Microwave backscattering from water waves with non-uniform crests

Abstract

Sea spikes are events in low grazing angle (LGA) microwave backscattering from the sea surface where the instantaneous backscattering is much larger the mean background level. In this paper. the backscattering from breaking wave crests with more complicated shapes is examined.

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Microwave Backsattering from Water Waves with Non-Uniform Crests
Yanzhong Li and James C. West
Electrical & Computer Engr., Oklahoma State University, Stillwater, OK
74078, jwest@okstate.edu
Introduction
Sea spikes are events in low grazing angle (LGA) microwave backscattering from the sea
surface where the instantaneous backscattering is much larger the mean background level.
Sea spikes often include “super events” where the horizontally polarized backscatter (HH)
exceeds that at vertical (VV) by 10 dB or more. Sea spikes/super events have been ex-
perimentally correlated with breaking water waves. West [1] examined the scattering from
the crests of breaking waves and showed that interference between the direct back-reflection
from distinct points on the jetting crest contributes to the sea spike signatures (in addition to
the previously identified mulitpath interference mechanism). The back-reflections from the
convex reflection point on the jet and the concave reflection point in the cavity under the jet
undergo differing phase shifts at the two polarizations when the surface radii of curvature at
the two points are less than an electromagnetic wavelength, leading to constructive interfer-
ence at HH and destructive interference at VV. The two-dimensional numerical study in [1]
was extended to three dimensions by Li and West [2]. However, the wave crest was limited
to a smooth shape with little azimuthal variation in [2]. In this paper, the backscattering
from breaking wave crests with more complicated shapes is examined.
Method
The test surfaces were derived from the crests of the waves in the numerically generated
LONGTANK series, shown in Fig. 1 [3]. The two-dimensional crests were aligned az-
imuthally to give crests that vary in the third (azimuthal dimension). Spline interpolation
was used to find the points between the individual LONGTANK profiles. The scatter-
ing from the profiles was found using the multi-level fast multipole algorithm (MLFMA).
The particular implementation of MLFMA used is described in Zhao and West [4]. This
implementation uses standard RWG basis functions to describe the complicated three-
dimensional variation of the waves, Impedance boundary conditions are used to represent
the finite conductivity of the water surface. Diffraction from the edges of the wave surface
introduced by the truncation of the LONGTANK profiles is suppressed by the addition of
resistive loading near the edges. This procedure is described in detail in [4] and [2]. All
scattering calculations shown were performed at 10 GHz.
Results
The effect of the introduction of azimuthal variation of differing degree on the backscatter-
ing isfirstexamined. Fig. 2shows aseries of test cases derived from the LONGTANKseries
at the time when the jet is first becoming distinctly formed. In each of the three surfaces
shown, the maximum extents of the jet (six points per surface) were derived from LONG-
TANK wave 13. The jet minima were found from LONGTANKprofiles 12.5, 12, and 11 in
parts a, b, and c respectively. (LONGTANK profile 12.5 means it was interpolated halfway
between waves 12 and 13.) Part d of the figure shows the calculated upwave-looking
backscattering cross-sections. The backscattering from the small and medium roughness
This work was supported by the U.S. Office of Naval Research under grant N00014-03-1-0134.
0-7803-8883-6/05/$20.00 ©2005 IEEE

