Observation of Hurricane-Generated Ocean Swell Refraction at the Gulf Stream North Wall With the RADARSAT-1 Synthetic Aperture Radar

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1 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER Observation of Hurricane-Generated Ocean Swell Refraction at the Gulf Stream North Wall With the RADARSAT-1 Synthetic Aperture Radar Xiaofeng Li, Member, IEEE, William G. Pichel, Member, IEEE, Mingxia He, Sunny Y. Wu, Karen S. Friedman, Pablo Clemente-Colón, and Chaofang Zhao Abstract In this study, we analyze the refraction of long oceanic waves at the Gulf Stream s north wall off the Florida coast as observed in imagery obtained from the RADARSAT-1 synthetic aperture radar (SAR) during the passage of Hurricane Bonnie on August 25, The wave spectra are derived from RADARSAT-1 SAR images from both inside and outside the Gulf Stream. From the image spectra, we can determine both the long wave s dominant wavelength and its propagation direction with 180 ambiguity. We find that the wavelength of hurricane-generated ocean waves can exceed 200 m. The calculated dominant wavelength from the SAR image spectra agree very well with in situ measurements made by National Oceanic and Atmospheric Administration National Data Buoy Center buoys. Since the waves mainly propagate toward the continental shelf from the open ocean, we can eliminate the wave propagation ambiguity. We also discuss the velocity-bunching mechanism. We find that in this very long wave case, the RADARSAT-1 SAR wave spectra should not be appreciably affected by the azimuth falloff, and we find that the ocean swell measurements can be considered reliable. We observe that the oceanic long waves change their propagation directions as they leave the Gulf Stream current. A wave current interaction model is used to simulate the wave refraction at the Gulf Stream boundary. In addition, the wave shoaling effect is discussed. We find that wave refraction is the dominant mechanism at the Gulf Stream boundary for these very long ocean swells, while wave reflection is not a dominant factor. We extract 256-by-256 pixel full-resolution subimages from the SAR image on both sides of the Gulf Stream boundary, and then derive the wave spectra. The SAR-observed swell refraction angles at the Gulf Stream north wall agree reasonably well with those calculated by the wave current interaction model. Index Terms Gulf Stream, refraction, surface waves, synthetic aperture radar. I. INTRODUCTION IT IS WELL KNOWN that oceanic surface wave characteristics, i.e., wavelength, propagation direction, and significant wave height, can be retrieved from airborne and spaceborne Manuscript received September 30, 2001; revised May 14, This research was funded in part by the Visiting Scholar Foundation of the Key-lab in the University of Ministry of Education of China and in part by the National Oceanic and Atmospheric Administration (NOAA) NESDIS Ocean Remote Sensing Program. X. Li, W. G. Pichel, K. S. Friedman, and P. Clemente-Colón are with the NOAA/NESDIS, Camp Springs, MD USA. M. He and C. Zhao are with the Ocean Remote Sensing Institute, Ocean University of Qingdao, Qingdao , China. S. Y. Wu is with the National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD USA. Digital Object Identifier /TGRS synthetic aperture radar (SAR) images [1]. For spaceborne wide-swath SAR, it is possible to obtain large swath coverage of oceanic gravity wave fields, where the actual wave propagation can be followed. The observation of oceanic gravity waves on a global scale with SAR was first demonstrated with Seasat SAR data in the late 1970s [2]. Since the launch of the European Space Agency s ERS-1 in 1991, spaceborne SAR images have been used to derive information on global ocean waves, in particular on the spectral and angular distribution of energy of oceanic long waves, or swell, with wavelength longer than 200 m [3]. However, the SAR spectrum and the real oceanic long wave spectrum are different due to nonlinear distortion of the modulation transfer function caused by Doppler shift induced by the orbital motion of surface waves. The nonlinear distortion is particularly apparent in the imaging of short waves and of waves traveling in the azimuth direction. However, hurricane-generated range-traveling oceanic waves with wavelengths above 200 m are less affected by nonlinear