Introduction
Mapping of shallow water bathymetry by air or space borne Synthetic Aperture Radar (SAR) has not been yet received any attention by coastal engineering and hydrographical services. However, shallow bathymetry information plays a vital role for navigation safety, various economics proposes and environmental protection. The extraction of shallow waters bathymetry from SAR images is much operational compared to the traditional methods such as advanced ship-borne echo sounders and multi-beam system. This is because of the fact that SAR images can cover area of 100 km x 100 km. In addition, the traditional methods are rather expensive and time consuming and cannot be operated in very shallow waters such the coastal waters of Kuala Terengganu, Malaysia.

SAR Imaging Mechanisms
According to Alpers and Hennings (1984), the under bottom topography can be shown in SAR images with moderate winds of 3 to 5 m/s and tidal current speed of about 0.5 m/s. This imaging mechanism is consisted of three stages. These stages are based on the effect of tidal current on the radar backscatter cross section. First, interaction between tidal current and bottom topography results in modulations in the surface current velocity. Second, the modulations in surface current speed generate variations in the wave spectra intensity. Third, the variations in the wave spectra intensity induce modulations in the level of radar backscatter (Hesselmans et al., 2000).

These techniques can only be applied in shallow waters with high current speed and requires certain geometry between bathymetry gradient, current and radar look direction.

Methodology

Radar Image
TOPSAR image was acquired at December 6, 1996 has been used to simulate the under water bottom topography. C band with vv polarization has been chosen for this propose.

Gaussian Kernal Model
TOPSAR data are dominated by speckle noises. This problem could be effect the accuracy of water depth estimation. The convolving the TOPSAR raw data with a Gaussian kernal will produce smooth image. The change of the grey level can be detected easier. In this case, the image contours will be generated. The change of the image contours will be function of the grey level variation. The linear model assumed that the change of image signature would be followed by the change of the sea state pattern along the image. This method is named by anisortropic diffusion. This relation can be given as follows:
I(t)=I₀(x,y)*G(x,y,t)           (1)
Simulation Model
Coastal water bathymetry features are imagined on SAR images due to the surface current signature on SAR images. Simulation model of coastal bathymetry will be based on the imaging mechanisms of surface current gradients by SAR. In doing so, the Volterra series expansion was used to model surface current signature gradients by SAR. The SAR intensity image is in linear Kernal, which could detect the current movements along the range direction . The SAR image intensity derived from Fourier transform will have a linear relationship with surface current component in range direction. This can be given by
U_r=(jjbv_x + k_yv.H)^-1.1(v_x,v_y           (2)
Where is function of the action and the wave spectrum at equilibrium stage. One the current have been estimated, the water depth can be computed from the continuity equation. Power –1 indicate the inversion of the inversion of the linear Kernal of Volterra model.
dh/dt+Ń {(D+h)u}=0           (3)
Where dh is the surface elevation above the mean sea level and D is the water depth.

Boundary Condition
The simulated water depth area is divided into square meshes of 2000 m x 2000 m and the water depths at each grid square are interpolated. This interpolated water depths data is then used to create the bottom contour map. The western boundary is the line parallel to the coastline of Kuala Terengganu started from Kuala Terengganu river towards the north which approximately 20 km. The eastern boundary is extending towards the offshore by 5 km away from the western boundary. The tidal elevation was 1 m in initial time and increased to 1.6 m. The current speed in initial time less than 0.5 m/s and higher than zero m/s

Results and Discussion
Figure 1 shows the C band TOPSAR data with underwater bottom topography signature. This image contains a lot of speckle noises which cannot be directly utilized. Figure 2 shows the smooth image by anisotropic diffusion filter. It is noticed that speckle noises have been reduced and the signature of underwater singularities do not broaden. This is because of the fact that anisotropic diffusion filter model preserved the mean grey level and kept the singularities in place. This result is similar to Inglada and Garello, (1999).

Figure 1 TOPSAR C-vv band showing the bottom features.

Figure 2 Output result from anistropic diffusion approach

Figure 3 Shows the current spectra density, which varied along the distance. The current intensities varied along the range direction. The maximum current speed is 1.3 m/s. This is because of the fact that Volterra series expansion considers as linear transform. This linear transform filtered the current flowing on the range direction. In addition this linear transform contains inverse filter which clear in equation 2 with power –1. This inverse model was highly sensible to current signatures and bottom topography change with the current follow. Figure 4. Shows the output bottom topography results from the current information. It is noticed that the bottom contours have a gentle slope along the coastal water of Kuala Terengganu. However, the sharp slope was noticed near to the mouth river of Kuala Terengganu. This could be due to strong output current from the mouth river. This result is similar to Maged (1994).

Figure 3 Simulation of current flow from TOPSAR data

Figure 4 Simulation of bathymetry

Conclusion
In conclusion, the inversion of linear kernal model can be used to simulate the under water bottom topography based on the current pattern. The contour lines of bottom topography are ranged from 1 m to 20 m depth with gentle slope. There is a sharp slope was found near the Kuala Terengganu river. The inversion linear Kernal of Volterra model shows a good result. However there must be improvements in future work to have a high accuracy.

References

• Alpers, W., and I., A. Hennings, 1984. theory of the Imaging of Underwater Bottom topography by Real and synthetic Aperture radar. Journal of Geophysical research, Vol.89C, pp10,529-10,546.
• Inglada J., and R. Garello 1999. Volterra Model for imaging mechanism of ocean surface currents by synthetic aperture radar. In proceedings of IGARSS’99.
• Hesselmans, G.H, G.J Wensink C.G. V. Koppen, C. Vernemmen and C.V Cauwenberghe , 2000. Bathymetry assessment Demonstration off the Belgian Coast-Babel. The hydropgraphic Journal . No.96. pp.3-8.
• Maged M, 1994 “ Coastal Water Circulation off Kuala Terengganu, Malaysia”. MSc. Thesis Universiti Pertanian Malaysia.