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.

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 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.)

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 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 (info) file.

3. Processing

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 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 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 - 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 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 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 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 anti-symmetric spectrum.

• 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 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 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 Cartesian grid.

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 polar grid.

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. .