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Polarization dependency ofenhanced multipath radarbackscattering from an ocean-likesurfaceS G Hanson a c & V U Zavorotny ba Environmental Technology Laboratory, NOAA , 325Broadway, Boulder, CO, 80303, USAb Cooperative Institute for Research in EnvironmentalSciences , University of Colorado/NOAA , Boulder, CO,80309-0216, USAc Risø National Laboratory , 4000, Roskilde, DenmarkPublished online: 11 Feb 2011.

To cite this article: S G Hanson & V U Zavorotny (1995) Polarization dependency ofenhanced multipath radar backscattering from an ocean-like surface, Waves in RandomMedia, 5:2, 159-165, DOI: 10.1088/0959-7174/5/2/001

To link to this article: http://dx.doi.org/10.1088/0959-7174/5/2/001

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Waves in Random Media 5 (1995) 159-1651 Printed in the UK

LETTER.TO THE EDITOR

- ~ Polarization dependency of enhanced multipath radar backscattering from an ocean-like surface

S G Hansonts and V U Zavorotnyt t Environmental Technology Laboratory, NOAA, 325 Broadway, Boulder, CO 80303, USA $ Cooperative InstiNte for Research in Environmental Sciences, Univeniry of Colorado/NoAA, Boulder, CO 803094216, USA

Received 5 January 1995

Abstract. Previous analyses of eledmnagnetic scattering from a two-scale ocean surface assumed the tilts on a large-scale surface to be small. This means that multiple scattering between largescale roughnews is insignificant If the tilts are not small, multipath-enhanced backscattering may occur due to quasi-specular reflections between the oppasite slopes of a large- scale surface component. We have considered the simplest situation; this involves one reflection from the large-scale component and one single-scattering from the small-scale component. The coherent addition of this process to the reciprocally reverse one creates multipathenhanced backscattering. The relalive m* in the HH backscattering cross section up to the level of the VV signal was obtained for surface-wave slopes of about 30' and for large incidence angles. This gain occurs because the VV signal experiences an extinction during reflection at incidenr angles close to the pseudo-Brewster angle. The presented model provides insight into one scattering mechanism lhat is possibly responsible for the d e p h of radar sea experimental data from predictions by the conventional two-scale model.

The standard theory of electromagnetic scattering from rough surfaces which is generally used for the interpretation of microwave radar observations includes: (i) the Kirchhoff approximation, which is usually applied for near-normal incidence and describes quasi- specular reflection from largescale gravity waves; and (ii) first-order perturbation theory for larger angles of incidence, which describes Bragg resonant scattering by ripples [I]. Modification of the latter approach, the two-scale model, takes into account a large-scale tilt modulation 121. Although these two approaches cover a rather wide range of incidence angles, there is a region of large incident angles where the signal behaviour cannot be explained merely by Bragg scattering. Signals received by radars wi$ a high spatia-temporal resolution usually contain so-called radar sea spikes with an HH/W ratio close to 0 dB [3,4]. Returns from radars with a low spatia-temporal resolution may demonstrate HH/W ratios from about -10 dB to 0 dB. This depends on the overall conhibution of the spiky component to the signal integrated over large radar footprints or over large registration times 151.

Various explanations for the polarization peculiarities of radar sea backscattering have been proposed. The most well known are: (i) a quasi-specular scatter model used to explain results for moderate grazing angles (see e.g. [3]); (ii) a wedge model describing diffraction from sharply crested waves [ H I ; (iii) a spilling breaker plume model in which the spilling breaker produces some kind of local comer reflector on the front face of long waves 191; and

- 3 Permanent address: Rise National Laboratory, 4000 Roskilde, Denmk.

0959-7171195/010159+07$19.50 @ 1995 IOP Publishing LLd 159

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160 Letter to the Editor

(iv) a shadowing model, which incorporates a polarization-dependent shadowing function into the conventional two-scale model [lo]. Each of these probably reflects some specific part of the phenomenon.

Below, we discuss another important mechanism that relies on multiple scattering at a moderate grazing incidence. Of course, this mechanism can be considered in combination with the others listed above. This model, along with conventional Bragg scattering from small-scale roughnesses (ripples), involves a specular reflection from the backside of a large- scale roughness (a gravity wave) toward its next face slope. Such a reflection produces additional illumination of ripples at the face slope. At the same time, due to a reciprocity of this process, radiation also scatters from the face slope towards the back slope, and is then reflected from the back slope towards the radar (see figure 1). It is known that, near the pseudo-Brewster angle, the amplitude of the specularly reflected wave at vertical polarization experiences a significant decrease, whereas the wave at the horizontal polarization does not. If this fact is incorporated into the suggested multiple-scattering model, it could qualitatively explain the relative increase in the HH/W ratio observed at large incident angIes compared to the HHjW ratio calculated from the Bragg-scattering model.

