What are the mechanisms for non-bragg scattering

Transcription

1 Radio Science, Volume 34, Number 1, Pages , January-February 1999 What are the mechanisms for non-bragg scattering from water wave surfaces? P. H. Y. Lee, J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, H. R. Thompson Jr., L. Wang, and R. Yee TRW Space & Electronics, Redondo Beach, California Abstract. Experimental data obtained in the past several years have provided conclusive evidence that non-bragg scattering plays a major role in X-band microwave backscatter from water wave surfaces, and non-bragg scattering events are especially noticeable at small grazing angles, for wind-roughened surfaces, in the presence of breaking waves. We have conducted scattering experiments under a variety of wind wave conditions in an attempt to determine the different mechanisms which contribute to non-bragg scattering. At small grazing angles we find that non-bragg scattering is due to fast scatterers generated by the wave breaking, and with increasing wave steepness and surface roughness, mechanisms of multiple scattering and multipath interference become increasingly important. 1. Introduction Almost 50 years ago, Goldstein [1951] noticed HH > VV signals in X-band backscatter from rough seas. His observation, reported in volume 13 of the MIT Radiation Laboratory Series, is probably the earliest documentation of superevents observed in microwave backscatter. From the mid-1960s to the mid-1970s, Pidgeon [1968] documented the separation of VV and HH Doppler peaks; Mel'nichuk and Chernikov [1971] noted the failure of the Bragg scattering mechanism to explain small grazing angle backscatter; Long [1974] correlated return spikes with wave breaking; Leykin et al. [1975] noted that at small grazing angles, the horizontal polarization returns are mainly due to backscatter from the crest region of larger waves and stated that breaking wave crests contributed significantly to the horizontal returns; and Kalmykov and Pustovoytenko [1976] documented the observation of spiking and superevents. In 1991, Jessup et al. [1991] observed superevents but tentatively attributed the signals to wedge scattering, "ran- dom fluctuations in the measurements or the effects of averaging." In our Scotland data [Lee et al., 1995b] we reported that in addition to superevents, radar cross section (RCS) spiking events in which HH VV and HH < VV were also observed in the fast scatterers. We will call HH VV RCS spikes spec- Copyright 1999 by the American Geophysical Union. Paper number 1998RS /99/1998 RS ular-like events, and we will call HH < VV RCS spikes subevents. While subevents may be due to scattering from bound Bragg waves (i.e., Bragg waves that are bound to steep gravity waves and are hence called "fast" scatterers) and specular-like events may be due to a single bounce reflection from specular facets, superevents were conjectured to result either from a single bounce from horizontally elongated objects or from multiple reflections [Lee et al., 1995b]. It is important to note that bound Bragg waves are Bragg scatterers which do not contribute to non- Bragg scattering. Aside from the above mentioned examples of experimentally observed non-bragg scattering, an important paper by Kwoh et al. [1988] deserve special mention. Whereas all of the above examples are for small grazing angles, Kwoh et al. [1988] described a sea-scattering experiment at large grazing angles and low wind speeds where the scattering was performed at close range (-1 m) and the temporal radar backscatter was correlated with video images. They ob- served single-bounce backscatter from specular facets and gave quantitative results of the measured distribution of facet size. Closer scrutiny of their data reveals that the specular reflection they observed was not due to fast scatterers but rather to the slowest scatterers and was due to backscatter from the smoother patches in the troughs of larger waves. However, the notion of "specular reflection," which produces signals with HH = VV, was quickly adopted by theoreticians and modelers, and it was assumed that single-bounce reflection from specular facets was

2 124 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS also the dominant non-bragg scattering mechanism for fast scatterers at small grazing angles. Singlebounce specular reflection from specular facets may play an increasing role as the grazing angle is increased, but we find that other non-bragg mechanisms are predominant at small grazing angles. There is nothing logically inconsistent with the assumption that reflection from specular facets is the principal non-bragg mechanism, and it is rather convenient to use for modeling purposes. Even superevents (with HH/VV ratios much larger than unity) could be argued to fit within the framework of speculareflection, if straight "horizontal line scatterers" of great length were allowed. Experimental scattering results, however, exhibited some problems with the specular reflection model in the fact that first, long, horizontal line scatterers were not observed, and second, depolarization (i.e., production of crosspolarization signals) was also quite vigorous [Lee et al., 1998a]. If single-bounce specular reflection were the true mechanism, polarization should be preserved (i.e., no cross polarization produced) and there should be no depolarization at all. Thus the physics appears to be somewhat more complex than that of specular reflection alone and points to the possible existence of other scattering processes. Given the importance of non-bragg processes which provide large cross sections for all polarizations, especially for HH, which responds almost exclusively to non-bragg processes at small grazing angles, we believe that they deserve special attention. However, while superevents have come to be recognized as the hallmark of non-bragg scattering and are evident in much of the data we present in this paper, we wish to emphasize that this condition by itself is too restrictive as a definition of non-bragg scattering. We therefore define a non-bragg scattering event to be one which is inconsistent with composite surface scattering theory in copolarization ratio, cross-polarization ratio, or spectral decomposition line shape. Inconsistency in Doppler frequency may also attend the presence of non-bragg scattering mechanisms, but this inconsistency is not conclusive. Each of these various backscattering signatures violates the predictions of conventional composite surface scattering theory [Wright, 1968; Valenzuela, 1978] in one or more aspects, including copolarization ratio (HH/VV), cross-polarization ratio (HV/ VV), Doppler frequency, spectral decomposition line shapes [Lee et al., 1995a, 1998b], or coherence time [Lee et al., 1995b]. Accordingly, backscattering re- turns are conveniently classified operationally as "Bragg" or "non-bragg" as the return signatures conform to or differ from composite surface theory [Lee et al., 1996b]. Bragg scattering always yields HH _< VV and is a single-bounce return where the mechanism can be characterized as polarization by diffraction [see Lee et al., 1996b, Figure 6]. Non- Bragg scattering has been earlier characterized as due to polarization by reflection (e.g., Fresnel reflection) involving single-bounce or multiple-bounce returns [Lee et al., 1995b, 1998a]. Scattering from bound Bragg waves will show Doppler frequencies descriptive of the longer waves to which they are bound, but since it is still Bragg scattering it will exhibit polarization ratios appropriate to composite surface scattering theory and can be recognized as such by consideration of the complete scattering signature. While some are working to include bound Bragg scatterers in the composite surface scattering theory framework [Plant, 1997], and others have shown the inadequacy of composite surface theory and that curvature of the substrate wave (instead of simple wave slope) is also an important consideration in bringing composite surface theory into agreement with experiment at low grazing angles [Voronovitch, 1996], we are concerned in this paper with the description of non-bragg scattering mechanisms which do not conform to the composite theory mold. Bound Bragg scatterers contribute to the signals embedded in the higher Doppler frequency portion of the spectrum and can exhibit spiking behavior in the RCS. However, experiments reveal that although evidence of the presence of bound Bragg can be found (see, for example, the discussion of Plate 2a), it is often masked by the much stronger returns from non-bragg scatterers which appear in the same context. In an earlier paper we reported on backscatter experiments which answered several important questions regarding the phenomenology of non-bragg scattering from breaking waves in the absence of wind [Lee et al., 1998a]. In the present paper we describe further laboratory experiments which investigate the mechanism governing the backscatter from windroughened surfaces which include breaking waves. The experimental facility, the X-band pulsechirped radar (PCR) that was used as the principal instrument in this experiment, the operating modes of the PCR, and the gate numbering correspondence to the PCR line-of-sight range have been described elsewhere [Lee et al., 1997a]. The optical specular event detector (OSED) [Barter and Lee, 1996] is an

