Effect of Tilt-Modulation and Shadowing on Backscatterer of Ocean Surface

Jae-Won Rim and Il-Suek Koh

Department of Electronic Engineering, Inha University, Incheon, Korea

Abstract – The effect of the tilt modulation and shadowing on the radar backscatterer of an ocean surface is investigated. Using the JONSWAP spectrum, a wind-driven ocean surface is generated. Then, the backscattering coefficients are computed where the modulation and shadowing effects are examined.

Index Terms — Tilt modulation, Shadowing, Ocean Backscattering.

1. Introduction

There have been many studies about the synthetic aperture radar (SAR) images on the ocean surface [1]. As the SAR images intensity are significantly affected by the radar cross section (RCS) of the ocean surface, it is crucial to accurately evaluate the backscattering by the ocean surface. For the accurate estimation of the backscattering, the dynamic effects such as the tilt modulation (TM) [2], hydrodynamic modulation [2], velocity bunching [3], shadowing [3], etc., are very important. The TM and shadowing among them, especially, are due to the geometric effect of the long ocean wave, which results in the fast spatial variation of the backscattering.

In this paper, we generate a wind-driven ocean surface based on a specific ocean spectrum. Then, we evaluate the backscattering coefficients on discretized ocean facets and numerically analyze the contribution of the TM and shadowing to the RCS.

2. Formulation

The ocean surface consists of two different scale waves, a long wave (gravity waves) and a short wave (capillary wave). It is numerically very hard to accurately discretize the capillary wave, so that only the gravity wave is usually discretized into relatively large flat facets. On the flat facets, the capillary wave propagates and generates large backscattering at a microwave frequency band. The backscattering enhancement by the capillary wave can be partially considered by using the modulation transfer function (MTF), ( )M K

. The modulated RCS is expressed as [2]

( )( ( ) )0 0 1 2Re ( ) ( ) j K r w K tM K H K e dKσ σ δσ σ ⋅ −= + = +

, (1)

where 0σ , δσ , K

, ( )w K

, and ( )H K

are the mean RCS and RCS variation due to the modulation, the wave number vector, the angular frequency, and Fourier transform of the surface elevation, respectively. In (1), the MTF usually includes the effect of the hydrodynamic modulation as well as the TM [2]. In this paper, we focus only on the TM effect. The

backscattering component can be decomposed into M along the line of sight (LOS) direction of the radar, and M ⊥

perpendicular to the LOS of the radar as [2] tiltM M M⊥= + . (2)

We assume that the incident wave vector ˆ ik is in the x-z plane, i.e., ˆ ( sin , 0, cos )ik θ θ= − − where θ is the microwave incident angle. The normal vector of the facet deviates by an angleψfrom y-z plane and by an angle δ from x-z plane. Then, the local incidence angle θ , is represented as

( )1cos cos cos( )θ δ θ ψ−= + . (3)

The RCS variation due to the tilt modulation is given by [2]

00 0 0

1 ( , , 0) ( , 0, ),

h hx yδψ

δσ σ θ ψ δ σ θ ψ δσ σ ψ δ ==

∂ = ∂ ∂ = ∂= + ∂ ∂ ∂ ∂

(4)

where xK and yK are the components of the gravity wave vector in and normal to the LOS of the radar, respectively. h is the ocean elevation. Considering the local incident angle, θ ,

0σ can be evaluated for a rough facet. For example, 0σ for the HH polarization is represented as [4]

( )

22 4

0, 0

2

0 0

sin( )cos sin4 cos ( )

sin sin

( ) 2 sin( ),2 cos( )sin ,

HH k g

g W k k

θ ψ δ δσ π θ θθ θ

θ θ ψ θ ψ θ

⊥⊥+ = +

× + +

(5)

where g⊥⊥ and g are the first-order scattering coefficients [4]. W is the ocean spectrum. The JONSWAP spectrum [5] is used.

