Mechanisms of low-grazing-angle scattering

Transcription

1 Radio Science, Volume 36, Number 5, Pages , September/October 2001 Mechanisms of low-grazing-angle scattering from spilling breaker water waves Shiou-Jyh Ja and James C. West School of Electrical and Computer Engineering, Stillwater, Oklahoma, USA Haibing Qiao and James H. Duncan Department of Mechanical Engineering, University of Maryland, College Park, Maryland, USA Abstract. The low-grazing-angle electromagnetic scattering from spilling breaker water waves has been examined using a numerical approach. A moment-method-based electromagnetic technique was used to find the instantaneous scattering from the crests of breakers generated mechanically in a wave tank in the absence of wind. A high-speed imaging system carried on an instrument carriage traveling at the phase velocity of the breakers provided continuous measurements of the temporal evolution of the crest shape, in turn allowing a continuous calculation of the microwave backscatter from the crest. As the wave steepens and a bulge forms on the forward face of the crest, horizontal-to-vertical polarization backscattering ratios (HH/VV) as high as 0 db are observed. Greatly reduced ratios are observed after breaking when no steep features remain on the wave. A time-dependent Fourier analysis identifies "fast" scattering whose Doppler shifts are nearly equal to or greater than the phase velocity of the breaker, and "slow" scattering whose Doppler shifts are consistent with the orbital motion of the breaker. Comparison of the Doppler shifts with the measured wave profileshows that the fast scattering identified is associated with very steep surface features that give specular (or nearly specular) reflection points on the surface, but the magnitude and HH/VV ratio of the response to a specific steep feature depends upon its electromagnetic size, thus giving a frequency dependence. The slow scattering identified (in the absence of wind) is correlated with the "turbulent scar" that remains after breaking. 1. Introduction polarized (VV) backscatter appears at a lower Doppler Recent experimental studies of the low-grazing-angle frequency than that of the horizontally polarized (HH) (LGA) microwave scattering from the sea surface have backscatter. The VV spectral peak appears at approxbeen characterized by the "Doppler splitting" effect [Lee imately the Doppler shift expected for scattering from et al., 1995; Smith et al., 1996; Plant, 1997; Rino et al., freely propagating small-scale waves on the surface, while 1997]. When looking upwind at large and moderate the HH spectral peak is closer to the frequency associgrazing angles (small to moderate incidence angles), the ated with the phase velocity of the larger-scale dominant waves. The higher Doppler-shifted energy has some- Doppler spectra of the like-polarized backscattering are approximately the same at both vertical and horizontal times been called "fast" scattering (associated with "fast" incident polarization. As the grazing angle is decreased surface scatterers) while the lower shifted energy is reto approximately 10 ø, the spectral peak of the vertically ferred to as "slow" scattering. The Doppler splitting phenomenon has been observed at S band [Lee et al., 1995], X band [Smith et al., 1996; Rino et al., 1997], and Ku Now at Nomadics, Inc., Stillwater, Oklahoma, USA. band [Plant, 1997]. When looking downwind, Doppler Copyright 2001 by the American Geophysical Union. Paper number 2000RS /01/2000RS splitting is not observed, and the scattering appears at the slow frequency at both polarizations [Smith et al., 1996]. Different theories have been introduced to explain the Doppler splitting phenomenon. It is usually agreed that

2 982 JA ET AL.: MECHANISMS OF LGA SCATFERING FROM SPILLING BREAKERS the slow scattering results from Bragg-resonant interac- served and found to correlate with jetting in the vigortions between the electromagnetic waves and the elec- ous breaking. After the breaking, lower shifts were obtromagnetically small-scale roughness that rides upon the served, thought to be due to Bragg scattering from the larger waves. Different mechanisms have been proposed turbulent "scar" that remains after breaking that is carried to explain the fast scattering. The experimental stud- by the orbital motion of the wave. In a subsequent paies have suggested that fast scattering is strongly corre- per, Lee et al. [ 1999] examined the scattering from windlated with wave breaking. Lee et al. [1995] suggested roughened wave tank surfaces both with and without a that the fast scattering is due to direct reflection from mechanically generated wave. They found polarization "specular facets" associated with steepening and breaking ratios that are consistent with bound-bragg fast scattering waves. The waves produce features that have faces ap- both with no mechanically generated wave at low wind proximately perpendicular to the radar look direction and speeds and with a generated low-energy breaker simultaare traveling at the wave phase velocity. The speculare- neous with a 9 m/s wind. At higher wind speeds and with flection is thoughto be strong enough to overwhelm the more energetic breaking they found that the fast polarizarelatively weak Bragg-resonant slow scatter at horizontal tion ratios are not consistent with the Bragg mechanism. polarization but is small compared to the much stronger Most recently, Lamont-Smith [2000] presented the mea- Bragg scattering at vertical polarization. Fast scattering sured Doppler spectra of scattering from wind-roughened thus dominates HH backscatter while slow scattering is wave tank water at frequencies ranging from 3 GHz to predominant VV. The asymmetry of the waves prevents 94 GHz. He suggested that the frequency dependence of specular points from appearing when looking downwind, the Doppler speed at which the strongest scattering apeliminating the fast scattering. pears indicates that it is at least partially due to Bragg resonance. An alternativexplanation of Doppler splitting was introduced by Plant [ 1997]. He suggested that the fast scat- In this paper we examine the LGA scattering from tering is due to a Bragg-resonant interaction with small- spilling breaker waves mechanically generated in a wave scale waves that are bound to the front face of steep, tank that break much less energetically than the plunglarge-amplitude waves. The bound waves are tilted to- ing breakers considered by Lee et al. [1998] and Fuchs ward the radar when looking upwind, decreasing the local et al. [1999]. Rather than experimentally measuring the incidence angle of the radar energy at that point and giv- scattering, we instead rely upon numerical calculation of ing a much stronger HH backscatter than that from the un- the scattering from measured surface profiles. An optibound, less strongly tilted background small-scale rough- cal measurement system traveling at the phase velocity ness. Since the resonant waves are bound to the large- of the breakers was used to provide a continuous twoscale wave, this gives a fast Doppler response. On the dimensional representation of the wave surface profile other hand, the magnitude of VV Bragg-resonant scatter- in the vicinity of the crest throughouthe breaking proing is much less dependent upon the local incidence an- cess. A numerical electromagnetic technique based on gle, so the tilting does not raise the fast scattering above the moment method was then used to find the instantathe background slow scattering. When looking down- neous scattering from the wave. The continuous temporal wind, the bound waves are tilted away from the radar, surface representation allows the calculation of the time raising the local incidence angle, or, in fact, may be com- history of both the amplitude and the Doppler shift of pletely shadowed from the radar by the long wave crest the backscatter from the wave under various illumination at low grazing angle, greatly reducing or eliminating the conditions. The Doppler history is used to identify the fast scatter. dominant scattering features at both HH and VV polar- Laboratory studies to identify the scattering mecha- izations throughouthe scattering process. Two different nisms responsible for the fast scatterers were performed wave profile histories generated under slightly different by Lee et al. [1998] and Fuchs et al. [ 1999]. In both cases, conditions are treated, and both up-wave and down-wave energetic breaking water waves that were mechanically scattering is considered. By limiting the surface descripgenerated in a wave tank in the absence of wind were tion to the crest region, multipath reflection from the front illuminated by radars at low grazing angles. Range gat- wave that leads to very large "superevents" (where the ing was used to isolate scattering features in both cases. horizontally polarized backscatter exceeds that at vertical The center operating frequencies were 9 GHz and 6 GHz polarization by 10 db or more) is avoided. The mechain the Lee et al. and Fuchs et al. studies, respectively. nisms of the scattering from the isolated crest alone are In both cases, Doppler shifts exceeding that expected therefore revealed. This analysis is limited to frequenfrom the phase velocity of the breaking wave were obcies of 10 GHz and above so that the measured surface

