the short wavelength. 1 INTRODUCTION Most f not all the technques used for extractng sea surface wth actve sensors are based upon analytcal forms of the sea wave spectrum. Ths has the obvous advantage of provdng a closed form for the functon whch relates the sensor response to the physcal parameters of nterest, but t also poses a strong constrant on the complexty of physcal effects whch can be taken nto account. In order to provde some nsght on the mage formaton mechansm, an alternatve approach s proposed here, whereby numercal smulaton of the sea state s carred out by pseudo randomly generatng the water surface accordng to any gven spectrum. Just lke any other two (or three) wavelength model, ths supples all the nformaton about surface tlt, whle backscatterng characterstcs whch depend on smaller scale phenomena such as capllary waves and whtecappng must be separately specfed. There s a dfference, though, n that numercal smulaton allows a much greater freedom n specfyng and testng non lnear hypotheses on the backscatterng functons; another advantage s that t poses no lmts to the shape of the spectrum. PSEUDO RANDOM SIMULATION OF SEA SURFACE The basc dea -.e. to smulate a great number of sea surface realsatons and to evaluate the scatterng coeffcent by ensemble averagng the statstcs of surface tlt an other parameters -s of course not new n prncple: t dates back to 199 (Bruenng et al.) and was used also to nvestgate nto wave rado altmeter data (Della Rocca & Puglese Carratell, 1 a,b). Unlke Bruenng s classcal work, however, the smulatons shown n ths paper are extended down to wave lengths of the order of one meter, well under SAR pxel sze, thus allowng a numercal rather than parametrc representaton of sub resoluton phenomena. The actual mplementaton of the procedure presented here s based on the large experence of wave synthess technques whch have been developed n the past: a Random Phase Double Summaton technque was employed, as descrbed for example by Mles and Funke (1987) and Goda (1989) and the phase lockng effect was lmted by adoptng a rather hgh number of spectral components as n (Garrusso & al., 1). An nstantaneous water heght feld realsaton η ( X, Y, t) can be generated by assumng a dscrete drectonal spectrum form Sd( ω, θ ), and by settng A, = Sd( ω, θ ) dϑ df. By pseudo-randomly settng the phase parameters ε, : N M ( X, Y, t) = A, cos( k ( X snθ + Y cosθ ) ωt + ε, ) η (1) (a cosne form of the transformaton s assumed here). Proceedngs of SEASAR 6, 3-6 January 6, Frascat, Italy, (ESA SP-613, Aprl 6)

2 q=1 q= q= The most obvous choce for Sd( θ ) ω, would be a JONSWAP spectrum wth a drectonal spreadng functon, but of course any shape can be easly taken nto account..dfferent spectral parameters lead to dfferent wave feld realzatons (Fg.1). 3 SAR AND WIND RESPONSE Once a satsfactory descrpton of the sea surface s obtaned, the smulated mage depends on the local scatterng coeffcents σ l Here local refers to the spatal resoluton of the smulaton, whch s smaller than the typcal gravty wavelength. Assumng a Valenzuelastyle backscatterng functon (Eqs. - 3 and fg. ): 4 σ l = β cos ϑ (HH polarzaton) () ( 1+ sn ϑ) 4 cos ε σ = β ϑ l (VV polarzaton) ( ε cosϑ + ε ) (3) 1. q= q= q=3 q= q=4 n= n=3.8.7 POLARIZATION VV POLARIZATION HH Peak Perod Tp= 8s; Sgnfcant Wave Heght Hs = 3m; Two values of drectonal spreadng functon parameter n Fg.. Valenzuela-style backscatterng functon. Fg. 1. Drectonal wave spectrum and smulated sea surfaces for two values of drectonal spreadng functon parameter n. the local σ l /β s known, and smulatng a RAR (Real Aperture Radar) mage s smply a queston of takng nto account the local slope, a smple dervatve of the sea elevaton η ( X, Y, t). The actual β wll depend on the local surface condtons (Bragg resonant capllary waves, whtecaps, etc). The slope s thus a very mportant parameter: (Fg 3) shows ts computed frequency dstrbutons for dfferent sgnfcant wave heghts and wnd drectons. In order to reconstruct the smulated mage from the SAR sgnal orbtal velocty values are also necessary to evaluate Doppler related effects: followng the same approach the tme varyng local velocty s gven by the sum of the surface veloctes of each spectral and drectonal component: so, for example, the X velocty component wll be (Eq. 4): V x N M 1 ( X, Y, t) = ga, k cos( ωt k ( X cos θ + Y snθ ) ε, ) + ω (4) RAR and SAR cross secton for varous values of parameters such as wave heght, spreadng functon parameter and peak spectral perod for both horzontal and vertcal polarzaton can thus be computed ust lke n any analytcal model, but non-spectral and non lnear nformaton such as dfferent dstrbuton of the capllary Bragg resonant water waves on the two sdes (wndward and leeward) of the long waves can easly be added.

