Requirements of Optimal Synthetic Aperture Radar (SAR) Frequency, Polarization and
Incidence Angle for Mapping Underwater Bottom Topography: A Simulation Study
Weigen Huang, Bin Fu, Changbao Zhou, Jingsong Yang, Aiqin Shi and Donglin Li
Second Institute of Oceanography
State Oceanic Administration
Hangzhou, P. R. China
Keywords: Underwater bottom topography,
radar parameters, simulation.
Abstract
A simulation model for the radar
backscattering cross section of the sea
surface has been developed based on the
radar imaging mechanism of underwater
bottom topography. The model consists of
the Navier-Stokes equation, the action
balance equation and the radar backscatter
model. The simulation model is solved
numerically using the method of
characteristics. The results of the simulation
model have been used to study the optimal
SAR parameters (frequency, polarization
and incidence angle) for mapping
underwater bottom topography. It is shown
that long wavelengths are required. P band is
the optimal band for mapping underwater
bottom topography, followed by L, C and X
bands. Although mapping underwater
bottom topography is independent of the
polarization, the V V polarization is the best
choice because of its large signal-to-noise
ratio. The incidence angle between 20°to
40°are needed to map underwater bottom
topography by spaceborne SAR.
Introduction
It is well known now that under certain
environmental conditions underwater
bottom topography can be mapped by
imaging radars operating at different
frequency, polarization and incidence angles.
The phenomenon was first imaged by a Ka
band side looking airborne radar (SLAR) off
the Dutch coast in 1969(de Loor, 1981).
Later, bottom topography was found on
images acquired by spaceborne synthetic
aperture radar (SAR) systems such as Seasat
HH polarized L band SAR, ERS-1/2 VV
polarized C band SAR and Radarsat HH
polarized C band SAR. The optimal SAR
parameters (frequency and polarization) for
mapping bathymetric features based on the
Spaceborne Imaging Radar-C, X-Band
Synthetic Aperture Radar (SIR-C/X-SAR)
observations have been reviewed by
Schmullius and Evans (1997). The aim of
this study is to simulate the radar
backscattering cross section of the sea
surface and present the optimal SAR
frequency, polarization and incidence angles
for mapping underwater bottom topography.
Model Description
The understanding of the radar imaging
mechanism of underwater bottom
topography has been improved since the first
explanation by Alpers and Hennings in 1984.
It is generally accepted that the imaging
mechanism of mapping underwater bottom
topography by imaging radar consists of
three stages: the interaction between tidal
flow and bottom topography which results in
modulations in the surface flow velocity, the
interaction between the variable surface
flow and the short surface water waves, and
the interaction between the short surface
water waves and radar signal. The present
simulation model for radar signatures of
underwater bottom topography includes the
Navier-Stokes equation, the action balance
equation and the radar backscatter model,
which describe above three stages.
Navier-Stokes equation
The Navier-Stokes equation describes the
interaction between tidal flow and
underwater bottom topography and is given
by
where (u,v) is depth averaged flow vector in (x,y) direction ,
x is
water elevation relative to reference surface, h is distance between bottom and reference
surface, g is acceleration due to gravity,
r is water density, C is
chezy coefficient modeling bottom roughness, and (
tx
,
ty ) is wind stress in (x,y) direction.
Action balance equation
The action balance equation describes the
evolution of the energy of a wave packet
that travels through a slowly varying surface
current field and reads
where A is the action spectral density of
the wave packet, t is the time,
W is the
apparent frequency in the moving medium, (k
x,ky )
is the wavenumber vector of the
wave packet, and S is a source function.
The action spectrum related to the energy
spectrum E by E =
wA. The intrinsic
frequency is
w=(gk+Tk
3)
1/2 ,
T being
the ratio of surface tension to water density.
The apparent frequency
W is related to the
intrinsic wave frequency by
where
is the surface current vector. For the source function, the linear
equation suggested by Alpers and Hennings(1984) is used because it allows an explicit solution of the
action balance equation. S is given by
S=-m(A-A0) (6)
where
m is a relaxation parameter and A
0 the equilibrium spectrum.
The relationship between the action spectrum A and the waveheight spectrum
y
is given by
A=yrw/k (7)
Radar backscatter model
The radar backscatter is based on the Bragg
mechanism. The radar backscatter model has
the form
s 0pol=16
p
k
04 cos
4(
q)|g
p
(
q |
2y(k
b)
(8)
where k
0 is the radar wavenumber and
q
the incidence angle of the radar. The
magnitude of the Bragg wavenumber vector
k
b is given by
kb=2k0sinq
(9)
The complex scattering coefficient g
p can
be approximated for horizontal (HH)
polarization by
and for vertical (V V) polarization by
where
e is the relative dielectric constant
of sea water.
Method of simulation
Description of the parameters
The radar, environmental and underwater
bottom topography parameters for
simulation are listed in table 1. Satellite is
assumed to fly from south towards north.
Current and wind flow along the x direction.
The underwater bottom topography is shown
in Fig.1.
Table 1 The radar, environmental and
underwater bottom topography
parameters for simulation
|
| Radar band |
P,L,C and X |
| Polarization |
V V and HH |
| Incidence angle |
20°,23°,30°,40°,
50°,60° and 70° |
| Current speed (u0) |
0.5m/s |
| Wind speed (u10) |
5m/s |
| Height of sandwave (d) | 1,4,7 and 10m
|
| Water depth above sandwave (h1)
| 1,5,10,15,20,25 and 30m
|
|
Fig.1 Schematic of the underwater bottom Topography.
