ADVANCED REMOTE SENSING OF OCEANIC INTERNAL WAVES BY SPACEBORNE ALONG-TRACK INTERFEROMETRIC SAR Roland Romeiser and Hans C. Graber

Rosenstiel School of Marine and Atmospheric Science (RSMAS), University of Miami, Florida, USA

Roland Romeiser, RSMAS-AMP, 4600 Rickenbacker Causeway, Miami FL 33149 USA Phone: +1 305 421 4645, Fax: +1 305 421 4701, E-Mail: rromeiser@rsmas.miami.edu

This work has been funded by the U.S. Office of Naval Research under grant N00014-11-1-0280

Since the SEASAT mission in 1978, scientists have used satellite-based synthetic aperture radar (SAR) images to study oceanic internal waves [1]. Internal waves become visible in SAR images because their orbital currents modulate the surface roughness [2]. While this leads to an accurate spatial representation of wave patterns, the complexity of the imaging mech-anism makes it difficult to estimate currents and in-ternal wave amplitudes quantitatively from conven-tional SAR images [3]. A more direct interpretation is possible with along-track interferometry (ATI), which

permits direct scatterer velocity retrievals from a pair of SAR images. ATI data are currently available from the satellite TerraSAR-X as an experimental product. We present an example dataset with strong signa-tures of internal waves at Dongsha (South China Sea) and demonstrate how internal wave properties can be estimated using a simple parameterization of internal solitons and a numerical SAR imaging model. Further model results show how ATI signatures are more sen-sitive to currents and less sensitive to secondary model parameters than conventional SAR signatures.

[1] J. R. Apel, Oceanic internal waves and solitons, in An Atlas of Oceanic Internal Solitary Waves, 1-39, Global Ocean Associates, 2002, available at http://www.internalwaveatlas.com/Atlas2_index.html. [2] W. Alpers, Theory of radar imaging of internal waves, Nature, 314, 245-247, 1985. [3] P. Brandt, R. Romeiser, and A. Rubino, On the determination of characteristics of the interior ocean dy- namics from radar signatures of internal solitary waves, J. Geophys. Res., 104, 30,039-30,047, 1999. [4] R. M. Goldstein and H. A. Zebker, Interferometric radar measurement of ocean surface currents, Nature, 328, 707-709, 1987. [5] J. Mittermayer and H. Runge, Conceptual studies for exploiting the TerraSAR-X dual receive antenna, in Proc. IGARSS 2003, 2140-2142, IEEE, Piscataway, N. J., USA, 2003.

[6] R. Romeiser and H. Runge, Theoretical evaluation of several possible along-track InSAR modes of Terra- SAR-X for ocean current measurements, IEEE Trans. Geosci. Remote Sensing, 45, 21-35, 2007. [7] T. P. Stanton and L. A. Ostrovsky, Observations of highly nonlinear internal solitons over the continental shelf, Geophys. Res. Lett., 25, 2695–2698, 1998. [8] R. Romeiser and D. R. Thompson, Numerical study on the along-track interferometric radar imaging mechanism of oceanic surface currents, IEEE Trans. Geosci. Remote Sensing, 38-II, 446-458, 2000.

The TerraSAR-X data used in this work were obtained from the German Aerospace Center (DLR) within the framework of the 2010 DRA Mode Campaign and TerraSAR-X Science Project MTH0929. © German Aerospace Center (DLR). The SAR processing was done by Steffen Suchandt of DLR.

A High-Resolution Image of the Surface Velocity Field

TerraSAR-X Along-Track Interferometry Along-track interferometry requires an acquisition of two SAR images with a time lag on the order of milliseconds [4]. Interferometric combination of the two images reveals phase differences that are pro-portional to the Doppler shift of the backscattered signal and thus to line-of-sight scatterer velocities. The typical ATI setup uses two antennas separated by a distance in flight direction (i.e. along track) equal to the platform displacement within the de-sired time lag. The German TerraSAR-X is the first

satellite with experimental ATI capabilities. It cre-ates two receiving antennas by splitting its 4.8-m long phased-array antenna into two halves electron-ically [5]. This leads to very suboptimal system pa-rameters and noisy interferograms [6], but the data quality is sufficient for a demonstration of the tech-nique at selected test sites. The University of Miami's Center for Southeastern Tropical Advanced Remote Sensing (CSTARS) has full capabilities to order, downlink, and process TerraSAR-X ATI data.