3 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS 125 imaging detector at visible wavelengths which measures two-dimensionally resolved plane polarized returns. When used with a suitable light source it can yield polarimetric information equivalent to the plane polarimetric radar. 2. Background Scattering Results In order to find clues to the mechanisms of non- Bragg scattering, we perform three categories of controlled laboratory experiments to isolate various scattering processes: scattering from (1) fabricated targets, (2) breaking waves, and (3) wind waves. After briefly reviewing the results of fabricated targets and scattering from breaking waves in the absence of wind, we report on scattering from wind waves in the absence and presence of mechanically generated 4-m gravity waves Scattering From Fabricated Targets In order to elucidate the effect of the various scattering mechanisms, both Bragg and non-bragg, which may be in operation simultaneously in scattering from a wind-toughened water surface, we have demonstrated the response of the PCR to various targets which illustrate the action of each category of scattering separately. In a previous paper [Lee et al., 1997a], Bragg scattering was studied in detail. To summarize the results, we may say that Bragg scatter is a single-bounce process which is described correctly by Rice's theory and that cross polarization is entirely negligible. On the other hand, specular reflection is also a single-bounce process where HH = W, and, since polarization is conserved in a single bounce, depolarization is also absent. For two bounce processes we have investigated Fresnel reflection from a metal-water dihedral [Lee et al., 1997a] and a metal-metal dihedral [Lee et al., 1996a] and have confirmed that HH always exceeds VV, in agreement with the Fresnel laws of reflection when the dihedral "crease" is horizontal, and that depolarization may occur if the dihedral crease is rotated about the radar boresight. A simple model based on anholonomic transport was constructed to describe the phenomenon of depolarization [Lee et al., 1996a]. To demonstrate multipath processes which occur entirely within the plane of incidence, we used a ball-above-water configuration and showed that multipath interference permits a variety of HH/VV polarization ratios which depend on the height of the ball above the water, as shown in Figure 1. In the following we list some known scattering mechanisms and provide our fabricated target results with indications of experimental accuracy: 1. For single-bounce processes the Bragg scattering result follows the theory very well. According to first-order Bragg theory, the cross polarization to VV ratio should be zero (i.e., - db). Laboratory experimental results indicate that the HH and VV results follow the theory closely, and the cross-polarization to VV ratio is -<-40 db. 2. For single-bounce processes, specular diffraction and specular reflection at normal incidence both yield HH/VV = 0 _+ 1 db, and while theory indicates that the cross-polarization to copolarization ratio should be zero (i.e., - db), experiments yield a cross-polarization to VV ratio of -<-30 db. 3. For two-bounce backscatter, scattering from dihedrals yields results which are well described by theory, showing the expected rotation of the incident plane of polarization as a function of the orientation of the dihedral crease [Lee et al., 1996a, 1997a]. 4. For in-plane multipath interference, as indicated, for example, by the ball-above-water experiment, a variety of HH/VV ratios are possible, depending on the height of the ball above the water surface. According to theory, the cross-polarization to VV ratio should be zero (i.e., - db), while experiments yield a cross-polarization to VV ratio of -<-30 db Scattering From Breaking Waves Without Wind Scattering from breaking waves without wind, at small grazing angles, has been reported elsewhere [Lee et al., 1998a]. We briefly summarize here a few points which are important to the present analysis. 1. In the study of backscatter from vigorously breaking waves without wind at small grazing angles, one must bear in mind that the unbroken crest lasts for only a short while and contributes at the beginning of the breaking event. However, the major contribution to the fast scatterer cross section (-80-90%) comes from the evolving broken crest, or broken wave surface, which is composed of a disordered mass of water, foam, and bubbles. 2. The backscatter from breaking wave surfaces is clearly non-bragg due to the fact that HH is predominantly greater than VV and that the cross-polarized components are not small. The predominance of HH can be explained by multipath effects and Brewster damping of VV.

4 126 LEE ET AL.' NON-BRAGG SCATTERING MECHANISMS.:. lx10 ø o ee"----. l e e-'- ee" - e;ee lee ee._n lx10 - E o z v >o 0-2 : lxl vv 1 xl 0 ø o ' N lx10 - O z -.-- lx10- ß 1 xl o 2 i % /!! -2O -4O -6O 0.0 0' ' 1. '5 ' ' 2 z sin% / % Figure 1. An example of in-plane multipath backscatter for a ball-above-water configuration. In this case, a 1-inch metal sphere is located at height z above the water, 0g (7.2 ø) is the grazing angle, and X is the X-band wavelength. The backscatter power of both VV and HH polarizations, normalized to their respective peak values, are plotted against the normalized height above water (2 z sin 0g/X); the solid curves through the data points are theoretical results based on multipath interference. In the bottom panel, notice that a wide range of HH/VV values is possible depending on the height of the ball above the water surface. 3. The speed of the breaking wave scatterer initially exceeds the phase speed of the gravity wave but slows down as the wave breaks, ages, and decays. Since the broken crest contributes to the bulk of the returns and its average speed is slightly less than the phase speed, it follows that the peak power spectral density (PSD) frequency, which represents a time average, should be less than the Doppler frequency corresponding to the phase speed of the gravity wave.

