2.7.1 ASAR Level 2 Algorithms
The Synthetic Aperture Radar (SAR) is so far the only
satellite-borne instrument that can measure
the directional characteristics of the ocean
wave field. At present, the SAR imaging of ocean
waves is fairly well understood. An analytic
expression for the non-linear ocean-to-SAR
spectral transform exist describing the SAR
image spectrum as a function of the
underlying ocean wave field. The transform was
derived by Hasselmann and Hasselmann (1991),
reformulated by Krogstad (1992), and later
extended to the cross-spectral case by Engen and
Johnsen (1995). The existing SAR spectral
inversion schemes are based on approximations of
the nonlinear transform of Hasselmann, and have
successfully been applied to ERS SAR data. The main
drawbacks of the algorithms are the need of
an a priori wave spectrum in order to solve the
propagation ambiguity and find a unique solution
for the wave system. The a priori spectrum
is usually taken from Wave Models. Extensive
validation of the inversion schemes and the
impact of assimilation of ERs data into Wave
Models has been undertaken (Breivik et. al.
1995). It can be concluded that the impact is on
average limited due to sparse data coverage
and limited new information in the SAR-derived
wave spectra compared to the Wave Model spectra.
The latter is partly due to non-optimal
processed input SAR data combined with imperfect
inversion schemes. By using the cross-spectra
methodology the a priori spectrum is no
longer needed for solving the ambiguity problem
and for finding a unique solution. In addition
the contribution from speckle is avoided.
The only limitations are the poor along-track
resolution and the limited
knowledge of the behaviour of the transfer
functions for various sea and wind
conditions. The transfer function problem can be
overcome where dual-polarised (i.e.,
simultaneously acquired HH and VV
polarisations) data is available by using
cross-spectra between different polarisations.
The wave spectra retrieval
algorithms are based on minimizing, with
respect to the wave spectrum, the mean square
difference between the observed and the computed
SAR image spectrum under certain
constraints. The computed SAR image spectrum is
derived using the nonlinear transform with the
current wave spectrum, as input. This
transform is for the general case of a
multi-channel cross-spectrum derived by Engen
(1997). The standard image spectrum, and the
single-channel cross-spectrum are just special
cases of the general transform.
The discussion of the algorithm used to create
the Wave Mode Ocean Wave Spectra product is
given below in the following sections.
18.104.22.168 General Description
The processing system will access the
external input data, which consist of the
SLC (Level 1) data and the processing setup
data. The setup file may include and
estimate of the local wind field. A
pre-processing of the data will be done
before the core processing is started.
The preprocessing consists of inter-look
cross-spectral processing. The core
processing performs a wave spectral
inversion of the cross-spectra with
respect to the detected SAR ocean wave-like
pattern. This is done by first evaluating
the nonlinear contribution to the
imaging process assuming that this is caused
only by the local wind field, and then to
apply a quasi-linear inversion in the most
energetic part of the SAR
cross-spectrum. The former step is based on
the asymptotic development of the full
nonlinear SAR mapping transform and its
identification in the least energetic SAR
observed cross-spectrum. The major
requirements for the second step is
knowledge of the Real Aperture Radar
Modulation Transfer Function (RAR MTF), the
azimuth cut-off (orbital shift
variance), and the nonlinear part of the
spectra. The RAR MTF is computed using
a backscattering model including non-uniform
distribution of scatterers on the long wave
field. The RAR MTF amplitude is provided as
part of look-up table used to estimate
the nonlinear part of the cross-spectra.
After the core processing is finished, the
spectrum is converted to polar grid and an
output product is generated and stored on
the ASAR Level 2 WVW
format 2.7.2. which follows a format similar to
the ASAR Level 1 WVS format.. (The wave
spectra is substituted with the
cross-spectra and the extra header
parameters are put into the spare fields.)
22.214.171.124 Processing Steps
The main ASAR Level 2 processing steps to
create the Wave Mode Ocean Wave Spectra
product (ASA_WVW_2P) are summarised below in
|Figure 2.60 Flowchart of the Level 2 processing algorithm
1. Data Input
The data input combines the SLC information
and the processing set up parameters into a
global parameter list required for the processing.
2. Look_Up Table
Lookup tables consisting of a set of
simulated cross-spectra are provided with
the software, and used to retrieve the
nonlinear cross spectra, the smearing
parameter, the RAR MTF and the wind field.
One lookup table is provided for each swath
and polarisation that will be used for the
Wave Mode. The lookup tables are stored on
one unformatted data file for each
table, and a common formatted information
The processing module performs the look
extraction and cross-spectra estimation
according to the steps below:
Image Detrending - Detrend the
input SLC image using a Gaussian
low-pass filter operation where the
the filter can be
specified in the setup file.
This procedure removes the low frequency
effects from the SLC image that are due
to non-wave features. This is done by
computing a low-pass filtered
image from the SLC image and then
dividing the SLC image with the square
root of the computed low-pass filtered
intensity image. The procedure also
provides the image intensity of the
original input SLC image.
Image Cross Co-variance Spectrum
Estimation - Compute the
co-spectrum and the two cross-spectra
corresponding to three looks.
This procedure performs the look
extraction and computes all combinations
of spectra. Default is 3 looks providing
3 spectra - one co-spectra and two
cross-spectra. The spectral processing
is based on the periodogram method.
