Surface Wave Parameters Retrieval in Coastal Seas from Spaceborne SAR Image Mode Data

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1 PIERS ONLINE, VOL. 4, NO. 4, Surface Wave Parameters Retrieval in Coastal Seas from Spaceborne SAR Image Mode Data Jian Sun 1,2 and Hiroshi Kawamura 1 1 Graduate School of Science, Tohoku University, Sendai, Japan 2 Physical Oceanography Laboratory, Ocean University of China, Qingdao, China Abstract We have developed a retrieval scheme of surface wave parameters (wave height and wave propagation direction) from ERS Synthetic Aperture Radar (SAR) image mode data in coastal seas around Japan. In this study, we investigated the energy of simulated SAR spectrum at different wind speed using nonlinear wave-sar imaging mechanism, derived the criteria to differentiate swell from wind waves, and accordingly processed SAR images containing swell and wind waves in different way respectively. SAR spectra are converted to surface wave spectra of swell-dominated or wind-wave dominated cases. The SAR spectrum and SAR-derived wind speed are used for the derivation of surface wave spectrum. The wind-wave dominated case and swelldominated case are differentiated by the wind speed of 6 m/s, and processed in different ways because of their different nonlinear degree. It is indicated that the cutoff wavelength for retrieval of the wind-wave dominated spectrum is proportional to the root of significant wave height, which is consistent with the results of previous studies. We generated 66 match-ups coupling the SAR sub-images and the in-situ surface wave parameters, which were measured by the wave gauges installed in near-shore seas. Among them, the number of swell-dominated case is 57, and the number of wind-wave dominated case is 9. The SAR-derived and in-situ significant wave heights agree well with the bias of.24 m, the RMS error.92 m and the correlation coefficient of.66. The averaged absolute deviation of wave propagation directions is 18.4±, and the agreement tendency does not depend on the wave height. It is proven through the comprehensive validation that the developed SAR surface wave spectrum has high accuracy in the Japanese coastal seas. 1. INTRODUCTION Synthetic Aperture Radar (SAR) is one of the most efficient instruments to observe sea surface wave field in a large scope with high resolution. The effort to retrieve surface wave information from SAR data has never stopped. It is generally accepted that for intermediate incident angle like ERS SAR, long waves detected by SAR are due to the existence of decimetric Bragg waves modulated by these long waves. At different phase of long waves (including wind waves and swell), there is the different modulation effect to Bragg waves, which makes long waves appear in SAR images as the wave-like stripes pattern. The modulation of long waves to Bragg waves includes tilt modulation, hydrodynamic modulation and velocity bunching and the modulation transfer function are investigated by some authors [1, 2]. On the basis of the modulation theories [3], a closed spectral integral transform relation between SAR spectra and wave spectra has been proposed and widely accepted [4]. To retrieve wave parameters from SAR data is not a strait-forward procedure. One of the retrieval methods called MPI method [4, 5]. The main idea of the MPI scheme is to use WAM model spectra as first-guess spectra to eliminate the 18 directional ambiguity and augment the spectrum information beyond the azimuthal cut-off. In another scheme call SPRA [6], only SAR image spectra and scatterometer wind vector measurement are needed as input in this model. The model was validated with SAR wave mode data. Coastal area is important for human activities. The surface wave dynamics in the coastal area is much more complex than that in the deep ocean. It is known that the wave model result is much hampered by the dominance of swell and the dramatic change of the water depth in coastal area. As the result, the direct observation of coastal waves from SAR becomes an important way to acquire wave information. ASAR single look complex (SLC) data is used to extract ocean wave fields near the coast of France recently [7]. However, the application of the image mode SAR images containing wave information is much limited because of the poor knowledge of the retrieval of wave parameters from SAR scene and its validation in coastal areas. In this study, wave information such as wave height, wave direction and cutoff wavelength is retrieved from SAR image mode precision image (PRI) data around the coast of Japan. The in-situ

