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Analysis of dual-polarization microwave ocean images obtained with a high-resolution X-band radar

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A
n a l y s is o f
D
u a l - P o l a r iz a t io n
w it h a
H ig h - R
M
ic r o w a v e
e s o l u t io n
O c e a n Im a g es O
b t a in e d
X -B a n d R a d a r
A Dissertation Presented
by
Y
ong
L iu
Subm itted to the Graduate School of the
University of Massachusetts Amherst in partial fulfillment
of the requirements for the degree of
Doctor
of
P
h il o s o p h y
September 1997
D epartm ent of Electrical and Computer Engineering
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© Copyright by Yong Liu 1997
All Rights Reserved
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A n a l y s is
of
D
u a l - P o l a r iz a t io n
w it h a
H ig h - R
M ic r o w a v e O c e a n I m a g e s O
X - B a n d Ra d a r
b t a in e d
e s o l u t io n
A Dissertation Presented
by
Y o n g L iu
Approved as to style and content by:
Robert Jhf. McIntosh, Chair
Calvin T. Swift,
CL M
D
,
iH. Schaubert, Member
George Kn/gmly, Mei
ler
Daniel H. Schaubert, D epartm ent Head
Electrical and Computer Engineering
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To m y wife, Dilei.
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A cknow ledgem ents
I want to express my gratitude to my thesis advisor Professor Robert McIntosh
for giving me the opportunity to study and work in the Microwave Remote Sensing
Laboratory (MIRSL). T he incredible research facilities he and Professor Calvin
Swift established at MIRSL have made it possible for graduate students to develop
rem ote sensing instrum ents and to study the earth, ocean and atmosphere using
these instruments.
I would like to thank Professor Swift, Professor George Knightly and Professor
Daniel Schaubert for serving on my Ph.D. committee, and Professor Haluk Derin for
serving on my oral com m ittee. Professor Schaubert agreed to serve on my com m ittee
only three weeks before my defense due to the unavailabitiy of Professor Derin, and
deserves my special gratitude.
I would like to thank Professor Stephen Frasier, whom I worked with for most of
the years I spent at MIRSL, for showing m e how to approach a problem and solve
it w ith different tools, for teaching me little things that a foreigner will not learn
in a classroom, and for allowing me enough space to develop and get used to the
workings of MIRSL.
Focused Phased Array Imaging Radar (FOPAIR) project was supported by
th e Office of Naval Research grant N00014-93-1-0261.
Dr.
Frank Herr of ON R
provided the early support of the project and suggested th a t FOPAIR be installed
on the Float Instrum ent Platform (FLIP). Dr.
Dennis Trizna maintained the
program and provided continued support through the later years. They deserve
m y acknowledgment and thanks.
The research results presented here took place on research platform FLIP with
help from Drs. Ken Melville and Anatol Rozenberg and their staff at the University
v
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of CaUfomia, San Diego (UCSD). I have benefited greatly from m any discussions
w ith them . I am also indebted to the crew members of FLIP for providing me my
first ever ocean cruise trips, and to the staff a t the Marine Physical Laboratory at
UCSD for installing FO PA IR on FLIP - a very non-trivial task!
Finally, I would like to thank all MIRSL staff members for th eir support during
my stay here.
vi
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A bstract
A
n a l y s is o f
D
u a l - P o l a r iz a t io n
w it h a
M ic r o w a v e O c e a n I m a g e s O b t a in e d
H ig h - R e s o l u t i o n X - B
and
Radar
Septem ber 1997
Y o n g L iu
S .B .E .E ., M a s s a c h u s e t t s I n s t i t u t e
P h .D ., U n i v e r s i t y
of
of
T
echnology,
M a ssach usetts A
C a m b r id g e
m h er st
Directed by: Professor Robert E. McIntosh
Dual-polarized X-band ocean images were obtained using a high-resolution phasedarray rad ar at 3° grazing angle. For vertical polarization, the backscatter can be
explained using resonant scattering and Composite Surface Theory. For horizontal
polarization, the backscatter is dominated by discrete strong scattering events with
high Doppler, or sea-spikes. Sea-spike properties are presented and compared with
several low-grazing-angle ocean scattering models. Comparison of larger sea-spikes
with surface wave features indicates that approximately 30% of observed sea-spikes
are associated with actively breaking waves (whitecaps), while the remainder are
identified with steep wave features which m ay or m ay not break.