Estimate and remove the Clutter Bias
of the Co-Spectra - Estimate
the clutter bias of the co-spectra and
remove it from the co-spectra.
This procedure gives one unbiased
co-spectra and two cross-spectra
generated with two different look
separation times -
. All of the spectra are
combined statistically and used in the
wave spectra retrieval.
4. Parameter Estimation
This module performs the estimation of a set
of parameters from the cross-spectra which
again are used in combination with the
lookup table to generate the RAR MTF,
the azimuth cutoff factor, and the nonlinear
part of the cross-spectra.
The RAR MTF (Real Aperture Radar Modulation
Transfer Function) estimation is based on
using the available wind information
extracted as part of the fitting of the
observed nonlinear part of the cross-spectra
to the look-up table, combined with a given
backscatter model function incorporating
non-uniform distribution of scatterers on
the long wave field. The RAR MTF
'amplitude' (i.e., derivative of
the phase function taken at Bragg
wave-number) is provided within the look-up table.
The estimation procedure also provides an
estimate of the local wind speed. The wind
speed is estimated from the radar
cross-section using CMOD assuming the
wind direction is known. The wind direction
can be estimated from the phase of the
cross-spectra or provided at input.
The computation of the nonlinear SAR image
cross-spectrum in the lookup tables is done
using an implementation of the full
nonlinear SAR transform including a
non-uniform distribution of scatterers on
the long wave field. The look-up table is
used in order to simplify the algorithm
and to decrease the processing load.
5. Inversion of Quasi-Linear Cross Spectra
The measured SAR image cross-spectrum can be
approximated as a sum of a nonlinear part
(mainly wind sea driven), a quasi-linear
part (detected SAR wave pattern, swell),
and a uniform distributed noise term, with
The procedure for inverting the ASAR Level 1
products with respect to the ocean swell
wave spectrum requires the following steps:.
- Express the co- and cross-spectra as
sums of the nonlinear approximation and
the well known quasi-linear part given
by the exponential cutoff factor,
transfer functions and swell spectrum.
- Remove the nonlinear contribution (using
look-up table) and solve the
quasi-linear part linearly with respect
to the swell spectrum inside the
SAR imaging domain, for each of the
spectra. Solve for the symmetric and the
- Compute the corresponding clutter noise
level of each of the wave spectra solutions.
The signal-to-noise ratio is needed
in order to establish the criteria
for ambiguity resolvement i.e. when
combining the symmetric and
the anti-symmetric spectra.
- Combine, using the clutter noise level,
the solutions of each of the spectra to
provide the final estimate of the wave
spectrum. Both for the symmetric
and the anti-symmetric spectra.
- Compute the clutter noise of the final
symmetric and anti-symmetric spectra,
combine them with the anti-symmetric
spectrum, and use the results to
remove the ambiguity of the symmetric spectrum.
The 180 deg. propagation ambiguity in
wave spectra can be resolved by
combining the symmetric and
the anti-symmetric spectra. The
basis idea is to perform an adaptive
smoothing (SNR dependent) of
the anti-symmetric spectrum,
followed by a detection of the sign
for the valid regions defined by
spectra and their
relation to the corresponding noise
level. The final wave spectrum is
combining the symmetric spectrum and
the sign function. The swell
inversion procedure will estimate
the swell wave spectrum
resolved by the SAR. Note that
although the extraction of the swell
is based on the quasi-linear
transform, the inversion is a
nonlinear inversion process through
the coupling with the nonlinear part.
- Set the inversion confidence measure.
- Convert the final wave spectrum to
log-polar grid, compute spectral
parameters and transfer the results to
the data output module.
The retrieval of ocean wave spectra is then
performed on the quasi-linear cross spectra.
An example of input and output results of
the inversion procedure described above
is shown in figure2.61 below, on
|Figure 2.61 Example of ASAR Level 1 cross-spectra (upper plots) and the corresponding wave-spectra (low left) achieved by the inversion procedure described above. Collocated Wave Model (WAM) spectrum shown in lower right plot. Note that here the spectra is shown in Cartesian representation.
The Cartesian to logarithmic polar grid
transformation is performed using bi-linear
interpolation. The polar grid will be given
in wave number-direction representation.
The wavelength region is specified in the
setup file. The number of wave number and
angular bins will be user-selectable
with default values 24 and 36, respectively.
The wave number samples will be on
logarithmic while the angular samples will
always be equidistant. The polar spectra is
given clockwise relative to north. The
Cartesian inverted ocean waveheight spectrum
is transformed in to log-polar grid representation.
The spectral peak parameter extraction,
discussed below, is to be performed on the
The spectral peak period and direction is
extracted from the one-dimensional spectra
obtained by averaging over direction and
wave number, respectively. See figure2.62 below.
|Figure 2.62 Typical non-directional (heave) and directional SAR wave spectra obtained by integrating out the directional and the wave number dependency, respectively. The heave spectrum is used to computed the spectral peak wavelength. The directional spectrum is used to compute the peak propagation direction. The dotted lines are the corresponding spectra derived from collocated WAM (Wave Model) spectra.
6. Output Data
The level 2 product that results from the
above processing is described in the section entitled
"Level 2 Product" 2.7.2. .