2 PIERS ONLINE, VOL. 4, NO. 4, NOWPHAS wave gauge data is used for matching up the SAR images and for validation. Windwave-produced SAR sub-images and swell-produced SAR sub-images are processed using different retrieval methods respectively according to the methods described in Section 2. In Section 3, the result is shown to demonstrate the relation between cutoff wavelength and the root of wave height and the agreement of wave information from SAR and from in-situ data. The summary and conclusions is given in Section DATA AND METHODOLOGY The ERS SAR image mode data and NOWPHAS in situ data is used in this study. ERS-1 and ERS-2, which carry Active Microwave Instrument (AMI) operating at C band and VV polarization, was launched in 1991 and 1995 respectively. The swath of the SAR images around 1 km for image mode data. SAR images are produced from raw signal by Sigma SAR Processor [8]. The NOWPHAS (Nationwide Ocean Wave information network for Ports and HArbourS) wave gauge data we use in this study include the data of 21 stations which are located in the coast of Japan. The wave sensors of NOWPHAS include Ultra-sonic Wave Gauge (UWG), Current meter type Wave Directional meter (CWD) and newly developed DWDM. These sensor are mounted on the sea bottom with the depth ranging from 1 to meters. NOWPHAS wave gauge data can provide the wave information such as wave propagation direction, significant wave height and significant wave period. NOWPHAS wave observation system has a sample rate of 2 hours. In this study, the first procedure is to derive a match-up database where the SAR sub-image and wave gauge data is coincident and quasi-simultaneous. The SAR image mode data processed by Sigma processor is 6656 pixels in azimuth direction and 5344 pixels in range direction. We choose 512*512 pixels, avoiding the interference of the very dark pixels value at the edge of the image. Then the image is divided into 4*4 sub-images, each of which has 128*128 pixels (approximately 1.6*1.6 km). There are some criteria for matching up. First, for one scene, the sub-image whose location of the center is nearest to a certain wave gauge is preliminarily chosen. Second, it should be satisfied that the distance between the center of the sub-image and the location of the wave gauge less than.5 degree. Third, the wave gauge record must be integrate (including wave height, wave direction and wave period) at the nearest time when this scene of SAR image was illuminated. Fourth, there must be clear wave stripe in the sub-image. In detail, the signal to noise (SN) of the corresponding SAR image spectrum should be larger than 3. As the result, we have chosen 98 match-ups. However, there are still some other factors which can affect the degree of these match-ups. First, there is possibility that the sub-image of SAR data and a certain wave gauge locate the different side of the peninsula or island, although they are close. Second, the image quality of the selected sub-image may be deteriorated by other phenomena in SAR image. For example, if there are atmospheric front, as the irregular dark lines or curves, and wave stripes in SAR image simultaneous, the sub-image containing wave stripe will be damaged by the background atmospheric front stripes. Third, if the wave gauge locates in the bay, there will be some mismatch with the increase of the distance between the wave gauge and sub-image owing to the bathometry. Table 1 shows the statistics of the data match-ups, 32 scenes, about 3% of total 98 scenes, was rejected due to the effect of bathometry, distance and image quality. Table 1: Match-up data statistics. Sample accepted Sample rejected Swell 57 Wind wave 9 Bathometry 4 Distance 12 Quality of image 16 total 98 We first derive the calibrated normalized radar cross section (NRCS) according to the sigma- derivation formula. NRSC of every pixel in db can be inverted using SIGMA SAR processor relationship NRCS = 2 log 1 (DN) + CF,

3 PIERS ONLINE, VOL. 4, NO. 4, where CF is the conversion parameter provided by JAXA. Wind speed is estimated by inverting the wind-vector-to-radar-cross-section relationship CMOD function at the presence of incident angle of radiation, a beam view angle, wind direction and NRCS value [8, 9]. The determination of wind direction is according to the background wind direction provided by NCEP/NCAR reanalyzed reanalysis surface wind field. The SAR sub-images are first filtered by using a Gaussian high pass filter to remove the low wave number signal which has no relation to surface waves. The coarse SAR spectra in Fig. 3(b) are computed by performing 2-dimensional Fast Fourier Transform (2-D FFT) to corrected sub-images. Then the smoothed SAR image spectrum in Fig. 3(c) are derived by performing low pass filter to coarse spectra. In practice, the observed SAR spectrum P obs (k) can be described as the combination of a wave image spectrum P I (k) and a background clutter noise spectrum P cl (k). To the first order, P I (k) and P cl (k) are simply linearly superimposed, the modulation of the clutter noise by the ocean Azimuth (mk) Range (km) (a) (b) (c) (d) (e) spectrum intensity cutoff wavelength=125.7m Azimuth wavenumber (rad/m) (f) Figure 1: An example of methodology for retrieving wind wave spectrum. (a) SAR sub-image of 128*128 pixels, (b) coarse SAR image spectrum, (c) filtered SAR image spectrum, (d) first guess spectrum constructed using retrieved wind speed, (e) retrieved wave spectrum, (f) cutoff wavelength calculation.