Using the imaging n atu re of the radar, statistics of sea-spike spatial and temporal
properties are derived and compared with surface wind and wave parameters. Seaspikes tend to travel in th e direction of the wind at a speed considerably slower than
the phase speed of the dom inant waves, but are consistent with a breaking wave scale
based on the downward acceleration spectrum. Surface coverage of sea-spikes has a
power-law dependence on friction velocity w ith an exponent of 2.3, while sea-spike
event density does not show a converging dependence on wind speed or friction
velocity.
vii
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Table
of
Contents
Page
A c k n o w l e d g e m e n t s ...................................................................................................
v
ABSTRACT............................................................................................................................ vii
L is t O
f
Ta
...................................................................................................................................
x
L is t O
f
F ig
................................................................................................................................
xi
1 . I n t r o d u c t i o n .................................................................................................................................
1
bles
u r es
C hapter
LI
1.2
1.3
2.
Motivation.......................................................................................................
Review of Literature.....................................................................................
Summary of Chapters...................................................................................
R a d a r Sy stem
2.1
2.2
e n t ....................................................................
7
Review of Imaging Principles....................................................................
7
2.1.1
2.1.2
Beamforming......................................................................................
Focusing..............................................................................................
7
8
Summary of Radar S ystem .........................................................................
10
2.2.1
2.2.2
2.2.3
2.3
H ardw are...........................................................................................
C alibration.........................................................................................
Data P ro cessin g ...............................................................................
11
11
15
MBL/FLIP Experim ent..............................................................................
16
2.3.1
2.3.2
2.3.3
Experiment O b jective.....................................................................
FOPAIR S e tu p .................................................................................
Data Sum m ary.................................................................................
3 . In t e r p r e t a t io n
3.1
3.2
ofR a d ar
Im
a g e s ................................................................................
16
17
17
22
Bragg Scattering M o d el.............................................................................. 22
Image Characteristics.................................................................................. 24
3.2.1
3.2.2
3.2.3
3.3
and
F ie l d E x p e r i m
1
2
4
Vertical Polarization....................................................................... 24
Horizontal Polarization .................................................................. 31
Range-Time Images.......................................................................... 31
Doppler Spectra............................................................................................. 33
viii
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3.3.1 Vertical P o la riz a tio n .......................................................................... 35
3.3.2 Horizontal P o la riz a tio n ..................................................................... 36
3.4 Evidences of Non-Bragg S c a tte r in g ............................................................
4. P h y s i c a l P
36
r o p e r t i e s o f S e a S p i k e s .....................................................................38
4.1 Identification of Sea-S pikes............................................................................ 38
4.1.1 Coherence M eth od ............................................................................... 39
4.1.2 Power M eth o d ...................................................................................... 41
4.1.2.1
4.1.2.2
4.1.2.3
Noise S t a tis t ic s .................................................................
Determ ination of Power T h r e s h o ld ..............................
Backscatter D istrib u tio n ..................................................
43
43
45
4.2 Sea-Spike P roperties........................................................................................
47
4.2.1 Doppler S p e c t r a ................................................................................. 47
4.2.2 Polarization C h a ra c te ristic s ............................................................. 49
4.3 Sea-Spike Classification and Comparison with W h ite c a p s ..................... 52
4.3.1
4.3.2
4.3.3
4.3.4
Comparison P ro ced u re.......................................................................
Sample Radar and Video Images ..................................................
Sea-Spike C lassificatio n ....................................................................
S u m m a ry ..............................................................................................
