Analyse de spectres Doppler de la surface de la mer en bande L G. Soriano*, M. Joelson**, P. Forget #, M. Saillard # * Institut Fresnel, UMR CNRS-Université Aix-Marseille III ** LCSE, UMR CNRS-Université d’Avignon # LSEET, UMR CNRS-Université de Toulon et du Var

Introduction Doppler spectrum Ocean surface is time varying: h(r,t) Harmonic      More information in backscattering radar configuration HF and VHF radars provide current maps at km resolution Coastal zone : UHF? In coastal zone, environmental parameters change faster Smaller wavelength provides better resolution  UHF Need for advanced hydrodynamic and electromagnetic models

Skin depth d << 2D surface Air Sea water Exponential attenuation Electromagnetic scattering Scattered field Curved surface impedance approximation Single non-singular integral equation MFIE operators EFIE Time-harmonic scattering

Small Slope Integral Equation Meecham – Lysanov approximation Horizontal distance d=|d| Interaction distance r=|r| Slope s Height h=sd Validity : khs<<1. Matrices associated to operators M and E are 2D Toeplitz Storage : 2N instead of N 2 Product : 2Nlog 2 N instead of N 2 1 st order

Ocean Surface Deep water - Open ocean - Irrotational motion  Linear surface: Simulation by spectral method Random gravity waves (ignore surface tension) Pierson-Moskowitz height spectrum Electromagnetic wavelength : 25cm Free waves

Doppler computation Time-harmonic scattering and time-varying surface At a given time step 2. Solve the scattering problem with SSIE 1. generate the surface 3. Store the backscattered complex amplitude 4. Compute deterministic Doppler complex amplitude 5. Statistical result by averaging Doppler intensity spectrum Then FT Finally Monte Carlo

f 0 =1.2GHz Doppler (Hz)

Small Perturbation Method 1. SPM2 applied to doppler spectrum 2. Contribution of non-linear wave interactions

Hydrodynamic Non-Linearities

UNDRESSED SPECTRUM 1.Start from a dressed (experimental) spectrum, 2.Generate linear waves, 3.Generate 2 nd order, 4.Undress the spectrum (*) 5.Generate linear waves, 6.Generate 2 nd order. (*) Elfouhaily and al.,CRAS B, vol.13, , 2003

f 0 =1.2GHz Doppler (Hz)

Experiments + december 03 and 04 + height: 90 m + VV, HH, VH, HV + 2 azimuts + in situ measurements: - omnidirectional spectrum - surface currents - wind East wind 5 km Cap Sicié Toulon Mistral Batterie de la Renardière

14/12/2004 de 12h à 15h Vent de 2 à 3 m/s Orienté 10 à 50° par rapport au faisceau incident Comparaison VV VH

Conclusion At UHF, the ocean surface height spectrum needs to be undressed before introducing hydrodynamic interactions At low winds, some Doppler spectrum features can still be interpreted with SPM. Some new characteristics: broadened side peaks, significant cross-polarization. Perspectives Find a more systematic way to undress the spectrum Study the influence of the hydrodynamic model Use more realistic (experimental) directional spectrum Improve SSIE for grazing angles (80, 85°) Remerciements au Dept. STIC du CNRS pour son soutien à l’Equipe Projet Multi-Laboratoires « Télédétection Active Océanique »

Creamer2undressed : doubling the Doppler frequency range