3 JA ET AL.: MECHANISMS OF LGA SCATrERING FROM SPILLING BREAKERS 983 lengths are at least 4A, where A is the electromagnetic 1.E wavelength. l Surface Profiles 0.B The crest profile histories of two spilling breakers are treated in this paper. The experimental techniques used to generate and measure these waves are discussed briefly below; a more detailed description is given by Duncan et al. [1999]. The waves were generated mechanically (without wind) by a vertically oscillating wedge in a E 0.0 I t I i I ' I 14.8 m long, 1.22 m wide, 1 m deep wave tank. The O.B 1.0 wave maker was set to produce a packet of ~ 10 smallamplitude waves that focused to a single large-amplitude A/Ao wave with sufficient energy to form a weak spilling breaker Figure 1. Dimensionless surface tension r/re versus dimenat a specified location in the tank. An instrument carriage sionlessurface area A/Ao from in situ measurements in the wave tank just before measuring the crest profile histories of the rides on tracks above the tank, and its motion was adclean wave (solid line) and the surfactant wave (dashed line) justed to follow the crest of the breaking wave. A 1 mm thick light sheet generated by a 5 W argon ion laser was projecte down from the carriage along the center plane of the tank onto the breaking wave crest. The water was mixed with Fluorescein dye. A high-speed 16 mm movie camera was also mounted on the instrument carriage and set to photograph the intersection of the light sheet and the breaking wave crest at a frame rate of 472 Hz. The camera viewed the wave from the side with a viewing angle of ~5 ø from the horizontal. Each frame of the resulting movie was digitized, and image processing techniques described by Duncan et al. [1999] were used to extract the wave crest profiles. This measurement technique yields the time history of a streamwise cut of the wave profile. Thus all electromagnetic calculations are limited to two-dimensions, and the surfaces are assumed to be uniform in one dimension ("one-dimensionally rough" surfaces are treated). Two breaking waves were studied. For both waves the average frequency of the wave packet was 1.42 Hz, and the carriage speed used to follow the wave crests '/ 'c(where r is the surface tension and re is the surface tension of clean water) versus A/Ao (where A is the area in the trough surrounding the Whilhelmy plate at any time and Ao is the initial area in the trough). Note that the surface tension is equal to that of clean water from A/Ao down to ~0.2. For this wave the crest profile history data used herein are identical to those reported in Figure 14 of Duncan et al. [1999]. This wave is called the "clean wave" in the following. The second wave differs from the clean wave in only two respects: The wave maker amplitude factor is a little larger (A/Ao = ), and liquid kitchen detergent was added to the water. The curve of surface tension versus area for this case is also given in Figure 1. As can be seen from the figure, the surfactant agents in the detergent have lowered the ambient surface tension (A = Ao) to ~0.Src, and at A Ao the surface tension has dropped to 0.37rc. This wave is called the "surfactant wave" in the was m/s. For the first wave the wavemaker am- following. plitude parameter was A o [see Duncan et al., 1999], and the water-surface-skimming system and surface cleaning procedures described by Duncan et al. [1999] were used. A limited characterization of the dynamical properties of the water surface was obtained with a Whilhelmy plate, which is used to measure surface tension, in combination with an in situ Langmuir trough, which is used to increase the surface concentration of The crest profile history of the clean wave is shown in Figure 2a. This figure was formed by stacking 329 individual profiles vertically, giving increasing time in the vertical axis. Each profile is referred to by the time at the intersection of the profile with the vertical axis. Some individual profiles are plotted in Figure 2b. The wave is propagating from right to left; however, since the camera was moving at the wave phase velocity, the crest remains surfactants around the Whilhelmy plate by compressing at the same e location in the plot. A surface feature shiftthe local water surface. The data from this measurement, which was taken just before measuring the wave profile history of the first wave, are given in Figure 1 on a plot of ing toward the left (upstream) or right (downstream) in Figure 2a with increasing time indicates that it is moving faster or slower than the wave crest, respectively. For ex-

