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

incseaairωμ

iseaair HnHnZE-EMM1

0

Curved surface impedance approximation

Single non-singular integral equation

MFIE operators EFIE

Time-harmonic scattering

Small Slope Integral EquationMeecham – Lysanov approximation

Horizontal distance d=|d|

Interaction distance r=|r|

Slope s Height h=sd

22

2

11 dsdsdr

zdsdr

Validity : khs<<1.

dπ4

dikexp

rπ4

rikexprG

Matrices associated to operators M and E are 2D Toeplitz

Storage : 2N instead of N2 Product : 2Nlog2N instead of N2

1st order

Ocean SurfaceDeep water - Open ocean - Irrotational motion

Linear surface: Simulation by spectral method

kdxkiexpt,k~t,x

kg

.C.C

tiexpk~t,k~

0

kPt,k~

00

Random gravity waves(ignore surface tension)

Pierson-Moskowitz height spectrum

Electromagnetic wavelength : 25cm

Free waves

Doppler computationTime-harmonic scattering and time-varying surface

1 6 3 2 4 8 6 4 8 0 9 6 1 1 2 1 2 8- 0 . 0 3

- 0 . 0 2

- 0 . 0 1

0 . 0 0

0 . 0 1

0 . 0 2

0 . 0 3

t i m e s t e p

B a c k s c a t t e r e d s i g n a l r e a l V V i m a g V V

1 6 3 2 4 8 6 4 8 0 9 6 1 1 2 1 2 8

- 0 . 0 0 0 2

- 0 . 0 0 0 1

0 . 0 0 0 0

0 . 0 0 0 1

0 . 0 0 0 2

0 . 0 0 0 3

B a c k s c a t t e r e d s i g n a l r e a l V V i m a g V V

ele

ctr

ic f

ield

f r e q u e n c y s t e p

At a given time step

- 9 0- 7 5- 6 0- 4 5- 3 0- 1 5 0 1 5 3 0 4 5 6 0 7 5 9 0

1 E - 6

1 E - 5

1 E - 4

1 E - 3 V

Bis

tati

c i

nte

ns

ity

S c a t t e r i n g a n g l e ( ° )

2. Solve the scattering problem with

SSIE

1. generate the surface

3. Store the backscattered complex amplitude

4. Compute deterministic Doppler complex amplitude

- 1 0 - 5 0 5 1 0

1 E - 1 0

1 E - 9

1 E - 8

1 E - 7

1 E - 6

Do

pp

ler

s

pe

ctr

um

f r e q u e n c y s h i f t ( H z )

5. Statistical result by averaging Doppler intensity spectrum

Then FT

Finally Monte Carlo

f0=1.2GHzDoppler (Hz)

Small Perturbation Method

1. SPM2 applied to doppler spectrum

2. Contribution of non-linear wave

interactions

Hydrodynamic Non-Linearities

gK,kkKgk,k

gk,k

2121222

111

0,1 1 101E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0,01

0,1

1 Linear surface

Creamer (2), J. Fluid Mech 89 Nlog

2N operations (FFT)

Barrick & Weber (2), J. Phys. Ocean. 77

N2 operations

he

igh

t sp

ect

rum

wavenumber

UNDRESSED SPECTRUM

1.Start from a dressed (experimental) spectrum,

2.Generate linear waves,

3.Generate 2nd order,

4.Undress the spectrum(*)

5.Generate linear waves,

6.Generate 2nd order.

(*) Elfouhaily and al. ,CRAS B, vol.13, 314-333, 2003

f0=1.2GHzDoppler (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

-10 -5 0 5 10-5

0

5

10

15

20

25

30

35

40

45

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 »

-20 -15 -10 -5 0 5 10 15 20

1E-12

1E-11

1E-10

1E-9

-20 -15 -10 -5 0 5 10 15 20

1E-12

1E-11

1E-10

1E-9

1E-8

1E-7

-20 -15 -10 -5 0 5 10 15 20

1E-12

1E-11

1E-10

1E-9

Dop

pler

spe

ctru

m

frequency shift

HVVH

HH

VV

Do

pp

ler

spe

ctru

m

dt=50ms dt=25ms

Dop

pler

spe

ctru

m

frequency shift

Creamer2undressed : doubling the Doppler frequency range