a i

I I V ,

Figure 1. Scattering geomeiry for a twoscale wave model

The conventional two-scale Bragg model takes into account only singlescattering events on ripples, a small-scale component (.$) of the ocean surface. However, for sufficiently steep large-scale waves, some part of the specularly reflected radar signal can again cross the ocean surface, producing an additional illumination. The conventional two-scale model does not account for this process, even though the contribution given by this multipath process is also of the first order of an elevation of the small-scale roughness, e. Analysis of this scheme was done in [ 11,121 for the example of a scalar problem with Dirichlet boundary conditions on a two-scale rough surface. It was shown that the complex amplitude of a backscattered scalar field can be represented as a sum

U = U% + Umfl-sc +- USC-refl (1)

where U- is the field directly Bragg-scattered on e-roughnesses; ulefi--sc is the wave field that first experiences a quasi-specular reflection by the large-scale roughness 5 and is subsequently scattered by the .&roughness; u s c - ~ is the wave field scattered as unfl-sc, but in an inverse sequence.

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Letter to the Editor 161

Finally, we may consider the intensity of the backscattered field averaged over fluctuations t :

I = (uu*) = ( U . , U 3 + (u8c(u;fl-sc + U L f l ) ) + (Uk(%-ree + 4d-d + (U,fl-scU:fl-s)

- i- (u,,-,flu:c-,fl) + (u,fl-sc~:c-,fl) + (u;fl-sc~,,-ml). (2)

The meaning of the first term in (2) is obvious. The second and third terms are the results of interference between the field U,, and the fields u,fi-scr usc-rcfl. After averaging over the statistics of the large-scale component these terms become negligible. The fourth and fifth terms are the mean intensities of waves that have experienced specular reflection before and after scattering on the small-scale roughnesses. Finally, the sixth and seventh terms are produced by the interference of waves ufi--sc and uSc-refl. For the monostatic backscattering geometry, i.e. for the collocated transmitter and receiver, coherent superposition of the fields u,fi-sc and u,,-,fl occurs constantly, because these waves have the same phase shifts. One can see that the last four terms are identical to each other because of their reciprocity. Hence, we can replace them by one term multiplied by 4. The last two terms in (2) demonstrate some specific type of enhanced backscattering from rough surfaces with moderate slopes of large-scale surface components. Other types of the enhanced backscattering effect are possible for very rough surfaces [13], when, for example, multiple scattering of higher orders occurs.

Although (1) and (2) are obtained for the scalar wave problem, it is clear that the same equations can be written for the electromagnetic case. However, the derivation of analytical expressions for each term in (2) for a general case is a difficult problem which will not be discussed here. Instead, we obtain the polarization characteristics of interest in quite an obvious way, using a simplified . . model for the surface shown in figure 1. It consists of two components: a large-scale (compared with the radiation wavelength) &angular-groove surface (modelling gravity waves) covered with small-scale random roughnesses (modelling resonant ripples). In this paper we will treat a homogeneous distribution of ripples over the triangular wave, and we assume that there is no geometrical shadowing of the large-scale surface with respect to the source and receiver. We further assume that the transmitted pulsewidth of our radar signal is much greater than the possible temporal broadening of the received pulse caused by multipath scattering from the surface.

We can calculate the horizontally and vertically polarized components of the field specularly reflected by the back slope toward the forward slope using the well-known expressions for Fresnel reflection coefficients, Rhor and Rvep It should be noted that the absolute values of RhOr and Rver behave differently. Where IRhOrl is slowly increasing at large~angles of incidence, IRverl is considerably lower and has a minimum at the pseudo- Brewster angle, OB. For A = 3 cm the relative dielectric constant of water is = 48 - 35i and & = 83". Knowing the approximated form of the wave and the complex reflection coefficient R, we can obtain an expression for the total incident field at the forward slope of the pvvity wave. At this point we neglect the influence of ripples on a surface reflectivity according to the approach presented in [ll, 121.

After incorporating specular reflection between slopes into our model, the corresponding effective backscattering cross section of such a surface becomes

1 2cos y

U&= - [U1 + U2 + 2"1 (3)

- where U, and m2 are the normalized backscattering cross sections of slopes 1 and 2, respectively; uI2 is a term due to the multiple scattering described above. We introduce the

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162 Leiter :o the Editor

factor N in the last term to account for the possible effect of an enhanced backscatter caused by double passage and coherent addition of scattered waves along the closed trajectory from the radar to slope 1 to slope 2 and back to the radar as well as in the opposite direction. If this is so, N = 2. If, for some reason, a coherent addition of these waves is unavailable, e.g. when transmitter and receiver are separated, then N = 1.