4 984 JA ET AL.: MECHANISMS OF LGA SCATIERING FROM SPILLING BREAKERS Toe Capillary waves \ t Bulge '\ Maximum /" elevation Wave propagation Figure 3. Mean water level Nomenclature for crest profile features during the formation of a breaking wave in clean water. a) b) x (mm) x (mm) Figure 2. "Clean" spilling breaker. (a) Complete time history. (b) Specific profiles. ample, there is a steep feature at x = 40 mm at 400 ms that is moving faster than the wave crest, and there are other slow features that are left behind after 350 ms. The measured surface profiles are 117 mm in length, which is sufficient to give a clear view of the temporal evolution of the crest. The complete data set lasts 697 ms. The initial crest height is 44 mm above the mean water level, and the maximum height reaches 53 mm at 190 ms. A schematic giving the nomenclature for the various features on the wave profile is given in Figure 3. As can be seen in the profile history, a bulge begins to form on the forward face of the crest at a time of at 210 ms. Capillary waves of approximately 5 mm wavelength are formed just below the "toe" of the bulge from 210 ms to 310 ms. At 370 ms the bulge collapses, and the water surface downstream of the toe becomes rough (the "scar" referred to by Fuchs et at. [1999]), indicating that the underlying flow has become turbulent. The toe and some features around it move faster than the wave phase velocity. The turbulent eddies, which are generated near the toe, create surface ripples which can be seen in the surface profile history. These eddies are fixed to the underlying fluid; thus they and their associated ripples are left behind the crest as it propagates. The time history of the crest profile of the surfactant wave is shown in Figure 4a. Some individual profiles are again plotted in Figure 4b. The total time of this data set is 803 ms. The surfactant affects the flow throughout the breaking process. The crest height starts at 39 mm and reaches a maximum of 54 mm at 300 ms. The bulge formation begins at 310 ms. No parasitic capillaries form in front of the toe. At ",380 ms a jet forms on the bulge near the toe. This jet impacts with the smooth water surface

5 ---.. Q) E i= JA ET AL.: MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS 985 / ahead of the bulge at ms. After the initial jet impact the features on the front face appear to be of larger amplitude than those in the clean wave data set. Also, additional small overturning events occur after the initial overturning, one at 570 ms and another at 740 ms. The last overturning is weaker than the previous two. At ",510 ms a feature that moves at the phase velocity of the long wave forms just downstream of the toe. This feature ) eventually causes the second overturning at 570 ms. The toe can be seen surging forward and back two and one half times during the breaking process with maximum upstream excursions at ms and 640 ms. Ripples are continuously shed from the crest during the breaking process. a) E.s >- b) o x (mm) r r ::::-:=== _/' _ m9/..// r/- - "/ - -'-'--": " ' -../ //_._-- ---_ ? - r / ) r\.../ r // '--" 30 _,) /-. / ,---.. 'o, r JDS-// // ) ,. / ' O / r / 81 ms-/ x (mm) Figure 4. "Surfactant" spilling breaker. (a) Complete time history. (b) Specific profiles. 3. Electromagnetic Calculation The backscattering from the individual surface profiles was found using a numerical electromagnetic technique based on the moment method (MM) and extended using the geometrical theory of diffraction (GTD) that was first introduced by Burnside et al. [1975] and then extended to finite conductivity, rough surfaces by West et al. [1998]. A complete description of the approach is given by West et al., so only a brief overview is given here. The hybrid MM-GTD approach requires that the surface profile be extended to infinity to eliminate the artificial edges introduced at the edge of the measurement region. An example surface is shown in Figure 5. The solid line shows the surface detected from the video image, while the dashed lines are the extensions. The sections from points A to C and from points B to D have fixed radii of curvature of 2A and so depend upon the electromagnetic frequency being modeled. The sections of surface beyond points C and D are planar and extend to infinity at 30 to horizontal. Use of larger radii for the connecting section or extension tilt angles of greater than 30 had no signifi- E.s , -- ori inal surface Wit extensions -10 t-, " 2'04 -:::-----'- -20 o x (mm) Figure 5. Example of surface extensions used with MM-GTD numerical technique. Points C and D are the diffraction points, and the GTD regions begin one-half electromagnetic wavelength from the diffraction points.

6 986 JA ET AL.: MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS -10 vv HH õ -30 : -so I '"' "'... ' Figure 6. The 10 GHz backscattering from cle wave looking up wave at 10 ø grazing. (All crossections are decibels relative to lm.) cant effects on the results. The points on the planar extensions are shadowed from the remainder of the surface, so the electromagnetic field in the vicinity of the exten- sion consists entirely of a field diffracted from point C or D, plus the geometrical optics field (incident plus reflected fields on unshadowed extensions). This allows the unknown surface current on an extension a sufficient distance from the diffraction point to be described entirely by a single moment method basis function derived from GTD. Ordinary moment method pulse basis functions are used to discretize the current on other surface sections. The net result is that the unknown current on the infinitely extending surface is described using a finite number of basis functions. Uniform plane wave illumination may therefore be used at all incidence angles, avoiding inaccuracies that can be introduced through the use of an illumination weighting function. The finite conductivity of the surface is treated using impedance boundary conditions. The scattering medium was assumed to be seawater at room temperature, and the complex permittivitivy was found from Ulaby et al. [ 1986]. In this work we began the GTD region 0.53, from the diffraction point, and moment method basis functions of 0.053, in width were 60 ø4o... i... i i i i... "-, 2200' Figure 7. Doppler shift of 10 GHz backscattering from clean wave looking up wave at 10 ø grazing (a) VV polarization normalized to 15.7 db. (b) HH polarization normalized to 11.5 rib.