3 The nfluence of such parameters as geometrcal and sea-state parameters can easly be taken nto account. Fg 4 thus shows the σ l dstrbutons for the same wnd drecton and sgnfcant wave heght H S assumng VV polarzaton 3 SIGNIFICANT WAVE HEIGHT H s = m WIND DIRECTION = SIGNIFICANT WAVE HEIGHT H s = m WIND DIRECTION = _ 1 9 _ 1 1 _ 13 _ 16 1 _ 4 _ 7 _ 8 3 _ _ 4 4 _ 43 4 _ 46 1 _ 4 _ 7 _ 8 6 _ _ 7. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Incdence Angle q [deg] Local Backscatterng s l /b 3 WIND DIRECTION = WIND DIRECTION = _ 1 9 _ 1 1 _ 13 _ 16 1 _ 4 _ 7 _ 8 3 _ _ 4 4 _ 43 4 _ 46 1 _ 4 _ 7 _ 8 6 _ _ 7. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Incdence Angle q [deg] Local Backscatterng s l /b 3 WIND DIRECTION = WIND DIRECTION = _ 1 9 _ 1 1 _ 13 _ 16 1 _ 4 _ 7 _ 8 3 _ _ 4 4 _ 43 4 _ 46 1 _ 4 _ 7 _ 8 6 _ _ 7. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Incdence Angle q [deg] Local Backscatterng s l /b Fg. 3. Frequency dstrbutons of local ncdence angles for dfferent sgnfcant wave heghts and wnd drectons. Fg. 4. Frequency dstrbutons of local σ l / β for dfferent sgnfcant wave heghts and wnd drectons. The nfluence of wnd drecton and ntensty on σ (.e. σ l averaged over many wavelengths) s a well known effect (as shown by CMOD models, Fg. ), but part of s due to tltng and part to local roughness effects. The smulaton technque proposed here may help clarfy the dstncton, snce t completely separates short wave local phenomena from the gravty wave spectrum transformaton, gvng a much greater freedom to ntroduce fully non lnear and non spectral effects n the short wavelength range. Dfferent hypotheses on the backscatterng functons can be tested to nqure nto the relatonshp between SAR wave sgnals and actual wave descrpton, such as expermentally nvestgated for nstance Y-Yu Kuo et al (1999). Fg.. Values of σ for dfferent wnd drectons and speed values (CMOD).