53
54
59
66
4.4 D iscussion.......................................................................................................... 66
4.4.1
4.4.2
5. B r e a k i n g
5.1
5.2
5.3
5.4
w a v e pr o p e r t i e s an d en v i r o n m e n t a l p a r a m e t e r s
66
71
75
I n tro d u c tio n ..................................................................................................... 75
R adar D ata and Wind and Wave M easurem ents..................................... 77
Sea-Spike Event Detection and T r a c k in g .................................................. 78
Geometrical Statistical Properties of S ea-Spikes..................................... 83
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.5
Scattering M o d e ls ..............................................................................
Breaking W aves...................................................................................
Event D u r a tio n s .................................................................................
Propagation D ire c tio n .......................................................................
Event Propagation S p e e d .................................................................
Breaking Wave Scales and Sea-Spike V e lo c ity .............................
Sea-Spike Event Coverage and D e n s ity .........................................
83
83
87
90
96
D iscussion........................................................................................................... 104
6 . C o n c l u s i o n s .............................................................................................................. 107
References
..................................................................................................................... 109
ix
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L is t
of
T ables
Table
4.1
Sea-spike classifications. < Pv > and < Ph > are the backscatter
power normalized to the m ean V-Pol Bragg backscatter level for V
and H sea-spikes. Vv and Vk are Doppler centroids, < 7 > is the
m ean polarization ratio, and Cp is the phase speed of the dom inant
gravity waves....................................................................................................
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L is t
of
F ig u r e s
Figure
2.1
Page
Focused phased array geometry. The array is along the Y-axis. The
arc represents th e range interval to be focused on.....................................
9
2.2
FOPAIR system block diagram .....................................................................
12
2.3
Calibration and alignm ent of W /H H radar images.Scales are exag­
gerated
14
FOPAIR configuration on FLIP during MBL experiment. FLIP is in
the “flipped” or vertical mode........................................................................
18
Wind and wave conditions during the MBL phase II experiment (cour­
tesy of S. Miller of UC Irvine) and FOPAIR data collection times.
Winds were measured a t 16.5 m above the mean surface, and the
direction is given relative to North. Significant wave height H 1 / 3
is calculated as four times th e RMS surface height. FOPAIR data
collection times are marked as circles and other symbols in the bottom
plot. The arrows m ark four radar data sets th at will be com pared with
video d ata............................................................................................................
21
2.4
2.5
3.1
Bragg scattering coefficient (top) and polarization ratio (bottom ) de­
pendence on incidence angle using small roughness model....................... 25
3.2
Radar images for an upwind look, developing sea. Top: vertically
polarized radar images. Bottom : horizontally polarized radar images.
The backscatter is normalized to the mean V backscatter........................
26
3.3 Radar images for an upwind look, developed sea........................................
28
3.4 Radar images for an upwind look, decaying sea..........................................
29
3.5 Radar images for an downwind look, developed sea...................................
30
3.6 Range-time contours of backscatter and Doppler corresponding to case
B shown in figure 3.2. Both W and HH power are normalized with
respect to the m ean W backscatter.............................................................
32
3.7
Doppler spectral density for cases A, B, C and D. Solid curves are W
spectra, dashed curves are HH spectra.........................................................
xi
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34
4.1
Coherence histogram and power-weighted histogram distribution. . . .
40
4.2
Illustrative plot of the relation between P& and Pja. Area under the
dashed curve to th e right of PthreshoU is
while area under the solid
curve to the right of Pthreahoid is P i...............................................................
42
Cumulative probability distribution of noise for d ata record 95050104.
“O ” are measured values and the solid curve is a x 2 distribution with
32 degrees of freedom.......................................................................................
44
4.3
4.4
Top: histogram of the HH backscattered power using all pixels with
p > 0.8 for a d a ta set taken during May 3, when the radar was
looking upwind a t a developing sea. Bottom: cum ulative probability
distribution. 0 dB on abscissa corresponds to an HH backscatter level
equal to the mean W backscatter level....................................................... 46
4.5
Doppler spectra of sea-spikes for four representative cases: (A) down­
wind look, developed sea, (B) upwind look, developing sea, (C) up­
wind look, developed sea, and (D) upwind look, decaying sea................... 48
4.6
VV and HH sea-spike Doppler velocity scatter plots for four repre­
sentative cases: (A) downwind look, developed sea, (B) upwind look,
developing sea, (C) upwind look, developed sea, and (D) upwind look,
decaying sea........................................................................................................