7 ß. JA ET AL.' MECHANISMS OF LGA SCATI'ERING FROM SPILLING BREAKERS 987 ) , !... ;... i!...!!... i... i... : b) db : J! -.i.. "!.' " , / :,' " ' '... " '" Figure 7. (continued) used. This is sufficiento provide accurate results at all but the lowest cross sections [West et al., 1998]. The numerical electromagnetic technique maintains the phase of the backscatter, allowing the calculation of the plied by p(t) - exp[j2kvctcos (0a)] to compensate for the camera motion during the measurement, where Vc is the camera velocity, k - 2rr/A is the electromagnetic wave number, and 0 a is the illumination grazing angle. Doppler shift of the backscatter. We found the time dependence of the Doppleresponse using the "short-time 4. Results Fourier transform" approach of Oppenheirn and $chafer [1989]. The response was divided into subwindows of All scattering results shown here were calculated with 106 ms duration (the response from 50 individual pro- a 10 ø illumination grazing angle (an 80 ø incidence angle). files) and weighted with a Hamming window within the Similaresults were obtained with grazing angles as low subwindow. A discrete Fourier transform of the subwin- as 2 ø. This weak dependence on grazing occurs because dow response gives a measurement of the Doppler spec- only the crest region itself is modeled, eliminating the trum at the time center of the subwindow. Adjacent sub- multipath effects that are very dependent upon grazing windows overlapping by 80% of their duration give a [Trizna, 1997]. smooth representation of the Doppler time history. There is a trade-off between time and Doppler frequency reso "Clean" Wave lution using this approach. The Hamming window gives a 3 db time resolution of approximately 40 ms and a corresponding Doppler 3 db resolution of ~ 18 Hz, which is sufficiento resolve the major scattering features. Note that the complex backscattered field must first be multi The 10 GHz up-wave look. Figure 6 shows the time dependence of the amplitude of the 10 GHz backscattering from the clean wave when looking up wave (corresponding to an upwind look in a wind-roughened sea). Since two-dimensional calculations were performed,

8 988 JA ET AL.: MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS Q) E i= x (mm) Figure 8. Dominant scattering features of clean wave. Numbers 1, 2, and 4 mark groups of two, two, and four arrows, respectively. the scattering cross section is given in decibels relative to I m (lologlo (1/A), or 15.2 db at 10 GHz, should be added to these cross sections to give units of decibels relative to 1 A that can be directly compared to the accuracy study by West et at. [1998]). Prior to 150 ms, the wave crest is quite round, and there is no distributed-surface roughness because of the absence of wind. The scattering cross sections are therefore quite low and may be affected by numerical errors in the MM-GTD approach, so the backscatter within this time interval is not further considered. After 150 ms the wave bulge begins to form, and the backscattering increases smoothly with time at both polarizations, peaking just after 300 ms in both cases. The HHNV polarization ratio is -4 db at the peak. At 370 ms the bulge collapses, shown by a rapid drop in the scattering at both polarizations. As turbulent ripples are shed from the crest the signal strength oscillates rapidly at both polarizations. However, HH polarization shows a strongly decreasing overall trend that is not matched at Vv. In fact, the peak VV backscattering achieved remains approximately constant throughout the response. The Doppler history of the backscattering in Figure 6 is shown in Figure 7. Each contour represents a change of 2 db (normalized to the peak response in Figures 7a and 7b), and the gray scale trails track the position and magnitude of the local maxima in the response. The VV response is shown in Figure 7a. Four distinct responses appear. The strongest occurs first and is centered at approximately at 300 ms and 64 Hz. This Doppler shift is slightly greater than that expected for a scatterer moving at the phase velocity of the large wave (62 Hz) and therefore represents fast scattering. Another, slightly weaker response is approximately 2 db lower magnitude than the first and is centered at 480 ms and 48 Hz. Two additional distinct, but weaker, responses appear, centered at 430 ms-72 Hz and 600 ms-40 Hz. The HH time-doppler response from the clean wave under the same illumination conditions appears in Figure 7b. The normalization level of Figure 7b is approximately 4 db below that Figure 7a. In this case a single strong response appears centered at 300 ms-64 Hz. The second and third strong responses identified at VV at 430 ms-72 Hz and 480 ms-48 Hz just barely register as relative maxima at HH but are more than 10 db below the initial peak response. Any HH response at 600 ms-40 Hz, corresponding to the fourth VV response, is too weak to appear in the figure and so is at least 14 db below the peak response. The Doppler shifts of the primary responses appearing in Figure 7 can be directly correlated to the velocities of prominent features that appear on the wave profile. Arrows have been added to the profile history to show the movement of features relative to the camera motion in Figure 8. The arrow set numbered 1 (the first two arrows) -10, , , ,,-----, vv -- HH :8. c: o.30 U Q) en 40 0> c:.50. en.60, " F 'f-,!! lfl'!i)l\i\{v 7 0 '--'---' ''---- -''--'-'----'--' ''-----' o Figure 9. The 10 GHz backscattering from clean wave looking down wave at 10 grazing.