distortion to the SAR image spectrum. When the SAR is operating linearly over the ocean, the evolution of surface gravity fields can be accurately retrieved [4] [7]. Observations of refraction of oceanic gravity waves by airborne or spaceborne SAR have been made in coastal waters where the oceanic bottom topography changes [8], and in the vicinity of major ocean current fronts [9] [11], warm core ring boundaries [12], and ice edges [13]. The National Oceanic and Atmospheric Administration (NOAA) National Environmental Satellite, Data, and Information Service (NESDIS) has been actively monitoring the Atlantic Ocean during hurricane seasons with the RADARSAT-1 SAR since Recently, a cooperative program, called Hurricane Watch, has been established with the Canada Centre for Remote Sensing, Canadian Space Agency, NOAA/NESDIS, and the NOAA Atlantic Oceanographic and Meteorological Laboratory [14]. However, there have been very few cases of a RADARSAT-1 SAR image collected during the passage of a hurricane. This is because the RADARSAT-1 SAR image acquisition over the U.S. east coast has to be planned a few months in advance before each hurricane season (although some hurricane images are now being captured by last-minute reprogramming of satellite acquisitions for Hurricane Watch). In addition, the planned passes may or may not be acquired, depending on the RADARSAT-1 operation priority. Therefore, we can only randomly schedule wide-area coverage of the U.S. east coast region with the RADARSAT-1 ScanSAR Wide mode before /02$ IEEE

2 2132 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER 2002 wave spectra derived from the RADARSAT-1 SAR image on both sides of the Gulf Stream north wall. We extract 12 pairs of wave spectra along the Gulf Stream north wall from about 28 Nto32 N (about 400 km), and the wave refraction angles are measured. The two physical mechanisms that induce wave refraction are the wave shoaling effect and the major current effect. An analytical wave current interaction model is used to assess refraction-induced variations in wave direction for the straight current, i.e., the Gulf Stream. In addition, the wave shoaling effect is considered. From these two theoretical considerations, we derive the theoretical swell refraction angles when the waves cross the Gulf Stream north wall. We then compare the theoretical results with the SAR observations. The agreement is reasonably good. This paper is arranged as follows. In Section II, we describe the RADARSAT-1 SAR data and NOAA NDBC in situ wave measurement data. We then present the wave spectra derived from the SAR image and the validation of these derived spectra against those measured by three NDBC buoys off the Florida coast. The problem of resolving azimuth traveling ocean waves with the RADARSAT-1 SAR is also discussed. In Section III, we present the analytic wave current interaction model. The wave spectra on both sides of the Gulf Stream derived from the SAR image are also given in Section III. From these spectra, we calculate the wave refraction angle, and the local Gulf Stream orientation is measured directly from the SAR image. The comparisons are made between the SAR-derived wave refraction angles and the theoretical calculations. Conclusions and discussion are in Section IV. Fig. 1. Synoptic view of hurricane bonnie from GOES infrared and visible images. The SAR image has been superimposed on the lower left quartet of each GOES image. The GOES images and SAR image are taken about 3 min apart. each hurricane season. Fortunately, we captured Hurricane Bonnie on August From this SAR image, we have analyzed the signatures of atmospheric phenomena and the Gulf Stream patterns [11] in our previous research. The focus of this paper is to further examine this SAR image to study Hurricane Bonnie-generated oceanic long waves, swell, and refraction when the waves propagate from the Gulf Stream current to the continental shelf. We first extract wave spectra from three subscenes in the SAR image at three NOAA moored buoy locations, and we compare them with the NOAA National Data Buoy Center (NDBC) in situ buoy measurements. They agree remarkably well. We then further examine a series of II. DATA AND OCEAN SWELL SPECTRUM A. The RADARSAT-1 ScanSAR Image RADARSAT-1 is a Canadian polar orbiting satellite with an ascending equator crossing local time at 6:00 