2.7.1 ASAR Level 2 Algorithms
The Synthetic Aperture Radar (SAR) is so far the only
satelliteborne 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 nonlinear oceantoSAR
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 crossspectral 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 SARderived
wave spectra compared to the Wave Model spectra.
The latter is partly due to nonoptimal
processed input SAR data combined with imperfect
inversion schemes. By using the crossspectra
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 alongtrack
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 dualpolarised (i.e.,
simultaneously acquired HH and VV
polarisations) data is available by using
crossspectra 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
multichannel crossspectrum derived by Engen
(1997). The standard image spectrum, and the
singlechannel crossspectrum 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.
2.7.1.1 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
preprocessing of the data will be done
before the core processing is started.
The preprocessing consists of interlook
crossspectral processing. The core
processing performs a wave spectral
inversion of the crossspectra with
respect to the detected SAR ocean wavelike
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 quasilinear inversion in the most
energetic part of the SAR
crossspectrum. 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 crossspectrum. The major
requirements for the second step is
knowledge of the Real Aperture Radar
Modulation Transfer Function (RAR MTF), the
azimuth cutoff (orbital shift
variance), and the nonlinear part of the
spectra. The RAR MTF is computed using
a backscattering model including nonuniform
distribution of scatterers on the long wave
field. The RAR MTF amplitude is provided as
part of lookup table used to estimate
the nonlinear part of the crossspectra.
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
crossspectra and the extra header
parameters are put into the spare fields.)
2.7.1.2 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
figure2.60 :

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 crossspectra 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
(info) file.
3. Processing
The processing module performs the look
extraction and crossspectra estimation
according to the steps below:

Image Detrending  Detrend the
input SLC image using a Gaussian
lowpass filter operation where the
width of
the filter can be
specified in the setup file.
This procedure removes the low frequency
effects from the SLC image that are due
to nonwave features. This is done by
computing a lowpass filtered
image from the SLC image and then
dividing the SLC image with the square
root of the computed lowpass filtered
intensity image. The procedure also
provides the image intensity of the
original input SLC image.

Image Cross Covariance Spectrum
Estimation  Compute the
cospectrum and the two crossspectra
corresponding to three looks.
This procedure performs the look
extraction and computes all combinations
of spectra. Default is 3 looks providing
3 spectra  one cospectra and two
crossspectra. The spectral processing
is based on the periodogram method.

Estimate and remove the Clutter Bias
of the CoSpectra  Estimate
the clutter bias of the cospectra and
remove it from the cospectra.
This procedure gives one unbiased
cospectra and two crossspectra
generated with two different look
separation times 
and 2
. 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 crossspectra 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 crossspectra.
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 crossspectra
to the lookup table, combined with a given
backscatter model function incorporating
nonuniform distribution of scatterers on
the long wave field. The RAR MTF
'amplitude' (i.e., derivative of
the phase function taken at Bragg
wavenumber) is provided within the lookup table.
The estimation procedure also provides an
estimate of the local wind speed. The wind
speed is estimated from the radar
crosssection using CMOD assuming the
wind direction is known. The wind direction
can be estimated from the phase of the
crossspectra or provided at input.
The computation of the nonlinear SAR image
crossspectrum in the lookup tables is done
using an implementation of the full
nonlinear SAR transform including a
nonuniform distribution of scatterers on
the long wave field. The lookup table is
used in order to simplify the algorithm
and to decrease the processing load.
5. Inversion of QuasiLinear Cross Spectra
The measured SAR image crossspectrum can be
approximated as a sum of a nonlinear part
(mainly wind sea driven), a quasilinear
part (detected SAR wave pattern, swell),
and a uniform distributed noise term, with
known variance.
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 crossspectra as
sums of the nonlinear approximation and
the well known quasilinear part given
by the exponential cutoff factor,
transfer functions and swell spectrum.
 Remove the nonlinear contribution (using
lookup table) and solve the
quasilinear part linearly with respect
to the swell spectrum inside the
SAR imaging domain, for each of the
spectra. Solve for the symmetric and the
antisymmetric spectrum.
 Compute the corresponding clutter noise
level of each of the wave spectra solutions.
The signaltonoise ratio is needed
in order to establish the criteria
for ambiguity resolvement i.e. when
combining the symmetric and
the antisymmetric 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 antisymmetric spectra.
 Compute the clutter noise of the final
symmetric and antisymmetric spectra,
combine them with the antisymmetric
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 antisymmetric spectra. The
basis idea is to perform an adaptive
smoothing (SNR dependent) of
the antisymmetric spectrum,
followed by a detection of the sign
for the valid regions defined by
the spectra and their
relation to the corresponding noise
level. The final wave spectrum is
then obtained by
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 quasilinear
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
logpolar grid, compute spectral
parameters and transfer the results to
the data output module.
The retrieval of ocean wave spectra is then
performed on the quasilinear cross spectra.
An example of input and output results of
the inversion procedure described above
is shown in figure2.61 below, on
Cartesian grid.

Figure 2.61 Example of ASAR Level 1 crossspectra (upper plots) and the corresponding wavespectra (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 bilinear
interpolation. The polar grid will be given
in wave numberdirection representation.
The wavelength region is specified in the
setup file. The number of wave number and
angular bins will be userselectable
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 logpolar grid representation.
The spectral peak parameter extraction,
discussed below, is to be performed on the
polar grid.
The spectral peak period and direction is
extracted from the onedimensional spectra
obtained by averaging over direction and
wave number, respectively. See figure2.62 below.

Figure 2.62 Typical nondirectional (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. .
