Measurement of ocean surface slopes and wave spectra using polarimetric SAR image data
Introduction
Synthetic aperture radar (SAR) systems conventionally use backscatter intensity-based algorithms (Alpers & Rufenach, 1981) to measure physical ocean parameters. SAR instruments, operating at a single polarization, measure wave-induced backscatter cross-section, or sigma-0, modulations that can be developed into estimates of surface wave slopes, or wave spectra. These measurements require a modulation transfer function (MTF) to relate the SAR measurements to the physical ocean wave properties.
The studies reported here investigate the feasibility of using polarimetric SAR (POLSAR) data, and newly developed algorithms Schuler et al., 2003a, Schuler et al., 2003b to measure ocean wave slopes in both the radar azimuth and range directions. In the Fourier-transform domain, this orthogonal slope information can be used to estimate a complete directional ocean wave slope spectrum. The advantage of using the POLSAR-based algorithms is that a nearly direct measurement of the slope is made. The POLSAR measurement does not require the use of a parametrically complex MTF. Motion-induced nonlinear “velocity-bunching” effects still present difficulties for wave measurements in the azimuth direction. These difficulties may be dealt with by using the same proven algorithms Engen & Johnsen, 1995, Hasselmann & Hasselmann, 1991 that have reduced nonlinearities for previous measurement methods.
Modulations of the polarization orientation angle, θ, are largely caused by waves traveling in the azimuth direction. These modulations are also, to a lesser extent, affected by range traveling waves. A method, originally used in topographic measurements (Schuler et al., 1996), has been applied to the ocean in this study. The method will measure azimuth components of ocean wave slopes and wave spectra. An approximation for this method, valid over a large range of incidence angles and slopes, is introduced which measures only slopes in the azimuth direction. Slopes much smaller than 1° are measurable for ocean surfaces using this method.
An eigenvector/eigenvalue decomposition average parameter ᾱ described in Pottier (1998) is used to measure wave slopes in the orthogonal range direction. Waves in the range direction cause modulation of the local incidence angle φ that, in turn, changes the value of ᾱ. The alpha parameter is “roll-invariant”. This means that it is not affected by slopes in the azimuth direction. Likewise, for ocean wave measurements, the orientation angle θ parameter is largely insensitive to slopes in the range direction. An algorithm employing both (ᾱ,θ) is, therefore, capable of measuring slopes in any direction.
The ability to measure a physical parameter in two orthogonal directions within an individual resolution cell is rare. Microwave instruments, generally, must have a 2-D imaging or scanning capability to obtain information in two orthogonal directions.
Of the two measurement methods investigated, the orientation angle measurement of azimuth direction slopes is the best understood and has been shown to be accurate (Lee et al., 2000). The newer alpha method for measuring range direction slopes has shown promise in this investigation.
NASA/JPL/AIRSAR L-, and P-band ocean backscatter data has been used in the studies. Comparisons will be made of ocean wave spectra measured using these new POLSAR methods and spectra produced from conventional intensity-based methods.
Comparisons will also be made with in situ buoys maintained by the NOAA National Data Buoy Center (NDBC). These buoys are 3-m Discus buoys that measure non-directional ocean wave spectra vs. frequency and wind speed/direction at 5 m above the water surface.
Finally, Appendix A considers the special case when the data collection is done by a real-aperture radar (RAR) rather than by a SAR. The single-pol RAR MTF in the azimuth direction from all sources is near zero. Polarimetric RAR measurements, that are processed using the orientation angle measurement algorithm, instead of near zero, will have a large MTF in this direction. Wave properties in the azimuth direction may now be measured by a polarimetric RAR sensor.
Section snippets
Single polarization SAR measurements of ocean wave properties
Synthetic aperture radar (SAR) imaging systems have previously been used for imaging ocean features such as surface waves, shallow water bathymetry, internal waves, current boundaries, slicks, and ship wakes (Vesecky & Stewart, 1982). In all of these applications, the modulation of the SAR image intensity by the ocean feature makes the feature visible in the image Beal et al., 1986, Monaldo & Beal, 1995. When imaging ocean surface waves, the main modulation mechanisms have been identified as
Measurement of ocean wave slopes using polarimetric SAR data
Techniques are developed in this section for the measurement of ocean surface slopes and wave spectra using the capabilities of fully polarimetric POLSAR. Wave-induced perturbations of the polarization orientation angle are used to directly measure slopes for azimuth traveling waves. This technique is accurate for scattering from surface resolution cells where the sea return can be represented as a two-scale Bragg scattering process. If backscatter from the resolution cell is dominated, for
Ocean wave spectra measured using orientation angles
NASA/JPL/AIRSAR data were taken at L-band imaging a northern California coastal area near both the town of Gualala and the Gualala River (1994). This data set was used to determine if the azimuth component of an ocean wave spectrum could be measured using orientation angle modulation. AIRSAR data acquisition parameters for the Gualala flight (and a second data set “San Francisco” ) are given in Table 1. The radar resolution cell had dimensions of 6.6 m (range direction) and 8.2 m (azimuth
Two-scale ocean scattering model: measurement of orientation angle mean
In Section 3.2, Eq. (5) is given for the orientation angle. This equation gives the orientation angle θ as a function of three terms from the polarimetric coherency matrix T. Scattering has only been considered as occurring from a slightly rough surface the size of the radar resolution cell (see Fig. 2). The surface is planar and has a single tilt θs. This section will examine the effects of having a distribution of azimuth tilts, p(ϕ), within the resolution cell, rather than a single averaged
Alpha parameter measurement of range slopes
A second measurement technique is needed to remotely sense waves that have significant propagation direction components in the range direction. The technique must be more sensitive than current intensity-based techniques that depend on tilt and hydrodynamic modulations. Physically based POLSAR measurements of ocean slopes in the range direction may be achieved using a technique involving the “alpha” parameter of a recently developed Cloude–Pottier polarimetric decomposition theorem.
Measured wave properties and comparisons with Buoy data
The ocean wave properties estimated from the L-, and P-band SAR data sets and the algorithms are the (1) dominant wavelength, (2) dominant wave direction, (3) rms slopes (azimuth/range) and, (4) average dominant waveheight. The NOAA NDBC buoys provided data on (1) dominant wave period, (2) windspeed/direction, (3) significant wave height, and (4) wave classification (swell/wind waves). Not enough data was analyzed to quantify measurement capabilities of the new algorithm at L-band vs. P-band.
Conclusions
Methods have been investigated which are capable of measuring ocean wave spectra and slope distributions in both the range and azimuth directions. The new measurements are sensitive and provide nearly direct measurements of ocean wave spectra and slopes, without the need for a complex modulation transfer function. The Gualala data set orientation modulation spectrum has a higher dominant wave peak/background ratio than the intensity-based spectrum. The results determined for the dominant wave
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