p.m. The SAR onboard the RADARSAT-1 is a C-band radar with horizontal horizontal polarization. The SAR image used in this study is a ScanSAR Wide B scene that has a swath width of 450 km. The image was processed at the Alaska SAR Facility (ASF) to a spatial resolution of 100 m with a pixel spacing of 50 m. The image was acquired at 23:18:26 UTC on August 25, 1998 and covers the southeast U.S. coast from Florida to South Carolina. The image center is at about 29.0 N 78.5 W. The image is taken only 42 min before the National Weather Service in Miami, FL issued an advisory on Hurricane Bonnie. According to National Hurricane Center s report, 1 at the SAR image acquisition time, Hurricane Bonnie was moving N NW at 7.2 m/s with maximum sustained winds of 51.4 m/s and a minimum central pressure of 958 mb. Fig. 1 shows the RADARSAT-1 SAR image superimposed on Geostationary Operational Environmental Satellites (GOES) infrared [Fig. 1(a)] and visible [Fig. 1(b)] images that were taken about 3 min earlier. The SAR image coverage is in the lower left quarter of the figure. The spiral cloud pattern on both GOES images in Fig. 1 is Hurricane Bonnie. The SAR image covers the area to the left of Hurricane Bonnie s eye. 1

3 LI et al.: OBSERVATION OF HURRICANE-GENERATED OCEAN SWELL REFRACTION 2133 Fig. 2. RADARSAT-1 ScanSAR wide B SAR image acquired during Hurricane Bonnie at 23:18:26 UTC on August 25, Copyright Canadian Space Agency The three yellow boxes represent the three NDBC buoy stations. The red and blue boxes represent a series of areas on both sides of the Gulf Stream where the SAR image spectra are computed.

4 2134 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER 2002 Fig. 3. Subimage from Fig. 1. and Fig. 2 showing the position of Hurricane Bonnie s front (red line), the Gulf Stream north wall (blue line), and the oceanic long waves (yellow line). The oceanic long wave crests change direction after they leave the Gulf Stream current. and are swell propagation angles before and after leaving the Gulf Stream north wall. The full RADARSAT-1 SAR image is shown in Fig. 2. The three yellow boxes represent three NOAA moored buoys. The dark and bright boundary represents the Gulf Stream north wall. It is well known that SAR can observe the Gulf Stream. This is because the Gulf Stream s warm water produces an unstable marine atmospheric boundary layer, which increases the Bragg spectral energy density, therefore increasing the radar backscatter [15]. On the SAR image, the brighter region represents the higher Bragg backscatter region, so that we can identify the Gulf Stream current position according to the brightness of the SAR image. The cells to the upper right corner of the SAR image are rain cell signatures associated with rainfall and downdrafts from Hurricane Bonnie [11]. The blue and red pairs of boxes represent the locations on both sides of the Gulf Stream north wall where we extracted wave spectra. Fig. 3 is a full-resolution subimage from the green box in Fig. 2. Fig. 3 is extracted at the Gulf Stream north wall. The Gulf Stream north wall (blue line) can be clearly seen from Fig. 3 as a boundary between dark and bright areas. The storm front is indicated with a red line. When we zoom into the SAR image as shown in Fig. 3, one can see that the wave crests (yellow lines) change orientation after the waves leave the Gulf Stream. The SAR wave spectra are generated using ASF s wave product algorithm [7], including a two-dimensional digital fast Fourier transform, spectra smoothing, and energy peak finding. To derive the wave spectra, we extracted 256-by-256-pixel subimages from the full-resolution RADARSAT-1 SAR image. The radar spectra are represented as contour plots. The wave propagation direction has an 180 ambiguity. The real wave propagation direction can be resolved by assuming that the wave propagates from the open ocean toward the coast. The