9 JA ET AL.' MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS 989 follows the formation of the bulge on the crest prior to breaking and corresponds to the strong responses ranging from 200 ms to 350 ms in both polarizations. Arrow 3 shows a small, fast-moving steep feature behind the toe that gives the weak 72 Hz response centered at 430 ms. Four turbulent ripples moving slower than the wave phase velocity at approximately the same speed are marked by arrow set 4. Together these give the long-duration VV response centered at ~48 Hz that ranges from ~375 ms to 525 ms. Arrows 5 and 6 show features that are mov- ing much slower than the phase velocity. Arrow 6 corresponds to the 40 Hz response at 600 ms. Arrow 5 shows an even slower velocity than arrow 6. It is matched by a relative maximum in the VV time-doppler history at 560 ms-32 Hz that was not identified as a distinct re- sponse due to the finite resolution of the plot. Arrow set 2 shows two steep features that are moving slightly slower than the phase velocity of the wave that do not give distinct responses at 10 GHz. These will be further considered in section The 10 GHz down-wave look. The numerical calculations were repeated with the 10 GHz illumination when looking down wave-downwind at the clean wave at 10 ø grazing. The amplitude response is shown in Figure 9. The bulge is shadowed from the illumination in this case, so the scattering is initially quite small at both polarizations. The backscattering rises rapidly at 400 ms, well after the bulge has collapsed and the first turbulent ripple has moved to the back side of the wave and is illuminated. The scattering continues to increase more turbulent ripples are illuminated, with the average value leveling off at ~550 ms. The VV backscatter is at least 15 db above the HH level at all times. The corresponding Doppler response is shown in Figure 10. The Doppler shifts are negative since the wave is now moving away from the the radar look direction. The strongest response appears at Doppler shifts of about -30 Hz, centered at 570 ms at both polarizations. This is considerably lower than the shifts at the peak response when looking up wave. The initial responses have Doppler shifts of-45 Hz and-38 Hz at, o...! i... i...!....i ' ;i i... i ß Fibre ]6, Doppler shift of ]0 GHz backscattcfin from clean wave 1ooki do av at ]0 ø [razi. (a)

10 990 JA ET AL.: MECHANISMS OF LGA SCA3TERING FROM SPILLING BREAKERS 0 0>,_30 Max: db %0... '... ' ' J ' ' OO 650 b) ';::...;::!,F..? ;.t :( y -_ Figure 10. (continued) -2 VV and HH polarizations, respectively, which are also at frequencies considerably lower than the maximum shifts appearing the up-wave look The 20 GHz up-wave look. The calculations were repeated when looking upwave at 20 GHz. The ambeen doubled. The same distinct responses that appear in Figure 7 also appear at the the same times, but of course with double the Doppler shift. However, the relative magnitudes are quite different. Again the maximum response appears immediately before the initial wave breaking at plitude response is shown in Figure 11. The overall results are similar to the 10 GHz response in that the cross -10 VV ' section first increasesmoothly at both polarizations as HH... the crest steepens before breaking and the average scatteri i i i ß ing remains approximately constant at VV and decreases with increasing time at HH after the bulge collapses. A -30 primary difference between the two responses is that the HH cross section is equal to that at VV immediately before breaking (300 ms). Also, after breaking, the positions of the relative maxima and minima differ between the two frequencies. In particular, the null that appeared at 350 ms in the 10 GHz response does not appear at -40-5o GHz. The corresponding Doppler response of the 20 GHz backscattering is shown in Figure 12. Note that the 18 Hz Doppleresolution appears narrower in Figure 12 than it does in Figures 7 and 10 since the frequency scale has O Figure 11. The 20 GHz backscattering from clean wave looking up wave at 10 ø. I I

11 JA ET AL.: MECHANISMS OF LGA SCA'ITERING FROM SPILLING BREAKERS 991 c 120 '" c igure 12, Doppler shift of 20 GHz backscattering from clean wave looking up wave at 10 ø grazing. (a) VV polarization normalized to 15.6 rib. (b) HH polarization normalized to 15.5 rib. 280 ms, with a Doppler shift of 125 Hz Oust faster than the clean wave, the scattering increasesmoothly as the the phase velocity of the wave), but the relative strength bulge forms prior to breaking. The HH backscattering is of the response centered at 480 ms-96 Hz in e VV signal is much weaker. The fastest signal at 420 ms is now stronger in VV and also now appears as a distinct HH response. An additional strong, distinct response that was absent at 10 GHz appears at both polarizations at 370 ms approximately 5 db below that at VV in this period. After the initial breaking at 400 ms the response is somewhat different, however. Primarily, the average HH scattering remains approximately constant until ~570 s (although the signal oscillates throughout this time). Inspection of and a Dopplqr shift of 116 Hz Oust slower than the phase the surface profiles shows that very steep features appear velocity). The Doppler shift of this response corresponds on the wave throughouthis period, with a small overto the two features identified by arrow set 2 in Figure 8. Figure 2b shows that although the bulge has begun to collapse in this time period (the profile at 360 ms), these features are still quite steep (and one is actually reentrant). turning at 570 ms. The 10 GHz time-doppleresponse of the up-wave scattering from the surfactant wave is shown in Figure 14. The response is somewhat more complicated than that 4.2. "Surfactant" Wave with the clean wave since the breaking is more chaotic in this case, but there are five distinct regions of strong The 10 GHz up-wave look. The time history of the backscattering from the "surfactant" wave is shown in Figure 13. The frequency was again 10 GHz, with a 10 ø grazing angle and an up-wave look direction. As with backscattering that can be readily identified in the VV response. The first four are of approximately equal amplitude. The first response begins at ~320 ms and 63 Hz. This corresponds to the time that the crest initially steep-