5 LEE ET AL.' NON-BRAGG SCATTERING MECHANISMS 127 Table 1. Relevant Wind Wave Conditions Measured at 10-m Range (---36-m Fetch) Without Mechanically Generated Gravity Waves U0.8, U,, fpeak, Xdom, PSDneak, arms, m/s m/s Hz m m 2fI2iz m e e e e e e e e-2 instability [Yuen and Lake, 1982] that causes the waves to break at the appropriate location in the wave tank, which we call the test section (i.e., the location U0. 8 is the nominal wind speed at 0.8 m height, u, is the of the radar footprint). The essential conditions demeasured friction speed, fpeak is the dominant wave frequency corresponding to the spectral peak, Ado m is the dominant wind scribing the sideband-modulated gravity waves are wavelength corresponding to fpeak, PSDpeak is the peak value of the thus A W = 4 rn andfo = Hz, which denote the wave spectrum, and arm s is the rms wave height obtained by wavelength and frequency of the fundamental gravity integration of the wind wave spectrum. Read 3.22e-6 as 3.22 x wave, respectively, with f+ = Hz and f_ = Hz denoting the upper and lower sideband frequencies, respectively; asia o is the sideband amplitude to fundamental amplitude ratio at generation 2.3. Scattering From Wind Waves (the upper and lower sideband amplitudes are equal); In two reports [Lee et al., 1997b, 1997c] we pre- and ka is the characteristic wave slope, with k = sented the results and analysis of a set of backscatter 2,r/A w and a 2 - a o 2 + 2as 2. Avalueofka = data obtained for wind wave surfaces. We studied is used for all cases reported here for which mechanbackscatter from wind waves at two different small ically generated 4-m waves are present, and values of grazing angles, for three different nominal wind as/ao = 0.18, 0.22, 0.26, and 0.30 are used for the speeds, in the absence and presence of mechanically subcases which characterize increasingly vigorous generated 4-m gravity waves. In the latter case, it is wave breaking at a fixed radar range. further divided into the cases of nonbreaking and 3.3. Interpretation of Doppler Spectra breaking gravity waves. In this series of experiments, both the Doppler spectra and radar cross sections are For reference, the observed Doppler frequency for studied, and we find that for fixed wind speed and unshadowed free Bragg waves is given by grazing angle conditions, the progression of scattering 2 cos O mechanisms, from free Bragg, to free and bound- fd(bragg) -- A (Cp(Bragg) q- tad q- (kacp)gravity cos Bragg, and ultimately to Bragg (free and bound) plus (1) non-bragg, is observed as wave steepness and surface roughness are increased. In this paper we present a where 0 a is the boresight grazing angle and X small illustrative subset of data from the above men- cm is the wavelength corresponding to the center tioned reports. 3. Experimental Conditions and Interpretation of Results 3.1. Characterization of Wind Waves In order to obtain wind waves with and without 3.2. Characterization of Mechanically Generated Waves In addition to the wind waves, mechanically generated breaking gravity waves are used. A 4-m gravity wave is generated without or with sideband modulation, and it is the growth of the sideband-modulated frequency (9.05 GHz) of the PCR. Here Cp(Bragg ) is the Bragg wave phase speed of the Bragg-resonant water wavelength AB = X/2 cos Oa, given by rr2rr,/gxb Cp(Bragg) = 2 r BB + (2) where g is the gravitational acceleration and cr/p is the mechanically generated gravity waves, winds of vari- surface tension to water density ratio. Clearly, the ous speeds are selected. A summary of the wind wave Bragg wave phase speed is dependent on surface conditions in the absence of mechanically generated conditions. In practice, however, the phase speed 4-m waves is given in Table 1. Further details of the corresponding to X band at small grazing angles is wind profile and wave amplitude power spectral cm/s. The wind drift ud is taken to be ---3% of densities (PSDs) are given by Lee et al. [1997b] the nominal wind speed, and (kacp)gravity is the including representative spectral distributions with orbital spee due to the gravity wave, with Cp = and without mechanically generated waves. V'gXg/2 r being the unmodulated phase speed of the