5 LI et al.: OBSERVATION OF HURRICANE-GENERATED OCEAN SWELL REFRACTION 2135 (a) (b) (c) Fig. 4. Image spectra derived from 256-by-256-pixel subimages at nondirectional buoy (a), (b), and (c) locations. The dominant wave propagation direction has a 180 ambiguity. wave spectra derived from the SAR image at three NDBC buoy locations are shown in Fig. 4. The dominant wavelengths are given in Table I. One can see that the wavelengths determined at the three buoy locations all exceed 200 m. This indicates that in our study region, the ocean swell dominates. Due to the RADARSAT-1 SAR ScanSAR Wide-mode spatial resolution, the SAR cannot resolve the small wavelength wind wave spectrum. Therefore, in this study, we only focus on the long ocean swells off Florida. The Hurricane Bonnie-generated wave spectra have also been measured using the National Aeronautics and Space Administration s Scanning Radar Altimeter flown aboard one of the NOAA-3D hurricane research aircraft as documented in [16] and [17]. These two earlier published studies focus on the Hurricane Bonnie-generated

6 2136 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER 2002 TABLE I DOMINANT WAVELENGTH DERIVED FROM SAR IMAGE SPECTRUM AND BUOY MEASUREMENTS wave spectrum spatial variation in open water 400 km east of Abaco Island on August 24 [16] and at the land fall in North Carolina on August 26 [17]. These study regions and dates are different from those of this research. C. Velocity Bunching for SAR Image Spectra and the Significant Wave Height at Buoy Locations As we mentioned in the introduction and in the study by [7], the key to derive an accurate SAR wave spectra is that the SAR should be operating linearly over the ocean. Whether the SAR can image oceanic waves accurately depends upon the velocity-bunching mechanism [18] [20]. For waves with relatively low significant wave height, the velocity-bunching mechanism is a linear process. The critical velocity-bunching cutoff significant wave height can be represented as [20] (2) B. NDBC Buoy Data Three NOAA/NDBC buoys are located within the SAR image coverage. The buoy locations are shown in Fig. 2 as yellow boxes. These buoys report nondirectional spectral wave measurements (i.e., wave energies with their associated frequencies or periods). Buoy and are located in shallow water with water depths of 42 and 34.7 m, respectively. Buoy is moored in deep water at a water depth of m. The spectral wave density as a function of wave period is shown in Fig. 5(a) (41 008), Fig. 5(b) (41 009), and Fig. 5(c) (41 010). The dominant wave periods are 14.29, 12.50, and s at buoy , , and locations, respectively. The highest energy levels of the wave spectra are 1.9 m s, 6.8 m s, and 16.0 m s. At buoy , the highest energy level of the wave spectra is an order of magnitude lower than that measured at The wind-generated high-frequency waves that have peak band between 6 and 8 s also contribute significantly to the total wave spectra at At and 41010, the wind-generated waves are very weak. The dominant waves at these two buoys are long ocean swells. Using the surface gravity wave dispersion relation, we can calculate the dominant wavelengths at these three buoy locations. The dispersion relation for surface water waves at finite depth is where is wave frequency; is the wave number ( ); and is the water depth. Knowing the dominant wave period ( ) from the buoy measurements, we can calculate the dominant wavelength. The calculated dominant ocean swell wavelengths are 233.4, 208.1, and m at buoy , , and , respectively. Comparing the values in Table I, we found that the dominant wavelengths calculated using buoy data agree very well with those calculated from the SAR image spectrum. The relative errors are less than 10% for buoys and At buoy , both ocean swell and the local wind wave (peak band between 6 and 8 s) contribute to the wave spectrum. Therefore, there is a relative large difference at this location. We may then conclude that the SAR image spectrum, in this very long wave case, can be used to represent the real ocean wave spectrum. (1) where is the significant wave height defined as the average of the highest one-third of wave heights; is the satellite velocity (for RADARSAT-1, 7.48 km/s); is the wavelength; is the satellite orbit height (for RADARSAT-1, 798 km); is the acceleration of gravity (9.8 m/s ); is the satellite angle of incidence (for RADARSAT-1 ScanSAR Wide mode, is 20 to 46 ); is the angle between and wave number (for azimuth direction traveling waves ; for range direction traveling waves ). When imaging the ocean area, the SAR operates linearly when the actual significant wave height is less than the critical significant wave height value calculated using flight platform parameters. Otherwise, the nonlinear modulation transfer function between the SAR spectrum and the ocean wave spectrum