4 PIERS ONLINE, VOL. 4, NO. 4, waves being negligible. The clutter spectrum can thus be removed by subtraction. Below the high wave number roll-off due to the system impulse response function, the clutter spectrum is essentially white. We estimate the clutter noise spectrum by averaging the intensity of observed SAR spectrum of the first 1 bins near Nyquist wave number where there is no wave SAR signal. Then we treat swell-dominated SAR spectrum P I S (k)and wind-wave-dominated SAR image spectrum P I W (k)in a different way. For swell, we retrieved wave spectrum by using linear image relationship P I S (k) = k 2 [ T (k) 2 F (k) + T ( k) 2 F ( k) ] (1) giving the standard modulation transfer function. The retrieved elevation wavenumber spectrum by this procedure is known with 18 ambiguity. In order to remove the directional ambiguity and derive the right wave propagation direction, we adopt the fact that swell can only propagate forward the coast instead of backward the coast. For wind waves, the MPI scheme for retrieving wave spectrum is applied in this study. We use JONSWAP type spectrum [1] and wave direction function [11] to construct a parameterized wind wave spectrum as a first guess spectrum. Then according to the nonlinear imaging mechanism P I W (k) = Φ(F (k)), iteratively change wind wave SAR spectrum to match the observed SAR image spectrum by minimize the cost function defined as J = [ P (k) ˆP (k)] 2dk + µ [ F (k) ˆF (k)] 2dk (2) where ˆF (k) is first guess spectrum, ˆP (k) is observed SAR spectrum, F (k) is the best-fit wave spectrum and P (k) is the best-fit SAR spectrum. The cost function is written as the summation of the difference between best-fit SAR spectrum and the observed SAR spectrum, and the difference between best-fit wave spectrum and the first guess wave spectrum. SAR spectra are always affected by azimuth cutoff, an effect to roll off SAR spectra in the azimuth direction. The azimuth cutoff is caused by the nonlinearity of wave-sar relationship in azimuth direction and act as a low-pass Gaussian filter to SAR spectra [12]. The cutoff wavelength has been a parameter which can be calculated by fitting a Gaussian low-pass filter to range-integral SAR spectrum [13]. In this study, we estimate the cutoff wavelength for wind wave cases using the function ( ) ) 2 exp π where k c = 2π/L c and L c is cutoff wavelength. The fitting of range-integral SAR spectrum using low pass filter function is shown in Fig. 1(f). ( kx k c Figure 2: The relation between spectral energy within SAR Nyquist wave number and wind speed at different propagation direction.

5 PIERS ONLINE, VOL. 4, NO. 4, RESULTS 3.1. The Differentiating of Wind Waves and Swell Figure 2 shows the variation of SAR spectrum within Nyquist wave number with wind speed at the azimuth angle of 2, 4, 6 and 8. It is demonstrated that when wind speed is less than 6 m/s, the energy of simulated SAR spectrum in the Nyquist wave number is too weak to be detected. That means if there is detectable signal in SAR image spectrum while the retrieved wind speed is less than 6 m/s, the signal is produced by swell and the wave pattern in SAR image is swell dominated waves. So we set 6 m/s as a standard of wave category for retrieval. If the wind speed corresponding to SAR image is larger than 6 m/s, it is considered that there is wind wave produced spectrum energy in SAR image spectrum. If less than 6 m/s, it is totally swell produced The Validation of Retrieval Figure 3 shows the proportional relationship between cutoff wavelength and the root of wave height. The fit implies that in addition to cutoff wavelength, the wave height is another important parameter to reflect the degree of imaging nonlinearity. Wave height is more sensitive to the degree of nonlinearity than any other parameters such as wind speed or wave length. We now compare SAR-derived parameters to NOWPHAS wave gauge data. The comparison of Cutoff wavelength (m) root of wave height Figure 3: The cutoff wavelength with root of significant wave height for wind waves wind waves swell 4 4 <wave height.5.5<wave height 1 waveheight from buoy Wave Direction from SAR images(deg) <wave height <wave height 2 2<waveheight waveheight from SAR (a) Wave Direction from Wave Gauge(deg) (b) Figure 4: The comparison of wave height and wave direction from SAR and wave gauge.