6 128 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS gravity wave. Here X g = 4 m is the fundamental first as a function of wind speed without mechanically wavelength of the mechanically generated gravity generated waves and then with mechanically generwave. In the absence of mechanically generated grav- ated 4-m waves, as a function of the degree of ity waves, the dominant wind wave )kdo m (obtained breaking, at a constant wind speed. Then we present from Table 1 for the appropriate wind speed) is to be radar cross section (RCS) data for a similar set of used instead of X a. Cos is a phase factor which conditions. We will confine our discussion mainly to describes the apparent location of the Bragg waves one range only (R = 9.86 m), recalling that the range with respect to the phase of the gravity wave. Cos ½ - resolution of the PCR is 13.6 cm [Lee et al., 1997a]. 1 (½ - 0 ø) if the Bragg waves are located on the crest of the gravity wave, cos = 0 ( - 90 ø) if Bragg 4.1. Wind Only, No Mechanically Generated waves are located at the forward node (i.e., the Gravity Waves forward null displacement point), and cos ½ = -1 At 0 = 4.5 ø the time-integrated (8 miri) Doppler (½ ø) if the Bragg waves are located in the spectra, for both copolarizations (HH, VV) and one trough. At small grazing angles it is reasonable to cross polarization (HV), for wind speeds of 5.8, 9, and assume that the rear node, and even the trough, of a 12 m/s, are shown in Plates la, lb, and lc, respecgravity wave (or dominant wind wave) is shadowed. tively. In Plate la, note that the frequency of the Thus the apparent phase position of the Bragg scat- spectral peak of the cross-polarized signal, 23 Hz, is terers with respect to an underlying gravity wave may the same as the VV spectral peak, while the HH be expected to reflect not only any concentration of Bragg waves on the gravity wave profile, but also the illumination weighting due to shadowing, which favors the crest and front face regions of the profile [Barrick, 1995]. Returns from within the optically shadowed region are greatly reduced by a first diffraction of the transmitted energy around the wave crest to illuminate the shadowed scatterers and a second diffraction of the scattered energy back around the wave crest toward the receiver, so that returns from competing scatterers directly visible on the front face of a wave due, for example, to a breaking event may be expected to greatly outweigh the contributions from shadowed scatterers for the consideration of non-bragg scattering mechanisms. At higher grazing angles the effects of shadowing will be less pronounced, allowing the effects of the negative orbital velocity in the wave trough to be seen, as will be noted, for example, in the discussion of Plate l d. The reference Doppler frequency for the gravity wave, for the case of scatterers moving at exactly the phase speed of the gravity wave, is spectral peak falls at 47 Hz. This peak separation of Doppler spectra is also typical of wind waves observed in ocean data [Pidgeon, 1968; Lee et al., 1995b]. Using the formulas provided in section 3.3, one finds that the Doppler frequency of the VV signal of 23.7 Hz implies that the dominant Bragg scattering returns are centered near the front node of the dominant wind wave ( 90ø). The dominant wave crest moves at a speed corresponding to 46.8 Hz, which matches the HH peak frequency quite well. A "shoulder" may also be seen in the VV spectrum at Hz, indicating that some scattering from the vicinity of the dominant wave crest occurs also for the vertical polarization. Noting that the polarization ratio (HH/ VV) is -15 db, Bragg scattering of bound Bragg waves is the most likely candidate. The difference in polarization ratio between the slow and fast peaks indicates that although the free Bragg scattering centered near the front node of the dominant wave exceeds that of the bound Bragg scatterers near the crest by an order of magnitude, as seen in the VV PSD, the effective grazing angle for the bound Bragg must be significantly increased in order for the HH 2 cos 0a returns from the bound Bragg to exceed those of the fd(gravity) =. Cp. (3) free Bragg. Thus the dominant wave is apparently approaching breaking amplitude. In (3), the wind drift contribution (-<0.36 m/s) has At larger values of wind speed the dominant wavebeen neglected in comparison with the phase speed of length and the rms wave height of the wind wave a 4 m wave (2.5 m/s). spectrum are increased (see Table 1); thus the HH peak and the VV shoulder shift upward in Doppler 4. Discussion of Doppler Spectra Results frequency. The values of peak frequencies in Plates In the following discussion we will present exam- lb and lc may be analyzed in the same fashion as for ples of Doppler spectra for wind-toughened surfaces, the case in Plate la. When the wind is sufficiently

7 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS 129 large (12 m/s) to cause the dominant waves to break (Plate lc), scattering from the wind waves alone yields peak-separated spectra with specular-like events and non-bragg scattering. The fast scatterers due to non- Bragg scattering are evident from the HH/VV polarization ratios at Doppler frequencies above Hz. Notice also that when no wave breaking occurs (Plates la and lb), the cross-polarized spectrum is VV-like, but when wave breaking occurs (Plate lc), the cross-polarized spectrum is more HH-like. When the grazing angle is increased to 11 ø in Plate l d at wind speed 12 m/s, the effect of shadowing is lessened and the contribution of negative orbital velocity due to the dominant wave becomes apparent. The new feature at this slightly larger grazing angle is the presence of negatively convected Bragg waves, as evidenced in the VV PSD in the frequency region less than 10 Hz and extending into the negative frequency region Mechanically Generated Waves Superimposed on a Wind-Roughened Surface In the following sequence of examples, we show the time-integrated (8 min) Doppler spectra for a 4-m wave imposed on a wind-roughened surface where the wind speed is 9 m/s. The data are for the fixed grazing angle of 0g = 4.5 ø and as/ao = 0, 0.18, 0.22, 0.26, and 0.30, denoting cases which characterize increasingly vigorous wave breaking at a fixed radar range. When a nonbreaking gravity wave is superimposed on a wind-roughened surface, the gravity wave has the tendency to "sweep up" the Bragg waves [Phillips, 1981] and either to dampen them or to concentrate them at certain locations on the gravity wave. Plate 2a shows a typical result, for 0g = 4.5 ø, a wind speed of 9 m/s, and as/a o - 0, i.e., a nonbreaking 4-m gravity wave. Note that all the VV spectral peaks fall at Hz; this is the "slow" peak. Equation (1) predicts that the dominant Bragg scattering returns are centered near - cos- [(45-22)/(0.601 x x 250)] - 22 ø on the forward face (near the crest) of the 4-m gravity wave. This would be consistent with returns from free Bragg waves which have been concentrated near the crest and are being convected by the orbital motion of the 4-m gravity wave. The HH spectral peak falls at Hz, the "fast" peak. Clearly, this Doppler frequency is too high to be explained by free Bragg waves convected by the orbital velocity of the nonbreaking 4-m gravity wave. However, scattering features (e.g., bound Bragg waves) traveling with the dominant wind wave crests (X = 0.54 m, Table 1) which are themselves convected with the wind drift velocity and the orbital motion of the 4-m gravity waves could yield a Doppler frequency in the range Hz depending on the effective phase ½ of the 4-m waves at which the dominant wind wave crests reside. Again, since the polarization ratio (HH/VV) is less than unity at all Doppler frequencies, Bragg scattering must still be the dominant mechanism. Plates 2b, 2c, 2d, and 2e show the Doppler spectra of the cases corresponding to as/ao = 0.18, 0.22, 0.26, and 0.30, respectively, as the degree of wave breaking becomes increasingly vigorous, at the fixed range of 9.86 m. A comparison of the data for different values of a s/a o will indicate that as wave breaking becomes more vigorous, the progression of dominant scattering mechanisms, from free Bragg to free and bound-bragg and ultimately to Bragg (free and bound) plus non-bragg, is observed as wave steepness and surface roughness are increased. In Plate 2b, notice that when wave breaking is very gentle, non-bragg scattering is not dominant (being apparent only at Doppler frequencies above Hz). When the breaking is increased somewhat (Plate 2c), a Bragg (slow) population and a non-bragg (fast) population are clearly separated and distinguishable. When wave breaking is moderate (Plate 2d), superevents in the HH as well as the cross-polarized spectra become clearly dominant. Finally, for fully breaking waves (Plate 2e), there is still a distinct slow (Bragg) population and a fast (non-bragg) population in all polarizations, but non-bragg scattering has now clearly become the dominant feature in the HH and cross-polarized PSDs. The shape of the cross-polarized spectrum resembles the HH spectrum. Strong depolarization manifested by large cross-polarized contributions is a clear indication of multibounce scattering processes from the disordered mass of broken wave surfaces. Notice, however, that the VV spectra are always dominated by Bragg scattering, whether or not breaking waves are present. Again, from this sequence of plates, one notes that for nonbreaking or very gently breaking conditions, the cross-polarized spectrum is VV-like, but when breaking occurs, the cross-polarized spectrum becomes HH-like. Details of the spectra, such as the significance of each peak frequency of the various polarizations of each spectrum, are discussed by Lee et al. [1997b] and will not be given here. However, it may be mentioned that for a weaker wind (e.g., 5.8 m/s), the effect of a mechanically generated 4-m gravity wave is more effective in the sweep up of the wind-generated Bragg