should be applied. Fig. 6 illustrates the cutoff significant wave height as a function of satellite angle of incidence and wave-traveling azimuth angle with respect to the satellite flight direction. As increases (higher angles of incidence) and decreases (from range to azimuth), the cutoff decreases. For waves traveling in the range direction, the cutoff is large, so the velocity bunching is not critical. But for waves traveling in the azimuth direction, the cutoff becomes smaller, and the wave spectra derived from the SAR image may have severe nonlinear distortion when compared with the actual wave spectra. This is the so-called azimuth falloff. Considering the ocean wave spectrum in Rayleigh distribution, we can convert the wave energy spectrum to significant wave height by using the formula [21], [22] where is the total energy of the whole energy spectrum In (4), is the energy density spectrum measured by the buoy, and is the wave frequency. Therefore, we can integrate the energy curves measured by the three NDBC buoys in Fig. 5(a) (c) to get the total wave energy at each location. We then apply (4) to get the ocean swell significant wave height at the time when the SAR image was taken. The values at the three buoy locations are given in Table II. (3) (4)

7 LI et al.: OBSERVATION OF HURRICANE-GENERATED OCEAN SWELL REFRACTION 2137 (a) (b) (c) Fig. 5. In situ wave spectra measured by NDBC buoys, (a), (b), and (c). This RADRARSAT scene is an ascending pass, with the orbital plane oriented 12.5 to the west of north at this latitude. At the Gulf Stream north wall, the RADARSAT SAR incidence angle is about 30 for this pass. For buoy , the wave direc-

8 2138 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER 2002 tion is about 45 to the northwest [Fig. 5(a)]. Therefore, at this buoy location, the angle in (2) is about By examining Fig. 6, the corresponding cutoff is about 2.4 m, which is higher than the measured (1.74 m) shown in Table II. The wave direction for buoy is about 3 to the northwest [Fig. 5(b)], so is about 75. The cutoff at the location of buoy is about 6 m [Fig. 6]. For buoy , the wave direction is about 12 to the southwest. This is almost perpendicular to the RADARSAT pass, and thus the wave propagation direction is in the range direction at this location. The calculated cutoff is about 9.4 m for the SAR incidence angle of 40. All the calculated cutoff values at the three buoy locations are much higher than the in situ values in Table II. We can then use the SAR-image-derived spectra to represent hurricane-induced ocean swell spectra. In other words, for this set of RADARSAT-1 SAR data, the velocity-bunching mechanism is a linear process. Therefore, the SAR wave spectra should not be appreciably affected by the azimuth falloff, and SAR can be considered as providing reliable measurements of ocean swell. However, it is impossible to derive an accurate short wind wave spectrum using the RADATSAT-1 SAR ScanSAR Wide-mode data due to the relatively low SAR sensor spatial resolution. III. WAVE REFRACTION ANGLE COMPARSIONS BETWEEN SAR OBSERVATIONS AND WAVE REFRACTION MODEL RESULTS A. SAR Observations of Wave Spectra on Both Sides of the Gulf Stream We extracted 12 full-resolution 256-by-256-pixel SAR subimages within the Gulf Stream as indicated by the red boxes in Fig. 2. The SAR wave spectra were computed using the method described in Section II. The dominant wave propagation directions at these locations can be determined from the wave spectra. We then locate the Gulf Stream north wall position and follow its line orientation to measure the Gulf Stream local direction. The wave angle of incidence can then be computed. At each Gulf Stream north wall location next to each red box, we draw a cross line that is perpendicular to the Gulf Stream local direction. Given the wave angle of incidence and the cross line, we can locate the corresponding blue box location where we follow the incoming waves. The SAR-observed wave characteristics are given in Table III. The differences between the wave propagation angles measured in the red and blue boxes show the difference between the wave angle of incidence and angle of refraction. B. Wave Refraction Angle Calculated by Wave Current Interaction Model In the following analysis, we analyze the wave refraction by tracing the wave ray direction change. The wave rays are