12 ß ß. 992 JA ET AL.' MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS ß 160 ' N 140 v c 120, O. C ':'... Max: 15.5 db ß i , db i! I I J. 1.: b) Figure 12. (continued) ens. From 370 ms to 420 ms a small jet forms, and the speed of this response continually increases until a Doppler shift of 70 Hz is reached. This is much higher than that expected from the wave phase velocity alone (62 Hz). The initial jet impact occurs immediately after õ o : -5o i i! i i i i vv HH... i i i i i i, Figure 13. The 10 GHz backscattering from "surfactant" wave looking up wave at 10 ø grazing. this time. The second strong response is less localized, but the center occurs at,-,475 ms with a Doppler shift of,- 48 Hz. A third peak is at approximately 75 Hz, peaking at 570 ms, which indicates that some scatterers are moving much faster than the wave phase velocity. The fourth response is centered at 650 ms with a Doppler shift of 45 Hz, while the last, much weaker, response appears at 750 ms-65 Hz. The HH Doppleresponse also begins with a strong response centered at 380 ms and 70 Hz. Unlike with the clean wave, the response remainstrong after the initial breaking. A peak that is slightly weaker than the initial peak appears at 475 ms-50 Hz, followed by a third peak of about the same magnitude at,-,570 ms-75 Hz. The second overturning occurs at this time (at 570 ms), after which the scattering is greatly reduced. The final response of sufficient strength to appear in the plot is 8 db below the initial response and appears at 650 ms-45 Hz. The surface feature motions corresponding to the most prominent Doppleresponses are identified by arrows in Figure 15. The first arrow set identifies the initial steepening of the wave and the formation of a jet that gives

13 JA ET AL.' MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS ' 40 Max: 15.8 db... t i i... i... i!... 22ø Figure 14. Doppler shift of 10 GHz backscattering from "surfactant" wave in Figure 13. (a) VV polarization normalized to 15.8 rib. (b) HH polarization normalized to 9.46 rib. the first strong VV response ranging from 320 ms-63 Hz to 450 ms-70 Hz. Arrow set 2 corresponds to the turbulent ripples moving slower than the phase velocity that gives the responses maximized near 460 ms at 48 Hz. Arrow set 3 shows features moving at the phase velocity of the wave that would give a response at 62 Hz and approximately 540 ms. There is a small relative maximum in both the VV and HH responses at that point, but the fairly poor resolution of the plots makes it difficult to identify it as a distinct response. Arrow 4 identifies the fast-moving overturning that appears at 575 ms-75 Hz. Arrow set 5 shows slowly moving turbulent ripples centered at 650 ms-45 Hz (appearing much more strongly in VV than in HH), and arrow 6 shows a fast scatterer that appears weakly in the VV response at 740 ms-65 Hz. This corresponds to the final very small overturning event in the time history. Arrows 7 and 8 show very fast movements of the toe that do not give responses that can be resolved in the 10 GHz response The 20 GHz up-wave look. The amplitude of the 20 GHz, up-wave-upwind-looking backscatter from the surfactant wave is shown in Figure 16. Again the response is similar to the 10 GHz scattering, with the primary difference being that the HH-to-VV scattering ratio is higher. In fact, at three times (centered at 370 ms, 570 ms, and 730 ms) the HH response actually slightly exceeds that at VV, giving momentary superevents. Each of these events corresponds to times at which some overturning occurs on the wave crest. The Doppler response is shown in Figure 17. As at 10 GHz, the peak VV response appears centered at,- 540 ms, with a Doppler shift of 125 Hz, corresponding to the arrow set 3 in Figure 15. The response corresponding to the initial steepening and jetting of the wave from 320 ms-125 Hz to 420 ms-140 Hz maximizes at approximately 4 db below the peak of the later occurring response. At HH the relative levels of the responses are reversed, with the later response 2 db lower than the initial response. A slow re-

14 JA ET AL.: MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS )02 03;0 3' 15 ' ! '0... 5; '0 5i' i0'0 6':i50' b) Figure 14. (continued) sponse appears at approximately 500 ms-100 Hz at both polarizations, and a later weak response (~8 db below the peak) appears at 670 ms-105 Hz in the VV response that is not matched at HH. The fastest HH response occurs at 570 ms-145 Hz. (This response is not fully resolved from the 540 ms-125 Hz response in the contour plot, but separate relative magnitudes are clearly visible in the gray scale tails.) This corresponds to the second small superevent identified in the amplitude response, and the HH response does indeed exceed that at VV in the Doppler signal slightly (when the normalizations of Figures 17a and 17b are considered). The initial response to the jetting also reflects the small superevent, but the final response at 720 ms is of too low magnitude to appear in the plots. Very weak responses with Doppler shifts as high as 160 Hz, considerably faster than the wave phase velocity, occur in the VV signal at 500 ms and 625 ms. These correspond to the fast toe movements identified by arrows 7 and 8 in Figure 15 that did not appear in the 10 GHz Doppler signal. 5. Analysis The numerical calculations show that "fast Doppler" signals whose Doppler shifts are equal to or greater than the phase velocity of the breaking wave can appear in the LGA backscattering from low-energy spilling breakers at X band and above. This occurred even though there was no jetting or plunging with the clean wave that had no surfactant. Addition of the surfactant allowed the initial for- mation of a jet that led to stronger scattering velocities greater than the phase velocity. The fast signals do not appear when looking down wave, as expected. The Doppler shifts ranging from just below to significantly greater than the phase velocity of the breaker were always associated with very steep surface features that present a point that is perpendicular or nearly perpendicular to the radar look direction. The strongest response from the clean wave corresponded to the formation of the bulge immediately before breaking at both polarizations and frequencies considered. This response had a peak HH/VV polar-