8 130 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS waves but less effective in triggering other waves to break. For a stronger wind (e.g., 12 m/s), wave breaking (of the dominant wind wave) may occur even in the absence of a mechanically generated gravity wave, the sweep-up action of the long wave is masked, and the addition of a mechanically generated gravity wave, even a nonbreaking one, is sufficiento trigger breaking. These are nonlinear hydrodynamic aspects of the problem and will not be elaborated on here. 5. Discussion of Radar Cross Section Results Radar cross sections (RCSs) for the same "matrix" of grazing angle and wind speed cases as those of Lee et al. [1997b] are obtained and described by Lee et al. [1997c], of which selected examples will be shown. In some cases, a sample of a typical time interval will be examined more closely in order to highlight important features. As described elsewhere [Lee et al., 1998a], where temporal RCSs are shown in the figures, the vertical scale denotes relative cross sec- tion where 54 db corresponds to the RCS of a 1-inch metal sphere at 10-m range. The range cell is -- 1 m in azimuth and 13.6 cm in range, and thus the area of the range cell is m Wind Only, No Mechanically Generated Gravity Waves At 0g = 4.5 ø the radar cros sections, for both copolarizations (HH, VV) and one cross polarization (HV), for wind speeds of 5.8, 9, and 12 m/s, are shown in Plates 3a, 3b, and 3c, respectively. A comparison of the plates will quickly convince one that for small and intermediate winds, the mechanism is pure Bragg scattering, as may be verified by the temporal HH/VV polarization ratio. However, for strong winds, an occasional non-bragg superevent (HH > VV) may be observed. See, for example, Plate 3c at times t s,t 88s, t 108s, etc Mechanically Generated Waves Superimposed on a Wind-Roughened Surface The next examples we show are for 4-m gravity waves, either nonbreaking or vigorously breaking, superimposed on a wind-roughened surface. When a nonbreaking gravity wave (as/ao = 0) is also propagating on the wind-roughened surface, the RCS is strongly modulated by the gravity wave. This is seen in Plate 4a (for 0g = 4.5 ø and wind speed at 9 m/s), where the RCSs of all polarizations are modulated at the frequency of the 4-m gravity wave. Again, VV > HH > HV at all times. In this case, the scattering is best described by composite surface theory, where Bragg waves are not only modulated but also tilted by the substrate wave. Note that in view of composite surface effects the modulation of the RCS in Plate 4a is insufficient to prove that Bragg waves are being swept up by the gravity wave. To demonstrate this effect, one must consult the corresponding Doppler spectra in order to establish that the spectrum of the population of Bragg waves does not exhibit the full spread in frequency expected by the gravity wave orbital speed but is concentrated at certain locations on the gravity wave surface (see Plate 2a). Plate 4b (for 0a = 4.5 ø and wind speed at 9 m/s) shows the case of a vigorously breaking gravity wave (as/ao = 30) imposed on a wind wave surface. In this case, the RCS is modulated not only at the gravity wave frequency but also at the approximate wavebreaking frequency. Bragg scattering from the wind wave surface dominates at most times, except when the gravity wave breaks. In such cases, non-bragg scattering is strongly manifested by the appearance of superevents and large cross-polarization returns. Plate 4c shows several interesting examples: At t 28.8 s a specular-lik event (HH VV) occurs with a fairly large HV RCS; at t 30.2 s a local spiking event occurs, but with VV > HH > HV; at t 31.6 s, HH > VV, but the cross-polarized RCS is small; at t 32 s a superevent occurs where HH is much larger than VV but with a lower value of the crosspolarized RCS than at t 28.8 s; and finally, at t 33.7 s, the VV RCS peaks, but there is very little response from either HH or HV. Clearly, the events at t 30.2 and t 33.7 s are due to Bragg scattering, while the events at t , t 31.6, and t - 32 s are non-bragg. Note, however, that for non-bragg events in which HH -- VV, the cross- polarized RCS may be either large or small. More examples of spiking events are shown in Plate 4d (for 0 = 11 o and a wind speed of 12 m/s). At t 78.6 s one observes HH > VV but with HV small, while at t 79 s, the spiking is due to a vigorously breaking wave, as verified by the OSED [Barter and Lee, 1996] image, yet VV is only -- 3 db less than HH and the cross-polarized HV RCS is almost as large as the VV RCS. This shows that the cross-polarized RCS can sometimes be very large indeed. Thus there are various categories of non-bragg superevents, in which the cross-polarized component may be small, intermediate, or very large. Further examples are given by Lee et al. [1997c]. It should be mentioned that all these results can be accommodated by the