the paths traced out by points which move with the group velocity [12], [23]. The rays are, thus, orthogonal to the wave crests. The wave refraction by the one-dimensional ocean shear current for monochromatic waves can be expressed similarly to Snell s law as [10], [12], [24] (5) Fig. 6. This velocity-bunching diagram shows the cutoff wavelengths of oceanic waves at different SAR azimuth viewing angles. SAR can image only the oceanic waves with a wavelength longer than the cutoff wavelength. The diagram was plotted with RADARSAT-1 parameters. = 250 m. where and are the wave angles of incidence and refraction relative to the normal to the Gulf Stream current; is the current velocity; and is the phase velocity of oceanic long waves. In this case, the wave phase velocity calculated from the dispersion relation is about 20 m/s. Since we do not have coincident current measurements to determine, we use the typical Gulf Stream north wall velocity given in the literature. The detailed Gulf Stream horizontal velocity distribution across several Gulf Stream sections has been given in [25] and [26] in the 1950s, and those results are summarized in [27], [28]. Collectively, [25] and [26] found that there was 1) a sharply peaked distribution of velocity across the Gulf Stream with peak velocity near the edge of the north wall and 2) an asymmetrical horizontal shear on either side of the current velocity maximum. The mean current velocity is about 1 m/s in the middle of the Gulf Stream. The Gulf Stream velocity near the north wall is about 2.1 m/s at the surface and about 1.9 m/s at 100-m depth. The velocity drops from maximum near the north wall to negligible in a very short distance to the west of the Gulf Stream north wall. Therefore, in this analysis, we can assume that the current profile across the Gulf Stream north wall to the continental shelf is a step function. In this study, we focus on surface swells; therefore, we take the Gulf Stream velocity as the average current velocity between the surface and 100-m depth. The representative value of at the Gulf Stream north wall is chosen as 2 m/s. Using the incidence angle derived from the SAR data in the red boxes inside the Gulf Stream as input, we can then calcu-

9 LI et al.: OBSERVATION OF HURRICANE-GENERATED OCEAN SWELL REFRACTION 2139 Fig. 7. SAR image spectra derived at the red box locations within the Gulf Stream in Fig. 2. late the refraction angle. The results are given in Table III. In Table III, and are the difference between the refraction and incidence angles observed by SAR and calculated by the wave current model on both sides of the Gulf Stream. The and values agree reasonably well for all the boxes except boxes 4 and 7. The agreements at larger wave incidence angles (boxes 1 3 and 12) are even better. At locations of boxes 5, 8, 9, and 11, the swell incidence angle is almost zero. Under this normal incidence condition, the wave does not change direction greatly as seen in Table III. The disagreement between and values in the box 4 locations suggest that the wave refraction here is not induced by the Gulf Stream. In the box 7 areas, the observed SAR spectra show complex patterns. There is no well-defined wave energy peak. The complexity of the wave spectra leads to an inaccurate determination of the dominant wave propagation direction. IV. DISCUSSION AND CONCLUSION From this study, we see that ocean swells generated by Hurricane Bonnie have wavelengths over 200 m when they propagate to the Gulf Stream north wall. A velocity-bunching analysis for the RADARSAT-1 SAR confirms that the wave spectra derived from the RADARSAT-1 SAR data under the conditions of Hurricane Bonnie are reliable. The SAR-derived

10 2140 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 10, OCTOBER 2002 Fig. 8. Same as Fig. 7 except at the blue box locations outside the Gulf Stream. TABLE II SIGNIFICANT WAVE HEIGHT (H )MEASURED BY THREE NOAA NDBC BUOYS OFF THE FLORIDA COAST wavelengths are compared with in situ NDBC buoy measurements, and they agree remarkably well. From Table III, we can see that the wave refraction angles observed by SAR on both sides of the Gulf Stream are in good agreement with the theoretical calculations using a simple wave current interaction model. Since the swell propagates mainly toward the coast, the angles of incidence when they leave the Gulf Stream are relatively