15 JA ET AL.: MECHANISMS OF LGA SCATTERING FROM SPILLING BREAKERS 995 Figure 15. Dominant scattering features of surfactant wave. Numbers I, 2, 3, and 5 mark groups of three, three, two, and two arrows, respectively. ization ratio of -4 db at 10 GHz and 0 db at 20 GHz. Other than the frequency depencience, this is consistent with the "specular facet" model described by Lee et al. [1995]. The frequency dependence can be easily understood. At the higher frequency the radius of curvature of the steep features is sufficiently high with respect to the radar wavelength that optical models that predict equal backscattering at both polarizations are valid. The optical approximation fails at the lower frequency, and the HH back-reflection is lower than that at VV. The initial jetting of the surfactant wave showed a slightly different behavior, with polarization ratios of -4 db at 10 GHz and 2 db at 20 GHz. The slightly positive (in decibels) ratio with the 20 GHz wave might suggest some multipath backscattering, although recent results have shown that superevents can also occur with single scattering when a jet is forming and the optical approximations are not fully met [West, 2000]. This is also consistent with the small superevents that correspond to overturning at later times. There are also lower magnitude fast responses in the 10 GHz responses from both waves that have HHNV ratios of well below 0 db. These occur at 425 ms-72 Hz in the clean wave response (Figure 7) and 750 ms-65hz in the surfactant wave response (Figure 14) and have HHNV ratios of -1 0 db and -15 db, respectively. (Again, note the normalization levels in Figures 7 and 14.) These are Bragg-like polarization ratios but, in both cases, are again correlated with surface features that are quite steep (and, in fact, the surfactant wave has a small overturning at that time). The small polarization ratios result because the scattering feature is very small compared to the electromagnetic wavelength, and the radius of curvature at the specular points is far too small to give polarization ratios approaching unity. At 20 GHz the polarization ratios increased to -5 db for the clean surface feature and approximately -8 db for the surfactant surface feature, which is to be expected for very small specular features. (The 20 GHz surfactant wave response was too small relative to the peak to appear in the Doppler plots, so instead was taken directly from the data.) Moreover, a similar polarization ratio (-13 db) was observed with the dominant fast backscattering from the bulge of the clean wave at 2.5 GHz (not shown) at the Doppler shift corresponding to the wave phase velocity, a low enough frequency that the bulge is also electromagnetically small. Despite the Bragg-like polarization ratios for these features the scattering mechanism clearly does not meet the traditional definition of Bragg scattering, and the responsible features cannot be considered tilted bound waves. These results suggest that the polarization ratio of a response alone is not sufficient to determine if it is due to a Bragg or non-bragg mechanism. The relative contribution of specific steep features to the fast scattering can depend strongly upon frequency. OJ c: 0 U Q) CJ) CJ) CJ) e (J Cl c:. (J CJ) VV HH "---;'-;;o-;:;; ---:-: -,---,-----,-_J Figure 16. The 20 GHz backscattering from surfactant wave looking up wave at 10.

16 ., 996 JA ET AL.' MECHANISMS OF LGA SCAWFERING FROM SPILLING BREAKERS '140 ' 120,.- loo o C Max: 19 db ' a) Figure 17. Doppler shift of 20 GHz backscattering from surfactant wave looking up wave at l0 ø grazing. (a) VV polarizationormalized to 19 db. (b) HH polarizationormalized to 16.4 db. This is most clearly shown by the responses to the steep features moving slightly slower than the phase velocity at 360 ms on the clean wave (arrow set 2 in Figure 8) and to the steep features moving at the phase velocity of the surfactant wave at 540 ms (arrow set 3 in Figure 15). The 10 GHz responses to these features were quite weak (demonstrated by both the Doppler time histories as well as the corresponding amplitude histories), but at 20 GHz they gave either the strongest or second strongest responses at both polarizations. Conversely, the second overturning in the surfactant wave at 575 ms gave the dominant VV response at 10 GHz (75 Hz) but appears only very weakly in the 20 GHz VV signal at 150 Hz. This suggests a possible explanation other than Bragg scattering for the frequency dependence of the Doppler speed of the strongest signal experimentally observed by Lamont-Smith [2000]. The signals may be due to steep reflecting features as observed here, but each frequency simply responds most strongly to different types or amplitudes of steep features. As before, care should be used when concluding that fast responses are Bragg or non- Bragg responses the basis of the frequency dependence of the dominant Doppler speeds measured. After the initial breaking, turbulent regions are shed from the crest that are carried by the orbital motion of the wave. The Doppler shifts observed at this time are consistent with the underlying orbital velocities. The turbulent regions have small surface slopes and do not give speculareflection points. The scattering from the turbulent "scar" is thereforexpected to be primarily Bragg scattering, which is consistent with the polarization ratios observed. A full two-scale analysis of the scattering this time will be given in a later paper. We also point out that the nulls that appear in the 10 GHz clean wave scattering immediately after the bulge collapses are predicted by the two-scale treatment, so this effect is not due to the multipath interferenceffect predicted by Trizna [ 1997]. The correlation between the feature speeds and the Doppler shifts at a particular time shows that the roughness behind the wave crest does not contribute signifi-