9 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS [ (a) U = 5.8 m/s HH, :4.s... VV HV (b) : (c) 6O 4O (d) u_- //,_,,- -,%. 2O -2( ) Frequency (Hz) Plate 1. Time-integrated (8-min) Doppler spectra of HI-l, VV, and H¾ returns irom a wind wave surface in the absence of mechanically generated gravity wavus, measured at 9.86 m aage and 4.5 ø grazing angle. The polarizations are identified by the color coding: HH, magenta; VV, cyan; and tiv, gray. Shown are (a) nominal wind speed of 5.8 m/s, (b) nominal wind speed of 9 m/s, and (c) nominal wind speed of 12 m/s. (d) The grazing angle is 11 ø, with nominal wind speed of 12 m/s, and the influence of the negative orbital velocity due to decreased shadowing effect is evident by the fact that the power spectral density (PSD) has increased for Doppler frequencies more negative than 10 Hz. simple anholonomic transport model [Lee et al., 1996a]. 6. Discussion of Probability Densities of Polarization Ratios We now show examples of probability density functions (pdf's) of the polarization ratios of HHNV and HVNV distributions of fast scatterers for (1) wind waves without gravity waves and (2) the pdf for breaking gravity waves without wind, which may be compared with those of a previous paper [Lee et al., 1996b] in which we constructed pdf's from a timedependent sequence of PSDs. Bragg scatterers and "faster-than-bragg" scatterers were differentiated by

10 . ß 132 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS (a)... HH a /ao = VV ' HV 20 (b) a /ao = 0.18 i,,.,.. J, l l (c) as/ao = 0.22 (d) (e), ---, ,,,..,. '-. k.,k. ',..,,.. "%% Frequency (Hz) Plate 2. Time-integrated (8-min) Doppler spectra of HH, VV, and HV returns from a wind wave surface at 9.86 m range, with nominal wind speed of 9 m/s at 4.5 ø grazing angle. The polarizations are identified by the color coding: HH, magenta; VV, cyan; and HV, gray. A 4-m gravity wave is superimposed on the wind-roughened surface. The gravity wave is nonbreaking, i.e., (a) as/ao - 0, (b) as/ao = 0.18, (c) a /ao = 0.22, (d) a /a o = 0.26, and (e) a /ao = 0.30, where the modulated gravity wave is breaking vigorously.

11 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS (a)... HH U = 5.8 mts --- VV HV,,, i,,,!.,,,,,. I I.,, I i [. (b) U = 9 m/s 80 t ,, (c) U = 12 m/s I i i,i 20, ß ß. ß I O loo 120 Time (sec) Plate 3. Temporal radar cros section (RCS) records of HH, VV, and HV returns from a wind wave surface, in the absence of mechanically generated gravity waves, measured at 9.86 m range and 4.5 ø grazing angle. The polarizations are identified by the color coding: HH, magenta; VV, cyan; and HV, gray. Shown are (a) nominal wind speed of 5.8 m/s, (b) nominal wind speed of 9 m/s, and (c) nominal wind speed of 12 m/s. choice of the Doppler frequency range at which to record the polarization ratio at each time step. In the db. Clearly, there is an appreciable fraction of the distribution in which superevents (HH > VV) are present paper we use an RCS time record for which present; however, the fact that there are portions of the PSD transform has not been performed. In the the distribution where HH < VV and HH VV construction of these pdf's the 1-kHz raw data rate clearly indicates that there are different processes from the device has been downsampled by averaging (Bragg and non-bragg, in-plane multipath, etc.) to 31 Hz. Spiking events are selected for analysis which contribute to the scattering results. The result when the RCS exceeds a threshold response, and the events are binned according to their polarization ratio (HH/VV and HV/VV)values. In the absence of mechanically generated waves, pdf's for the nominal wind speed of 12 m/s at 4.5 ø grazing angle are shown in Figure 2. Similar to the case observed in ocean scattering, at larger wind in Figure 2 shows that single-bounce speculareturns in the absence of multibounce signatures (such as high cross-polarization levels), although possible, as mentioned earlier in this paper, are expected to be a highly unlikely occurrence when averaged over the entire gated footprint. This can be understood quite easily: If single-bounce speculareturns were the only speeds [Lee et al., 1996b], the probability density operative non-bragg scattering mechanism, then the distribution of HH/VV spans a range from --16 to pdf would be a delta function (or some very narrow

12 ß 134 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS 80 (a) U = 4.5ø: wind + non-breaking waves 40, 't... :: Time(sec) 60 (c) U = 9 m/s; e = 4.5ø; wind + breaking waves, as/a ø = Time (Sec) (d) U = 12 m/s; e = 11 ø' wind + breaking waves, as/a ø = ß ß ß i ß...& I, i,, I.. --t... a_ I ß ß ß Time (sec) Plate 4. Temporal RCS records of HH, VV, and HV returns from a wind wave surface, in the presence of mechanically generated 4 m gravity waves, measured at 9.86-m range. The polarizations are identified by the color coding: HH, magenta; VV, cyan; and HV, gray. Shown are (a) 4.5 ø grazing angle, with nominal wind speed of 9 m/s, and a nonbreaking 4-m gravity wave, (b) 4.5 ø grazing angle, with nominal wind speed of 9 m/s, and with a fully breaking (a. /ao = 0.30) 4-m gravity wave, (c) 4.5 ø grazing angle, with nominal wind speed of 9 m/s, and with a fully breaking (as/a o = 0.30) 4-m gravity wave, expanded timescale, and (d) more examples of spiking events, 11 ø grazing angle, with nominal wind speed of 12 m/s, and with a fully breaking (as/a o = 0.30) 4-m gravity wave.