3. Numerical Results

To analyze the effect of the TM and shadowing on the backscattering from the ocean surface, we generate a wind-driven ocean surface as

1 1

1 1

( , , ) cos( )M N

mn m n mn mnm n

h x y t A k x k y w t φ− −

= == + − + , (6)

where mnA denotes the amplitude proportional to W . 2 ( / 2) /m xk m M Lπ= − and 2 ( / 2) /n yk n N Lπ= − are assumed

where xL and yL are the dimensions of the generated ocean along x and y axes, respectively. 2 2( )mn m nw g k k= + , mnφ and gare any constant and the gravitational acceleration constant, respectively. For the case that the wind speed is 5 m/s and a microwave is incident at 75θ = , the generated ocean surface and its lit and shadow regions are shown in Fig. 1. The combination of the Kirchhoff approximation (KA) and the small perturbation method (SPM) [5], so called two-scale model (TSM) theory, is used to evaluate the backscattering.

[WeD2-2] 2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

111

(a) (b)

Fig. 1. (a) Generated ocean surface and (b) lit and shadow regions

when wind speed is 5 m/s and wave incident at 75θ = .

Fig. 2. Normalized RCS from ocean surface evaluated based on KA and SPM when wind speed is 5 m/s.

(a) (b)

Fig. 3. Shadowing effect on RCS for VV pol. (a) without shadowing effect and (b) with shadowing effect.

For the ocean in Fig. 1 (a), Fig. 2 shows the normalized RCS in good agreement with experimental results in Ku-band by SASS-II [6] for both HH and VV polarizations. Note that the backscattering for the VV polarization becomes far more dominant as the incidence angle decreases than for the HH polarization. Considering the local incidence angles, θ in each facet, the RCS is computed as shown in Fig. 3. Note that the RCS is calculated only in the lit region. For such low grazing angle, we can observe that the shadowing effect is important. The effect of the TM on the RCS is shown in Fig. 4 for HH polarization. Note that the TM effect is much larger for the HH polarization than for the VV polarization even though the RCS itself is smaller for the HH polarization than for the VV polarization. It is due to the fact that the backscattering for the HH polarization is more sensitive to the incidence angle [2]. The normalized spectral densities of the mean RCS are analyzed by including the TM and shadowing, which is shown in Fig. 4 (c). It is observed that the incorporation of the shadowing has little impact on the spectral distribution of the RCS for this large grazing angle. But, it can be observed that the TM generates higher frequency components in the RCS, which may result in more rapid deviation of the RCS than the RCS of the gravity wave. Hence, the capillary wave contribution can be partially included.

(a) (b)

(c)

Fig. 4. TM effect on RCS when 75θ = for HH pol. (a) without TM, (b) with TM, and (c) normalized spectral density.

4. Conclusion

The backscattering coefficients on a wind-driven ocean surface are calculated. Then, the contributions of the TM and shadowing to the backscattering are numerically analyzed. The normalized RCS of the ocean surface are evaluated by using the TSM theory, which is verified with experimental results. For the low grazing angle, the shadowing has significant impact on the spatial distribution of the RCS. The TM effect generates the higher frequency backscatterer. Thus, incorporating the TM, the capillary wave can be numerically and efficiently considered in the radar backscatterer of the ocean surface.

Acknowledgment

This work was supported by the Agency for Defense Development (ADD). [UD170083FD]

References

[1] G. R. Valenzuela, “Theories for the interaction of electromagnetic and oceanic waves—A review,” Boundary-Layer Meteorology, vol.13, no.1-4, pp. 61-85, 1978.

[2] W. R. Alpers, B. R. Duncan, and L. R. Clifford, “On the detectability of ocean surface waves by real and synthetic aperture radar,” Journal of Geophysical Research: Oceans, vol. 86, C7, pp. 6481-6498, 1981.

[3] L. M. Zurk, and W. J. Plant, “Comparison of actual and simulated synthetic aperture radar image spectra of ocean waves,” Journal of Geophysical Research: Oceans, vol. 101, C4, pp. 8913-8931, 1996.

[4] G. R. Valenzuela, “Scattering of electromagnetic waves from a tilted slightly rough surface,” Radio Science, vol. 3, no .11, pp. 1057-1066, 1968.

[5] A. K. Fung, and K. S. Chen, Microwave scattering and emission models for users, Artech house, 2010.

[6] T. M. Elfouhaily, and C. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Waves in Random Media, vol.14, no.4, R1-R40, 2004.

0 10 20 30 40 50 60Incident angle [deg]

-40

-20

0

20 KA+SPM: HHKA+SPM: VVExp. HHExp. VV

2018 International Symposium on Antennas and Propagation (ISAP 2018)October 23~26, 2018 / Paradise Hotel Busan, Busan, Korea

112