The dataset considered here was acquired by TerraSAR-X on April 22, 2010, 22:13 UTC, at Dongsha (South China Sea). This region is well known for its internal waves, but we had good luck to find a particularly well organized internal wave train, propagating almost exactly in radar look direction, in the center of the image. The intensity image on the left, cover-

ing an area of 29 km × 88 km, shows the typical surface roughness variations due to hydrodynamic wave-current interaction that have been observed in many satellite images. The phase image in the center is a unique product that is obtained from ATI data only. While the phase signatures are clearly noisier than the intensity signatures, some correlated

patterns are visible. Applying a special filter and converting the phases into scatterer ve-locities, we can derive a horizontal Doppler velocity field of the first two solitons, as super-imposed in color in the third figure. Profiles of image intensity and Doppler velocity varia-tions at Transects 1-3 are analyzed and inter-preted further in the box on the right.

Image Intensity (10 dB Range) –1.5° Interferogram Phase +1.5° +0.5 m/s Doppler Velocity –0.5 m/s

Dongsha Island

TRANSECT 1

TRANSECT 2

TRANSECT 3

Data Analysis and Interpretation To estimate properties of the internal waves from the SAR image intensity and Doppler velocity pro-files, we generate theoretical radar signatures for a variety of parameter combinations. We start with the "kink-antikink" solution of the Korteveg-de Vries equation with cubic nonlinearity [7,1], which de-scribes solitons with amplitudes and widths deter-mined by the upper and lower layer depths and densities and by a nonlinearity parameter ν with values between 0 and 1. To convert the pycnocline displacement η into a surface current U, we use

where V is the propagation speed of the soliton and h1 the height of the upper layer. For Transects 1 and 2 we generate two solitons, for Transect 3 a single one. The current field and a wind vector are fed into a numerical SAR imaging model [8], which com-putes spatially varying surface wave spectra and corresponding image intensity and Doppler velocity signatures that can be compared with the observed ones. The soliton parameters that lead to best agreement represent our best estimate of the conditions at the time of the TerraSAR-X overpass. Based on weather station data, we assume a wind speed of 4.4 m/s from 45°. Furthermore, like in [3], we use a reduced relaxation rate in the wave-cur-rent interaction model to be able to reproduce the observed image intensity modulations. For h1, which should be on the order of 80-110 m, we find that

large values make the simulated signatures too wide, indicating that the best choice is near 80 m. With this, the only remaining tuning parameter is ν. The diagrams below show our best model results (red curves) together with the observed intensity and Doppler velocity profiles (black). Good agree-ment of all profiles is obtained with a parameter combination that is consistent with known typical conditions at the test site. This is all we can say for now, since we have not been able to obtain refer-ence data from April 2010 for a complete validation. An important question is how sensitive the image intensity and Doppler signatures are to parameter changes – this sensitivity determines how accurate-ly internal wave parameters can be retrieved from radar data. The pink, blue, and orange curves in the diagrams show how the model results change if we reduce the internal wave amplitude or wind speed or if we use the full relaxation rate instead of the reduced one. We find that a change of 1 m/s in the wind speed has a stronger effect on some image intensity signatures than an internal wave amplitude change by 20%, while the Doppler signatures are clearly more sensitive to current than to wind varia-tions. Similarly, a modification of the relaxation rate has a much stronger effect on the intensity than on the Doppler signatures. The low sensitivity of Dopp-ler signatures to these secondary parameters is the main reason why the ATI technique permits more accurate and robust internal wave parameter re-trievals than the conventional SAR image analysis.

References and Acknowledgments

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