13 ._ LEE ET AL.' NON-BRAGG SCATTERING MECHANISMS o 008 ß 0.06 o 0.06 HV/VV pdf peak N HHNV (db) --HVNV (db) Figure 2. The probability density of HH/VV and HV/VV for fast scatterers, obtained from a wind wave surface, at 4.5 ø grazing angle at a nominal wind speed of 12 m/s in the absence of mechanically generated waves ' ' ' i i, i i HH/VV (db) Figure 3. The probability density of HH/VV for fast scatterers on a breaking wave surface at 4.5 ø grazing angle in the absence of wind. Superevents dominate the distribution, with HH/VV peaking at -- 8 db. The peak of the HV/VV probability density (at db) is indicated by the dashed line. distribution) centered at HH/VV - 0 db, which is not the case in Figure 2. The fact that the cross-polarized/ copolarized ratio HV/VV is not negligibly small (i.e., much larger than the discrimination level of the instrument) is a further indication that multipath and multibounce effects are present. At another extreme, it has been found [Lee et al., 1998a] that for breaking 4-m gravity waves in the absence of wind, essentially every breaking event is a non-bragg event. The HH/VV polarization ratio distribution compiled from a long record (8 min) and analyzed similarly to the previous case is shown in Figure 3. The predominance of superevents is clearly shown by the position of the peak at -8 db. The tail of the distribution toward lower polarization ratios is a result of the practical definition of breaking events as all data points, whether consecutive or not, for which the RCS exceeds a threshold. Cross-polarized data were not obtained for this run; however, on the basis of other similar runs where PSD data were obtained, we find that the time-averaged peak of the HV/VV probability distribution lies approximately between -8 and -10 db, as indicated by the dashed line in Figure 3. The polarization-ratio pdf's for wind waves with gravity waves of various degrees of breaking lie between the results shown in Figures 2 and 3. Single-bounce specular events in the absence of multibounce signatures are very rarely seen in the RCS records, but this does not prove that they do not exist. Obviously, then, the occurrence of superevents is the most direct indication of the presence of multibounce events. The clue that the single-bounce event is not the only process is the fact that crosspolarized signals are present and are not small. This is shown in the following examples, where "specularlike" events (defined as HH VV, independent of cross-polarization level) in the temporal RCS record are selected (HH/VV = 0 +_ 1 db), and their corresponding cross-polarization to copolarization ratio (HV/VV) distributions are plotted, for a variety of radar ranges. By comparison with PSDs for the same wind and wave conditions, these events are confined to higher Doppler frequencies and may be characterized as fast scatterers. The result, obtained for a -7-min RCS record of backscatter from wind waves, at 4.5 ø grazing angle with a wind speed of 12 m/s, in the absence of gravity waves, is shown in Figure 4. One observes that the HV/VV distributions peak at approximately db. If single-bounce specular returns were the only mechanism, then there should be no depolarization (HH/VV -< -30 db for our instrument). Certainly, a superevent with large HV/VV polarization ratio is a clear indication that at least two Fresnel reflections have occurred, with one reflection occurring near the Brewster angle so that the VV is attenuated. Obviously, then, the occurrence of superevents is the most direct indication of the presence of multibounce events. 7. Summary First, we summarize the results of the wind wave studies, and second, we will discuss, from the body of

14 ß ß 136 LEE ET AL.' NON-BRAGG SCATTERING MECHANISMS O o o o & o Range 11.6 m Range 10.4 rn Range 9.2 m Range 8.1 m HV/VV (db) Figure 4. The probability density of cross-polarized to copolarized ratio (HV/VV) for fast scatterers, selected from the "specular-like"(hh/vv = 0 1 db) population, for a variety of radar ranges. The results are obtained from a wind wave surface (12 m/s wind speed) at 4.5 ø grazing angle in the absence of mechanically generated gravity waves. accumulated data, what the most likely non-bragg scattering processes could be. A systematic study of the Doppler spectra and radar cross sections of wind waves with and without mechanically generated 4-m gravity waves, at two different grazing angles and three different wind speeds, has been completed [Lee et al., 1997b, 1997c]. We find that for low winds, the scattering is due mainly to the Bragg mechanism with either free or bound Bragg waves. A nonbreaking gravity wave contributes to the Doppler frequency by means of orbital motion convection and can concentrate the Bragg waves at certain phase locations on the gravity wave or suppress contributions to Bragg returns from shadowed areas. When winds are strong, non-bragg scattering may occur even without the addition of mechanical waves. When even slight breaking of the gravity wave occurs, non-bragg scattering immediately becomes the dominant feature in the HH and cross-polarized spectra, superevents become ubiquitous, and multibounce scattering is manifested by the large cross-polarized signals. Two Doppler-spectra observation should be noted for wind waves: (1) Bragg scattering is always dominant for VV polarization whether or not a wave breaking is present, and (2) the cross-polarized spectral shape is more VV-like in the presence of mild breaking but is more HH-like when wave breaking is vigorous. A nonbreaking gravity wave modulates the RCS at the frequency of the gravity wave. A breaking gravity wave further modulates the RCS at the frequency of wave breaking. When winds are strong, non-bragg scattering may occur even without the addition of mechanical waves. The presence of the specular-like and superevents, with either large or small cross-polarized RCS, indicates that different types of multipath and multibounce scattering are present. Two important RCS observationshould be noted: (1) When the crosspolarized RCS is small during a non-bragg scattering event, the wave breaking is incipient or very mild, and when the cross-polarized RCS is large during a non- Bragg scattering event, the wave breaking is vigorous, and (2) non-bragg scattering is more apparent at the smaller grazing angle of 4.5 ø. At the larger grazing angle of 11 ø, due to the increase of the VV RCS (from Bragg scatter), the modulations of the HH and crosspolarized RCSs appear to be less pronounced relative to the increased level of VV signals. We may also mention that the wind wave cases for different runs have been correlated with OSED [Barter and Lee, 1996] images, and the description of the scattering mechanisms given above has been verified by the optical imagery. In light of the data gathered so far, non-bragg scattering mechanisms for X-band radars at small grazing angles involve multipath and multibounce scattering, which could be a combination of diffractive and reflective processes. Here one might further distinguish the different types of multipath and multibounce processes. If the multipath scattering is confined to the plane of incidence (in-plane scattering), the polarization is conserved, and if not (i.e., if the scattering is out of plane), then depolarization will occur. Our results, obtained with ocean waves, laboratory wind waves, and breaking waves, indicate that it is unlikely that single-bounce specular reflection is the only mechanism. The origin of the multipath and multibounce processes arises because in addition to the presence of the ubiquitous Bragg waves (whether tilted or not), the underlying water surface itself may

