Measurement of Ocean Wave Spectra and Surface Slopes by Polarimetric SAR

Introduction: New methods that use the capabilities of fully polarimetric synthetic aperture radar (SAR) image data to measure ocean wave slopes and wave spectra have been developed. The methods have been tested by using aircraft-platform NASA/AIRSAR data obtained during flights over California coastal waters. Independent techniques have been developed to measure slopes in the SAR azimuth (flight) direction and the (orthogonal) range direction. Wave spectra measured using these new methods compare favorably with spectra developed using conventional intensity-based radar methods, and also with in situ National Data Buoy Center (NDBC) buoy data.

SAR instruments have traditionally operated by using a single polarization to measure wave-induced backscatter cross-section modulations. The backscatter measurements require a parametrically complex modulation transfer function (MTF) to relate cross-section values to physical wave properties, such as slopes or wave spectra.

In the Fourier-transform domain, orthogonal slope information is used to estimate a complete directional ocean wave slope spectrum. The advantage of using the new SAR algorithms is that a nearly direct physical measurement of the slope is made that does not require the use of a nonlinear, complex MTF.

A method1 that senses modulations of polarization orientation angle is used to measure wave slopes in the azimuth direction. Slope magnitudes smaller than 1° are measurable. An eigenvector/eigenvalue decomposition parameter Alpha is used to measure wave slopes in the range direction.2 Waves in the range direction cause modulation of the local incidence angle that, in turn, modulates the value of Alpha. From these azimuth and range slope pairs, a complete directional wave slope spectrum can be measured.

Ocean Slope Measurements: The wave-induced modulation in the orientation angle is directly related to the surface slope in the azimuth direction. To a lesser extent, the modulation is also dependent on the slope in the range direction and the incidence angle Φ. The average incidence angle for each image pixel is known from the flight geometry, and the range slope is determined using an algorithm that relates Alpha modulation to the slopes of long waves propagating in the range direction. Combining the measurements of azimuth and range slopes provides complete ocean wave slope information in any direction. The RMS slopes determined using these new techniques agreed well with values calculated from the NDBC buoy data.

Wave Spectra (Azimuth Direction): NASA/JPL/AIRSAR data at L-band imaging a coastal area in northern California was used to determine how well the azimuth component of an ocean wave spectrum could be measured using orientation angle modulation. Figure 4(a) is an L-band, VV-polarization (pol), false color-coded image that shows the imaged area and the measurement test site. A wave system with an estimated dominant wavelength of 156 m is propagating through the site with a wave direction of 320°. Figure 4(b) shows an orientation angle wave spectra of this wave system vs wavenumber (2π/(wavelength)) plotted radially. The white rings are located at 50-m wavelength intervals. The dominant wave, corresponding to a wavelength of 156m, can be determined from this spectrum.

FIGURE 4
(a) An L-band, VV-pol, AIRSAR image showing ocean waves propagating through the study area box. (b) Orientation angle spectra vs wavenumber for azimuth direction waves propagating in the study area. The dominant wave is propagating at a heading of 320°.

Figure 5(a) shows modulations in the polarization orientation angle induced by azimuth traveling ocean waves; Fig. 5(b) is a histogram of the orientation angles. The range of orientation angles was ±4 deg.

FIGURE 5
(a) Modulations in the orientation angle image; (b) histogram of the distribution of orientation angle values.

Figure 6(a) presents a profile through the orientation angle spectrum made in the direction (320°) of maximum wave spectral energy. Figure 6(b) is a similarly directed profile, but it represents a conventional VV-pol image SAR intensity spectrum. It is apparent that the orientation angle spectrum has a much higher dominant wave spectral peak/background ratio than the SAR intensity spectrum.

FIGURE 6
(a) Plots of spectral intensity vs wavenumber for wave-induced orientation angle modulations, and (b) for conventional VV-pol intensity modulations.

Wave Spectra (Range Direction): A new concept has been investigated for SAR measurements of ocean slopes in the range direction. This concept was developed as a means of circumventing some of the difficulties associated with conventional backscatter intensity-based methods.

The Alpha parameter, developed from the Cloude-Pottier polarimetric decomposition theorem,2 has useful properties for measuring slopes and slope spectra in the range direction. In the range direction, Alpha is sensitive to wave-induced modulations in the local incidence angle Φ. In the azimuth direction, it is roll-invariant and, thus, insensitive to azimuth slopes. Thus, the orthogonal slope measurement variables are well decoupled.

The wave spectra of range traveling waves can be determined using the Alpha parameter. A spectral profile was developed using the Alpha parameter technique, and a dominant wave was measured having a wavelength of 154 m and a propagation direction of 315°. The dominant wavelengths and wave directions determined from the wave spectra agreed well with NDBC buoy data.

Summary: New methods have been investigated that are capable of accurately measuring ocean slope distributions and wave spectra in both the range and azimuth directions. The new measurements are sensitive and provide nearly direct measurements of ocean slopes.

Using aircraft/satellite platforms, this new Navy remote sensing capability will provide large-area measurements of sea state in support of U.S. Navy Fleet operations.

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