17 ß ß.,... ß, o JA ET AL.: MECHANISMS OF LGA SCATI'ERING FROM SPILLING BREAKERS 997 i 'i... i... i ;... ':... i... i"... i" ' ' b) Max: 16.4 db dbi... :. :... '1 :'... "': -,', '.'-' T' Figure 17. (continued) cantly to the total scattering at either polarization. The dominant scattering features are on the top of the crest or on the front face of the wave at all times when looking up wave, or on the back face of the wave when looking down wave. The only possible exception corresponds to the turbulent ripple identified by arrow 4 in Figure 8. This gave a very weak 10 GHz, VV response at 550 ms-32 Hz. However, at this time the roughness in front of the wave was quite small, and the top of the ripple is directly illuminated at 10 ø grazing. Straightforward geometrical optics shadowing therefore appears to be realistic under these conditions. This was further demonstrated by artificially removing the back side roughness of the clean wave wave at 477 ms and repeating the 10 GHz scattering calculation. The scattering at 10 ø was altered by less than 0.5 db, with a significantly greater change at higher grazing where the back face is illuminated. The full response is shown by Ja [ 1999]. This behavior is consistent with the results of Sturm and West [ 1998], who showed that the finite conductivity of seawatereduces the contribution of shadow region roughness at VV to a much lower level than that predicted using perfect conductivity. 6. Conclusions The approach of applying a numerical electromagnetic technique to instantaneous measurements of the profiles of spilling breaker waves to find the LGA backscattering has offered a great deal of flexibility in identifying possible mechanisms responsible for several of the characteristics of the backscattering found in experimental measurements. Most importantly, the continuou surface profiles allowed specific surface features to be associated with distinct responses in the time-doppler history of the backscatter. Both "fast" scattering, with Doppler shifts approximately equal to or exceeding the phase velocity of the breaking wave, and "slow" scattering, with Doppler shifts associated with the orbital velocity of the wave, were identified in the up-wave-looking backscattering. Only slow scattering appears when looking down wave. In all cases considered, the fast scattering observed was directly correlated with very steep surface features that give specular or nearly specular backscattering points. This proved true even when the size of the scattering fea-

18 998 JA ET AL.: MECHANISMS OF LGA SCATI'ERING FROM SPILLING BREAKERS ture was electromagnetically small, so that the HH/VV backscattering ratio was also small. There is no evidence of Bragg-resonant scattering from bound smallscale waves leading to fast scattering in these results. However, we stress that the data set is quite limited, with surfactanthat prevents the formation of parasitic capillaries added to one wave and no wind-generated roughness appearing on either wave, so this is not offered as a conclusive result applying to open water scattering. However, these results do show that non-bragg scattering from steep surface features can sometimes mimic Doppler signatures expected for Bragg scattering from bound waves. The scattering from the turbulent "scar" after breaking gives Doppler shifts corresponding with the orbital velocity of the breaker as expected, and the characteristics are consistent with Bragg scattering. Finally, the scattering is dominated by features that are directly illuminated even at vertical polarization, so the geometrical optics approximation of shadowing may be used with some accuracy at low grazing angles. Acknowledgments. This work was supported by the U.S. Office of Naval Research through the Sensing and Systems Division (grant N ; program officer, Dennis Trizna), the Ship Structures and Systems S&T Division (program officer, Ronald P. Radlinski), and the Mechanics and Energy Conversion S&T Division (grant N ; program officer, Edwin P. Rood). J. H. Duncan also gratefully acknowledges the support of the National Science Foundation under grant OCE References Burnside, W. D., C. L. Yu, and R. J. Marhefka, A technique to combine the geometrical theory of diffraction and the moment method, IEEE Trans. Antennas Propag., AP-23, , Duncan, J. H., H. Qiao, v. Philorain, and A. Wenz, Gentle spilling breakers: Crest profile evolution, J. Fluid Mech., 379, , Fuchs, J., D. Regas, T. Waseda, S. Welch, and M.P. Tulin, Correlation of hydrodynamic features with LGA radar backscatter from breaking waves, IEEE Trans. Geosci. Remote Sens., 37, , Ja, S.-J., Numerical study of microwave backscatter from breaking water waves, Ph.D. thesis, Okla. State Univ., Stillwater, Okla., Lamont-Smith, T., Doppler spectra of laboratory wind waves at low grazing angles, Waves Random Media, 10, 33-41, Lee, P. H. Y., et al., X band microwave backscattering from ocean waves, J. Geophys. Res., 100, , Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. H. R. Thompson, and R. Yee, Scattering from breaking gravity waves without wind, IEEE Trans. Antennas Propag., 46, 14-26, Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. H. R. Thompson, L. Wang, and R. Yee, What are the mechanisms for non-bragg scattering from water wave surfaces?, Radio Sci., 34, , Oppenheim, A. V., and R. W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Old Tappan, N.J., Plant, W. J., A model for microwave doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves, J. Geophys. Res., 102, 21,131-21,146, Rino, C. L., E. Eckert, A. Siegel, T. Webster, A. Ochadlick, M. Rankin, and J. Davis, X-band low-grazing-angle ocean backscatter obtained during LOGAN 1993, IEEE J. Oceanic Eng., 22, 18-26, Smith, M. J., E. M. Poulter, and J. A. McGregor, Doppler radar measurements of wave groups and breaking waves, J. Geophys. Res., 101, 14,269-14,282, Sturm, J. M., and J. C. West, Numerical study of shadowing in electromagnetic scattering from rough dielectric surfaces, IEEE Trans. Geosci. Remote Sens., 36, , Tfizna, D. B., A model for Brewster angle effects on sea surface illumination for sea scatter studies, IEEE Trans. Geosci. Remote Sens., 35, , Ulaby, F. T., R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive, vol. 3, pp , Artech House, Norwood, Mass., West, J. C., LGA sea-spike backscattering from plunging breaker crests, in Proceedings of the 2000 International Geoscience and Remote Sensing Symposium, vol. 5, pp , IEEE Press, Piscataway, N.J., West, J. C., J. M. Sturm, and J.-S. Ja, Low-grazing scattering from breaking water waves using an impedance boundary MM/GTD approach, IEEE Trans. Antennas Propag., 46, , J. H. Duncan and H. Qiao, Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA. (duncan@eng.umd.edu) S.-J. Ja, Nomadits, Inc., 1024 S. Innovation Way, Stillwater, OK 74074, USA. (puck@nomadics.com) J. C. West, School of Electrical and Computer Engineering, 202 ES, Oklahoma State University, Stillwater, OK 74078, USA. (jwest@okstate.edu) (Received September 25, 2000; revised December 26, 2000; accepted May 24, 2001.)