small. Thus, the difference angle between the incidence and refraction angles is small. Even with such small angle changes, the RADARSAT-1 SAR successfully traces these variations along the Gulf Stream north wall for over 400 km. This demonstrates the advantage of the RADARSAT-1 wide swath SAR for providing ocean swell characteristic spatial variations over large areas. In this study, we did not consider the curvature of the Gulf Stream boundary and the profile of Gulf Stream current speed as discussed by other researchers [10], [12], because we have mainly focused on the local refraction angle change. It is not the purpose of this paper to trace the wave propagation from its source to the coast and the

11 LI et al.: OBSERVATION OF HURRICANE-GENERATED OCEAN SWELL REFRACTION 2141 TABLE III DOMINANT WAVE ANGLES ( AND )WITH RESPECT TO THE EAST DERIVED FROM SAR WAVE SPECTRA ON BOTH SIDES OF THE GULF STREAM NORTH WALL. IS THE LOCAL GULF STREAM ORIENTATION ANGLE WITH RESPECT TO THE EAST. IS THE ANGLE DERIVED FROM SAR DATAINTHERED BOXES IN FIG. 2INSIDE THE GULF STREAM. IS THE REFRACTION ANGLE DERIVED FROM SAR DATA IN THE BLUE BOXES OUTSIDE THE GULF STREAM. IS THE SAR-OBSERVED WAVE LOCAL INCIDENCE ANGLE = IS THE WAVE ANGLE DIRECTION CHANGE ON BOTH SIDES OF THE GULF STREAM NORTH WALL 1 = 0.IF 1 < 0, THE WAVES TURN TO THE RIGHT AFTER CROSSING THE GULF STREAM NORTH WALL. 1 = 0 ; 1 IS THE DIRECTION CHANGE BETWEEN THE REFRACTION ANGLE AND THE INCIDENCE ANGLE. AND ARE INCIDENCE AND REFRACTION ANGLES DEFINED IN THE ONE-DIMENSIONAL WAVE CURRENT MODEL. TO CALCULATE THE WAVE REFRACTION ANGLE USING THIS MODEL, THE SAR-MEASURED IS USED AS THE INCIDENCE ANGLE, AND THE GULF STREAM CURRENT VELOCITY IS TAKEN AS 2.0 m/s Most of the SAR wave spectra show a well-defined peak energy and propagation direction. We do not observe swell reflection at the Gulf Stream north wall. Swell refraction is the dominant mechanism modifying the propagation direction. Given the RADARSAT-1 orbit path orientation along the U.S. east coast, most of the hurricane- or severe-storm-generated and shoreward-propagating ocean swells are in the range direction. Therefore, RADARSAT-1 SAR can be used as a good tool to observe large-scale and high spatial resolution wave characteristics for the U.S. east coast waters during hurricane season. Most of the NDBC in situ moored buoys along the U.S. east coast are nondirectional buoys; therefore, SAR, among other uses, can provide additional wave propagation information to validate wave-predication models. ACKNOWLEDGMENT The RADARSAT-1 SAR data was obtained under the NASA RADARSAT ADRO-2 Program (RADARSAT ) and processed by the Alaska SAR Facility. oceanic wave wavelength change. Changes in the local bottom topography will also induce wave refraction. This is because the wave phase velocity depends on the water depth. We rewrite (1), so the wave phase velocity can be expressed as As one can see, the water wave velocity will change when the water depth changes. Therefore, when the wave crests are not parallel to the local isobaths, the portion of the wave on the deeper ocean side of the Gulf Stream will run faster than the portion on the shallower ocean side. Eventually, the wave crests turn to be parallel to the bathymetry. In this study, we are examining the ocean swell propagation in the deep ocean outside the continental shelf. The wavelengths are much smaller than the water depth, which suggests that the wave phase velocity is not sensitive to the small variation in bathymetry. 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Englewood Cliffs, NJ: Prentice-Hall, Xiaofeng Li (M 01) received the B.S. degree in optical engineering from ZheJiang University, Hangzhou, China, in He received the M.S. degree from the First Institute of Oceanography (FIO), State Oceanic Administration of China, Qindao, China in physical oceanography and remote sensing, in He received the Ph.D. degree in physical oceanography from North Carolina State University, Raleigh, in He currently works at the National Oceanic and Atmospheric Administration (NOAA) National Environmental Satellite, Data, and Information Service (NESDIS) Office of Research and Applications, Washington, DC. His research interests include remote sensing studies of ocean surface waves and internal waves, marine atmospheric boundary layer processes, sea surface temperature algorithms