4 The followng pctures show the effect of assumng dfferent backscatterng propertes along the wave, (Fg. 6) such as may derve from asymmetrcal dstrbuton of capllary waves or whtecappng; radar secton frequency dstrbuton s shown for β = 1, on the wnd sde of the waves and β =,8 on the lee sde and compared wth the β = 1 results. (Fg. 7 and 8). Whle the assumpton s admttedly sharp and unrealstc, the results stll t suggests that spatal roughness dstrbuton over a wavelength mght be relevant and can be smulated. Such a possblty appears to be partcularly nterestng snce new results are now avalable on the spatal dstrbuton of small scale roughness over sea waves, mostly to the work by Kudryavtsev et al.(1999,). WIND DIRECTION UPWIND. α max = UPWIND DOWNWIND b =.8 Fg. 6. Dfferent values of parameter β along the wave. The phenomena dervng from larger scale wave formaton and transformaton such as shoalng and current nteracton can then be taken nto account by makng use of the wdely tested model such as WAM or SWAN (Garrusso et al 4, Puglese Carratell et al ). 1 SIGNIFICANT WAVE HEIGHT H s = m. UPWIND. b =.8 DOWNWIND 1 SIGNIFICANT WAVE HEIGHT H s = m WIND DIRECTION = 78.. UPWIND. b =.8 DOWNWIND. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Local Backscatterng s l 1. UPWIND. b =.8 DOWNWIND. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Local Backscatterng s l 1. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1.. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Local Backscatterng s l 1 SIGNIFICANT W AVE HEIGHT H s = 4 m WIND DIRECTION = 78.. UPWIND. b =.8 DOWNWIND. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. Local Backscatterng s l 1. UPWIND. b =.8 DOWNWIND. _.1.3 _.4.6 _.7.9 _.6.6 _.63.6 _ _ _.7.74 _.7.77 _.78.8 _ _ _ _.9.9 _.93.9 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. WIND DIRECTION = 78.. UPWIND. b =.8 DOWNWIND Local Backscatterng s l Local Backscatterng s l Fg. 7. Frequency dstrbutons of local backscatterng Fg. 8. Frequency dstrbutons of local backscatterng for wnd drecton = for wnd drecton = 78..

5 ACKNOWLEDGEMENTS Work carred out wthn ESA-ESRIN Proect CAT-1 No 117: Remote sensng of wave transformaton ; The authors wsh to thank to Dr. Jerome Benvenste (Esa Esrn) for help and support REFERENCES 1. Bruenng, C., Alpers W. and Hasselmann K. Monte Carlo Smulaton studes of the nonlnear magng of a two dmensonal surface wave feld by a synthetc aperture radar Int. Journal of remote Sensng 11, 199. Della Rocca M. R., E. Puglese Carratell, Un modello per la calbrazone de dat d vento e moto ondoso medante altmetro radar, IDRA XXVII Convegno d Idraulca e Costruzon Idraulche, Genova a 3. Della Rocca M. R., E. Puglese Carratell, A model for Wnd Speed and Wave Heght Retrval from Radar Altmeter Measurements ERS_ENVISAT Symposum Gothenburg Sweden 16- October b 4. Garrusso C.C., E. Puglese Carratell and G. Spuls "On the Effects of Wave Drft on the Dsperson of Floatng Pollutants", Ocean Engneerng, May 1. Della Rocca, M.R., Fortunato,A. & Puglese Carratell,E. "Modellng wnd and wave remote sensng data", ASCE Conference Solutons to Coastal Dsasters ', February San Dego, CA 6. Garrusso C., E. Puglese Carratell, G. Spuls, Satellte SAR Sea and Wnd Response over Shallow Seas, XII Convencón Centífca de Ingenería y Arqutectura (CCIA 4), La Habana, Cuba Goda, Y., Comparson of sngle and double summaton models for multdrectonal wave generaton. XXIII IAHR Congress, Ottawa. 8. Kudryavtsev V.N., V.K. Makn, and B. Chapron, Coupled sea surface-atmosphere model. Part. Spectrum of short wnd waves, J. Geophys. Res., 14, C4, , Kudryavtsev, V.N., and V.K. Makn, Coupled dynamcs of short wnd waves and the ar flow over long surface waves, J. Geophys. Res., 17 (C1), 39, 1.19/1JC1. 1. Mles M.D, Funke, E.R., A comparson of methods for synthess of drectonal data. Sxth Internatonal Offshore Mechancs and Arctc Symposum Houston. 11. Puglese Carratell E., F. Dentale C.C. Garrusso, F. Reale G. Spuls, Applcaton of Satellte SAR Images to Sea and Wnd Montorng n Coastal Seas Araban Coast - Coastal Zone Management And Engneerng, Duba, Unted Arab Emrates, 7-9 November 1. Y-Yu Kuo, L-Guang Leu*, I Lang Kao Drectonal spectrum analyss and statstcs obtaned from ERS-1 SAR wave mages, Ocean Engneerng ( 1999)