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Figure 1: LONGTANK wave profiles used to synthesize test wave crests.
crests show the deep VV null at approximately 75◦incidence (15◦grazing) that was ob-
served in the 2-D backscattering from profile 13. This results from destructive interference
between the jet and cavity back-reflection points. At HH the phase shifts at the reflection
points are opposite so the interference is constructive. With the largest roughness, both
the depth of the VV null and the magnitude of the HH constructive interference decrease.
The VV null becomes smaller since the back-reflection from the minima between the jet
maxima becomes significant. The HH backscattering on the other hand decreases since the
azimuthal radius of curvature at the reflection points on the jet maxima becomes sufficiently
small to give much smaller cross-sections.
Fig. 3 shows another test case formed from the end of the LONGTANK series. The
jetting is therefore fully formed and about to impact the wave face in this case. The peak jet-
ting in each test crest was derived from LONGTANK wave 18. The jet minima were found
from waves 17.5, 17, and 16 in parts a, b, and c, respectively. The backscattering from the
small and medium roughness cases show super events at the smallest incidence considered
(largest grazing) which slowly disappear as the incidence increases to 90◦. The cavity re-
flection point under the jet is shadowed from direct illumination, so the super event is due to
a more complicated scattering process than simple quasi-specular back-reflection. The VV
backscattering is nearly unchanged as the roughness changes from small to medium, while
the HH backscattering drops approximately 3 dB. As the roughness is further increased to
the roughest case, the VV backscattering is again nearly unchanged. The HH backscatter-
ing is dramatically affected, however, showing a strong interference null at 74◦incidence.
This is the first time that a strong HH null has been observed in LGA backscattering from
a wave crest profile. It may may result from interference between the azimuthally convex
reflection point at the tip of the jetting maxima and the concave point at the minima.
A simplified model of the scattering from the wave crests is to treat the individual
reflection points separately, and to coherently add the scattering from the individual reflec-
tion points to yield the total crest reflection. To test the feasibility of the approach, narrower
sub-surfaces were formed with only one jet maximum (no minima), and with two maxima
and one minima between the jets. The scattering associated with the jet maxima was found
by applying MLFMA to the single-maximum surface. The scattering associated with the jet
minima was found by coherently subtracting the twice single-maximum-surface scattering
from the two-maxima-surface scattering. The backscattering from a crest with any num-
ber of maxima/minima could then be found by coherently adding the associated scattering
from each isolated feature. The results when applied to a crest of the form in Fig. 2a (but
with only three jet maxima) is shown in Fig. 4a. The synthesis procedure gives an excellent
prediction of the total MLFMA backscattering from the full surface. The indivdual scatter-
ing features can therefore be isolated and treated separately in this case. The results when

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(a) Small roughness(b) Medium roughness
(c) Roughest
60 6570
Incident Angle (degree)
75808590
−40
−35
−30
−25
−20
−15
−10
−5
0
RCS (dB − λ2)
VV (Smooth)
HH (Smooth)
VV (Medium)
HH (Medium)
VV (Rough)
HH (Rough)
(d) Backscattering
Figure 2: Test case near the initial formation of the jet. The widths of the profiles are
approximately 42 cm in each case.
applied to a three-maxima surface of the form shown in Fig. 3c are shown in Fig. 4b. The
performance is poorer here, indicating that the more extreme jetting leads to multiple inter-
actions between the features. Modeling the backscattering in this case will be considerably
more difficult.
References
[1] J. C. West, “LGA sea-spike backscattering from plunging breaker crests,” IEEE Trans.
Geosci. Remote Sens., vol. 40, no. 2, pp. 523–526, Feb. 2002.
[2] Y. Li and J. C. West, “Microwave scattering from 3-d breaking water wave crests,”
in Proceedings of the 2004 International Geoscience and Remote Sensing Symposium,
September 20-24, Anchorage, Alaska, 2004, pp. 406–409.
[3] P. Wang, Y. Yao, and M. P. Tulin, “An efficient numerical tank for non-linear water
waves, based on the multi-subdomain approach with BEM.” Int. J. Num. Meth. Fluids,
vol. 20, no. 12, pp. 1315–1336, June 1995.
[4] Z. Zhao and J. C. West, “Resistive suppression of edge effects in mlfma scattering from
finite conductivity surfaces,” IEEE Trans. Antennas Propagat., 2005, in press.

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(a) Small roughness(b) Medium roughness
(c) Roughest
606570
Incident Angle (degree)
75808590
−40
−35
−30
−25
−20
−15
−10
−5
0
RCS (dB − λ2)
VV (Smooth)
HH (Smooth)
VV (Medium)
HH (Medium)
VV (Rough)
HH (Rough)
(d) Backscattering
Figure 3: Test case near the end of LONGTANK series. The widths of the profiles are
approximately 52 cm in each case.
6065 70
Incident Angle (degree)
7580 85 90
−40
−35
−30
−25
−20
−15
−10
−5
0
RCS (dB − λ2)
VV (MLFMA)
HH (MLFMA)
VV (Syn.:A+2C)
HH (Syn.:A+2C)
(a) Crest similar to Fig. 2a.
60 6570
Incident Angle (degree)
758085 90
−40
−35
−30
−25
−20
−15
−10
−5
0
RCS (dB − λ2)
VV (MLFMA)
HH (MLFMA)
VV (Syn.:A+2C)
HH (Syn.:A+2C)
(b) Crest similar to Fig. 3c.
Figure 4: Synthesis of backscattering from crests with three jet maxima.