The backscattering cross section of a dielectric rough surface calculated in first-order perturbation theory is shown in [2] to equal

where W(q,, qy) is the two-dimensional wavenumber spectral density of the surface roughness t ( ~ ) . The wavevector of the incident radiation is assumed- to be in the x-z plane, where z is the vertical direction. The functions g:)()(B) are the first-order scattering coefficients that depend on the polarization state of the emitted radiation as well as on the polarization state of the detected radiation as indicated by the subscripts i, j . In the cases of transmitting and receiving the same polarization we have gi&) for horizontal polarization, and gg(6') for vertical polarization. According to the two-scale model [Z], which we follow below, equation (4) is applicable for a local description of wave scattering on each arbitrary tilted surface facet (the large-scale component of the surface wave). The absence of source-receiver shadowing by the triangular wave implies that

?( e o < - - Y 2

where 80 is the mean incidence angle, and y = a tan(2alA) is the angle of slope of the triangular wave. We also assume the period of the large-scale gravity wave, A >> A. The backscattering cross sections for each isolated slope in (4) are thus given by

u1 = U:)@ = eo + y ) ~ u2 = ,,!!)(e 11 =eo - yj. (6)

Under the condition of illumination of slope 2 by the radiation reflected from slope 1

the term u12 in (4) is simply the normalized bistatic cross section of slope 2 when the incident wave after reflection comes iiom the'side of slope 1, and the scattering wave propagates toward the receiver direction. The following expression for u12 can be derived using first- order perturbation theory for electromagnetic waves scattered by a rough dielectric surface (see e.g. [14]):

u , ~ = 4 ~ k ~ i ~ ~ ~ ( e ~ + Y ) I ~ C O S ~ ( ? T -eo - ~ Y ) C O S ~ ( O ~ - y) ib i j ( z -eo - , 3 ~ ; Y - eo)i 2

x W(Xsin(Bo+ y)cos2y,O) (8 )

where

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Letter to the Editor

and

163

(1) When e,, = -01, expressions (9) and (10) give the expressions for g,$!,(B) and gvv(e) for the monostatic case. The basic scattering mechanism for all components of the effective backscattering cross section (4) is Bragg scattering. Because ,of this the polarization behaviour of these components~ is determined by functions gij or bij. However, the third term, qz, contains an additional polarization factor, [RijI2: which suppresses this term for the VV polarization compared with the HH polarization i n the vicinity of the pseudo- Brewster angle. One may expect that, because of this effect, the values for the effective backscattering cross sections at different polaiizations could become closer than for the case of single Bragg scattering. Below, we present some numerical calculations to demonstrate the importance of this effect.

All calculations were performed with radiation in the X-band (at a wavelength of 3 cm), and a dielectric constant of 48 - 35i. The spechum of the ripples is chosen in the form: W ( q ) = Aq-4. For simplicity, it was assumed that the amplitude of the spectrum A does not depend on the position on the large-scale triangular wave, i.e. the case of a homogeneous distribution of ripples is considered. Also, our~calculations correspond to the case when the period of the large-scale wave is small compared with the spatial resolutions of the radar. In figure 2 we have plotted scattering cross sections normalized by a factor 4rrk2A for both horizontally and vertically polarized radiation as functions of the mean incident angle 00 for y = 30". Curves 1 and 2 show the result obtained from the first two terms of (4). These curves correspond to the standard two-scale model. Curves 3 and 4 are obtained using all terms of (4) and N = 2 (a coherent addition). .These curves demonstrate HH polarization cross sections approaching and even exceeding the levels of the W polarization ones at incident angles about 50"+0°.

It has been shown that the experimentally observable fact 13-51 of the relative increase in the horizontally polarized sea-radar return compared to the vertically polarized one at large incident angles can be explained by considering multipath scattering between sufficiently steep gravity waves.

This result is obtained using a triangular shape for the dominating gravity wave and a homogeneous distribution of ripples. It is shown that a 10 dB increase in the expected radar cross section could be achieved due to multipath scattering of the horizontally polarized radiation for the wave slope angle y = 30". This effect is based on having the back slope of the large-scale gravity wave as a specular dielectric reflector which creates an additional channel for both incident and scattered radiation. The same channel for the vertically polarized radiation causes a relative decrease in the multipath signal as the local grazing angle for the back slope approaches the pseudo-Brewster angle. At incident angles about 50"-60°, the resultant backscattering cross section (including the direct Bragg scattering) has HH polarization cross sections approaching and even exceeding the levels of the W polarization ones.

The presented theoretical consideration is limited by use of first-order perturbation terms for scattering from ripples and specular reflection from slopes of largescale gravily waves. However, our intention was to discuss the reliability of the idea of this effect. A direct comparison between this model and measurements might give slightly different quantitative

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I 40.0 42.0 44.0 45,O 48.0 10.0 52.0 14.0 56.0 58.0

Angle of incidence tdeg.1

Figure 2 Normalized backscattering cross sections for horizontally (curves 1 and 3) and vertically polarized radiation (curves 2 and 4) as functions of the incident angle.

results due to the unrealistic sea-surface model. In a more realistic sea-surface model, the use of a concave shape for the dominant gravity waves would create additional focusing of the secondary illumination on the forward slopes, as well as a more pronounced enhanced backscattering effect because the surface curvature gives a factor N >> 2. The latter effect is similar to that described in [15]. On the other hand, the homogeneously distributed wind ripples are not the only type of scatterer on the sea surface. Various non-Bragg scatterers associated with near-crest areas of breaking gravity waves should be included in a realistic sea-surface model.

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[IS] Zavorotny V U and Tatarskii V I 1982 Intensification of backscattering of waves by a body located near the irregular boundary of two media SOY. Phys.-Dokl. 27 566-7

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