development and validation from both polar orbiting and geostationary satellites, infrared measurements, coastal oceanography, fluid dynamics, marine fisheries, and remote sensing physics. William G. Pichel (M 94) received the B.S. degree in physics from the University of Florida, Gainesville, in 1969, and the M.S. degree in physical oceanography from the University of Hawaii, Honolulu, in He is currently Research Scientist with the National Oceanic and Atmospheric Administration (NOAA) Oceanic Research and Applications Division, Office of Research and Applications, Washington, DC. He is also serving currently as Program Manager of the NOAA National Environmental Satellite, Data, and Information Service (NESDIS) Ocean Remote Sensing Program. He has been with the NESDIS/NOAA since His assignments have included Product Area Leader for Oceanographic Products and Chief of the Product Systems Branch. His research interests include development of ocean and hydrologic applications of synthetic aperture radar data and the improvement of sea surface temperatures from satellite infrared measurements. Mr. Pichel has received four Department of Commerce Bronze Medals for his contributions to the development and demonstration of new satellite ocean remote sensing applications. Mingxia He is the director of Ocean Remote Sensing Institute (ORSI) of Ocean University of Qingdao, Qindao, China. She is also the director of Ocean Remote Sensing Laboratory, State Education Commission of China, Beijing, China. Her research interest is in ocean remote sensing. Sunny Y. Wu received the B.S. degree in physical oceanography from Ocean University of Qingdao, Qindao, China in She received the Ph.D degree in the same field from the Center for Coastal Physical Oceanography (CCPO), Old Dominion University, Norfolk, Virginia, in She is currently a Senior Analyst with the Caelum Research Corporation, NASA Goddard Space Flight Center Laboratory of Hydrospheric Processes, Greenbelt, MD. For the past few years, her primary focus has been on the mesoscale oceanic processes/features (e.g., marginal ice zone, oceanic fronts, internal waves, etc.) using satellite remote sensing data (especially that of synthetic aperture radar) and in situ measurements. Karen S. Friedman received the B.S. degree in geophysics from the University of California, Los Angeles, in 1995, and the M.S. degree in environmental engineering from Massachusetts Institute of Technology, Cambridge, in She is currently a Research Scientist with Caelum Research Corporation, National Oceanic and Atmospheric Administration, National Environmental Satellite, Data, and Information Service, Office of Research and Applications, Washington, DC. She works primarily with SAR applications. Pablo Clemente-Colón received the B.S. degree in physics from the University of Puerto Rico, Mayaguez, Puerto Rico, in 1977, the M.S. degree in oceanography from Texas A&M University, College Station, in 1980, and the Ph.D. degree in marine studies from the University of Delaware, Newark, in He is currently an Oceanographer with the National Oceanic and Atmospheric Administration (NOAA) National Environmental Satellite, Data, and Information Service (NESDIS), Office of Research and Applications, Washington, DC. He provides remote sensing expertise to NOAA/NESDIS in areas of satellite oceanography that include synthetic aperture radar applications, upper ocean dynamics, sea surface temperature, ocean color, remote sensing fisheries, marine boundary processes, and multisensor data fusion. Chaofang Zhao obtained the B.S. and M.S. degrees both in marine physics from Ocean University of Qingdao, Qindao, China, in 1985 and 1988, respectively, and the Ph.D. degree in ocean remote sensing from Tokai University of Japan, Tokyo, Japan, in He is currently pursuing the Ph.D. degree in air sea interaction and gas exchange at the Center for Environmental Remote Sensing (CEReS), Chiba University, Kashiwa, Japan. He currently works in the Ocean Remote Sensing Institute (ORSI), Ocean University of Qingdao. His research interests are mainly in ocean remote sensing, air sea interaction, carbon flux estimation, microwave remote sensing, and image processing. Mr. Zhao is a member of the Scientific Organizing Committee of Pacific Ocean Remote Sensing Conference Society (PORSEC) and a member of the Japan Advance Marine Science and Technology.