15 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS 137 be (and quite often is) of a complicated geometric Lee, P. H. Y., J. D. Barter, E. Caponi, M. Caponi, C. L. configuration, as one may casually observe at a beach Hindman, B. M. Lake, and H. Rungaldier, Wind-speed or on the ocean. For breaking wave surfaces [see, for dependence of small-grazing-angle microwave backscatexample, Lee et al., 1998a, Figure 3], the scattering tering from sea surfaces, IEEE Trans. Antennas Propag., indeed occurs from a mass of disordered and turbu- 44, , 1996b. Lee, P. H. Y., J. D. Barter, K. L. Beach, C. L. Hindman, lent water, which is intermixed with foam and bub- B. M. Lake, H. Rungaldier, H. R. Thompson Jr., and bles. Simple physical models to explain the physical R. Yee, Experiments on Bragg and non-bragg scattering results have been proposed [Lee et al., 1996a], but using single-frequency and chirped radars, Radio Sci., improved modeling of scattering from such surfaces 32(5), , 1997a. requires novel approaches, and some progress in that Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, direction is being made [Wang et al., 1998]. H. Rungaldier, H. R. Thompson Jr., and R. Yee, Microwave scattering physics, 2, Doppler spectra of scattering Acknowledgment. This work was supported by contract DMA C References Barrick, D. E., Near-grazing illumination and shadowing of rough surfaces, Radio Sci., 30(3), , Barter, J. D., and P. H. Y. Lee, Polarimetric optical imaging of scattering surfaces, Appl. Opt., 35, , Goldstein, H., Sea echo, in Propagation of Short Radio Waves, Mass. Inst. of Technol. Radiat. Lab. Ser., vol. 13, 1st ed., edited by D. E. Kerr, pp , McGraw-Hill, New York, Jessup, A. T., W. K. Melville, and W. C. Keller, Breaking waves affecting microwave backscatter, 1, Detection and verification, J. Geophys. Res., 96(Cll), 20,547-20,559, Kalmykov, A. I., and V. V. Pustovoytenko, On polarization features of radio signals scattered from the sea surface at small grazing angles, J. Geophys. Res., 81(12), , Kwoh, D. S. W., B. M. Lake, and H. Rungaldier, Microwave scattering from internal wave modulated surface waves: A shipboard real aperture coherent radar study in the Georgia Strait Experiment, J. Geophys. Res., 93(C10), 12,235-12,248, Lee, P. H. Y., J. D. Barter, K. L. Beach, E. Caponi, C. L. Hindman, B. M. Lake, H. Rungaldier, and J. C. Shelton, Power spectral line shapes of microwave radiation backscattered from sea surfaces at small grazing angles, IEE Proc. RSN, 142(5), , 1995a. Lee, P. H. Y., J. D. Barter, K. L. Beach, C. L. Hindman, B. M. Lake, H. Rungaldier, J. C. Shelton, A. B. Williams, R. Yee, and H. C. Yuen, X band microwave backscattering from ocean waves, J. Geophys. Res., 100(C2), , 1995b. Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, J. C. Shelton, H. R. Thompson Jr., and R. Yee, Depolarization in microwave scatterometry, in Proceedings, 1996 International Geoscience and Remote Sensing Symposium, vol. IV, pp , IEEE Press, Piscataway, N.J., 1996a. from wind waves with mechanically generated gravity waves, Rep UT-16.1, TRW, Redondo Beach, Calif., Oct. 22, 1997b. Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, H. R. Thompson Jr., and R. Yee, Micro- wave scattering physics, 3, Radar cross section of scattering from wind waves with mechanically generated gravity waves, Rep UT-17.1, TRW, Redondo Beach, Calif., Oct. 31, 1997c. Lee, P. H. Y., J. D. Barter, K. L. Beach, B. M. Lake, H. Rungaldier, H. R. Thompson Jr., and R. Yee, Scattering from breaking gravity waves without wind, IEEE Trans. Antennas Propag., 46, 14-26, 1998a. Lee, P. H. Y., J. D. Barter, B. M. Lake and H. R. Thompson, Jr., Line shape analysis of breaking-wave Doppler spectra, IEE Proc. RSN, 145(2), 135, 1998b. Leykin, A. I., I. Y. Ostrovskiy, A.D. Rozenberg, V. G. Ruskevich, and I. M. Fuks, The effect of long waves on energy spectra of radar signals scattered from a sea surface, Izv. Vyssh. Uchebn. Zaved Radiofiz., 3, , Long, M. W., On a two-scatterer theory of sea echo, IEEE Trans. Antennas Propag., 22, , Mel'nichuk, Y. V., and A. A. Chernikov, Spectra of radar signals from sea surfaces for different polarizations, Izv. Atmos. Ocean. Phys., 7, 17-24, Phillips, O. M., The dispersion of short wavelets in the presence of a dominant long wave, J. Fluid Mech., 107, , Pidgeon, V. W., Doppler dependence of radar sea return, J. Geophys. Res., 73(4), , Plant, W. J., A model for microwave Doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves, J. Geophys. Res., 102(C9), 21,131-21,146, Valenzuela, G. R., Scattering of electromagnetic waves from the ocean, in Surveillance of Environmental Pollution and Resources by Electromagnetic Waves, edited by T. Lund, pp , D. Reidel, Norwell, Mass., Voronovitch, A. G., On the theory of electromagnetic waves scattering from the sea surface at low grazing angles, Radio Sci., 3 (6), , Wang, L., P. H. Y. Lee, J. D. Barter, and M. Z. Caponi,

16 138 LEE ET AL.: NON-BRAGG SCATTERING MECHANISMS Electromagnetic wave propagation in and scattering from random media, Appl. Phys. Lett., 72(15), , Wright, J. W., A new model for sea clutter, IEEE Trans. Antennas Propag., 16, , Yuen, H. C., and B. M. Lake, Nonlinear dynamics of deep-water gravity waves, inadvances in Applied Mechanics, vol. 22, edited by C.-S. Yih, pp , Academic, San Diego, Calif., J. D. Barter, K. L. Beach, B. M. Lake, P. H. Y. Lee, H. Rungaldier, H. R. Thompson Jr., L. Wang, R. Yee, TRW Space & Electronics, Rl-1008 One Space Park, Redondo Beach, CA ( james.barter@trw.com) (Received November 28, 1997; revised October 1, 1998; accepted October 28, 1998.)