6 PIERS ONLINE, VOL. 4, NO. 4, 28 4 wave height from SAR images and from wave gauge is shown in Fig. 4(a). The comparison gives good agreement except for a few examples showing rather discrepancy. Totally the SAR-derived wave height is underestimated at some degree because the bias is larger than for both wind waves and swell. The swell comparison behaves better than wind waves for its smaller RMS, mainly due to the larger amount of samples and lower wave height samples. For swell, it is more accurate for the cases when the wave height is low, and when wave height increase, the error increase. The wave direction comparison in different wave height categories is shown in Fig. 4(b). The totally agreement is shown with the average difference of the direction below CONCLUSIONS In this paper, Using SAR image mode data, we have retrieved and analyzed the parameters of surface waves in the coast region around Japan. The wind speed information is also acquired from SAR data as the additional input information for retrievement. The match-up NOWPHAS wave gauge data is used for validation. The following conclusions are obtained. ERS-SAR image mode data is capable for wave information retrieval in the coastal region only if the clear wave stripe is available in the sub-image. As for the different nonlinear degree, the wind waves and swell should be dealt with different retrieval methods. The differentiating criteria of swell and wind waves can be reduced to the value of wind speed. The wave height from SAR data and from wave gauge agrees rather well. The bias and RMS of the comparison of swell is better than that of wind waves, mainly due to the degree of nonlinearity. The cutoff wavelength is proportional to the root of significant wave height. This implies that in addition to cutoff wavelength, the wave height is another important parameter to reflect the degree of imaging nonlinearity. Wave height is more sensitive to the degree of nonlinearity than any other parameters such as wind speed or wave length. REFERENCES 1. Alpers, W. R., D. B. Ross, and C. L. Rufenach, On the detectability of ocean surface wave by real and synthetic aperture radar, J. Geophys. Res., Vol. 86, No. C7, , Monaldo, F. M. and R. C. Beal, Comparison of SIR-C SAR wavenumber spectra with WAM model predictions, J. Geophys. Res., Vol. 13, No. C9, , Hasselmann, K., R. K. Raney, W. J. Plant, W. Alpers, R. A. Shuchman, D. R. Lyzenga, C. L. Rufenach, and M. J. Tucker, Theory of synthetic aperture radar ocean imaging: A MARSEN view, J. Geophys. Res., Vol. 9, No. C3, , Hasselmann, K. and S. Hasselmann, On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion, J. Geophys. Res., Vol. 96, No. C6, , Hasselmann, S., C. Bruning, K. Hasselmann, and P. Heimbach, An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra, J. Geophys. Res., Vol. 11, No. C7, , Mastenbroek, C. and C. F. de Valk, A semiparametric algorithm to retrieve ocean wave spectra from synthetic aperture radar, J. Geophys. Res., Vol. 15, , Collard, F., F. Ardhuin, and B. Chapron, Extraction of coastal ocean wave fields from SAR images, IEEE Journal of Oceanic Engineering, Vol. 3, No. 3, , Alpers, W., U. Paul, and G. Gross, Katabatic wind fields in coastal areas studied by ERS-1 synthetic aperture radar imagery and numerical modeling, J. Geophys. Res., Vol. 13, , Furevik, B. R., O. M., Johannessen, and A. D. Sandvik, SAR retrieved winds in polar regions- Comparison with in situ data and atmospheric model output, IEEE Trans. Geosci. Remote Sensing, Vol. 4, , Hasselmann, D. E., M. Dunckel, and J. A. Ewing, Directional wave spectra observed during JONSWAP 1973, J. Phys. Oceanogr., Vol. 1, , Donelan, M. A., J. Hamilton, and W. H. Hui, Directional spectra of wind generated waves, Philos. Trans. R. Soc., Vol. 315, 9 562, Kerbaol, V., B. Chapron, and P. M. Vachon, A global analysis of ERS-1/2 SAR wave mode imagettes, J. Geophys. Res., Vol. 13, , Schulz-Stellenfleth, J. and S. Lehner, Spaceborne synthetic aperture radar observation of ocean waves traveling into sea ice, J. Geophys. Res., Vol. 17, No. C8, 316, 1.129/21JC837, 22.