50
Polarization ratio ( y ) histograms for sea-spike pixels for four repre­
sentative cases: (A) downwind look, developed sea, (B) upwind look,
developing sea, (C) upwind look, developed sea, and (D) upwind look,
decaying sea. m i and m 2 are the mean and m edian polarization ratios.
51
Video image corresponding to the radar images in figure 3.2 for up­
wind look of a developing sea (Case B). (a) shows th e overall ocean
surface and the horizon, where the boxed area indicates the radar
footprint, (b) is a stretched version of the boxed area in (a), (c)
shows a color-composite of the radar images where the H backscatter
is coded in red and V backscatter in green. T he yellow area signifies
strong H and V backscatter. Radar images axe transform ed into video
coordinates..........................................................................................................
56
Radar and video images for an upwind look, developed sea (CaseC).
(a) Stretched video images; (b) Color-composite of radar images in
video coordinates...............................................................................................
57
4.10 Same as figure 4.9 for an upwind look, decaying sea (Case D).............
57
4.11 Same as figure 4.9 for a downwind look, developed sea (Case A)
58
4.7
4.8
4.9
xii
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4.12 Sea-spike categories and their percentages in terms of events, pixels,
and total V and H power. Category I: white-caps and active breaking
waves, Category II: steep wave features, Category III: active breaking
waves and steep waves both present, Category IV: no obvious features. 60
4.13 Sea-spike event classification sum m ary for Case A...................................
62
4.14 Sea-spike event classification sum m ary for Case B ...................................
63
4.15 Sea-spike event classification sum m ary for Case C...................................
64
4.16 Sea-spike event classification sum m ary for Case D...................................
65
4.17 Geometries of wedge scattering, (a) Kwoh and Lake’s model, (b)
Kalmykov’s model.............................................................................................
68
4.18 Polarization ratio (7 = ^ tL) variation as a function of depression
VV
angle and internal wedge angle for the wedge geometry depicted in
figure 4.17a.........................................................................................................
69
4.19 Polarization ratio variation as functions of depression angle and in­
ternal wedge angle for wedge geom etry depicted infigure4.17b...................70
5.1 Scatter plot of friction velocity u« and wind speed at 16 m u 16 above
the mean surface................................................................................................
79
5.2 Wave age estimates for the radar d a ta records studied. “O ”,
and
“A ” mark developing, developed, and decaying seas respectively. The
“□ ’s” correspond to the “O ’s” , but were calculated using the phase
speeds of dominant waves due to an early storm. All data were taken
upwind looking...................................................................................................
80
5.3 A space-time map where each blob represents a sea-spike event. The
X, Y and Z axes correspond to azim uth, range and tim e respectively.
Only sea-spike events th at persist longer than 1 second axeshown. . . 81
5.4 Breaking-event-duration distributions. Ti and r2 are the m ean du­
rations for all events and for trackable events. Plots correspond to
(from top to bottom) data taken under developing, fully developed
and decaying seas in May 3, May 4 and May 7 respectively................. 84
5.5 W ind dependence of mean breaking-event durations on log-log scale.
Slopes of the straight-line fits are th e exponents to u , in a power-law
relation r = K u“ , and are provided on the right side...............................
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85
5.6
Sample directional distribution of trackable sea-spike events. T he
plots correspond to data taken under developing (top), and developed
seas (m iddle and bottom ) in May 3, May 4 and M ay 5, respectively.
86
5.7
W ind, wave and event propagation directions. T he angles are given
relative to N orth, (a) T im e history of wind, wave and event directions.
T he developing sea cases are not plotted since th e dom inant waves for
those cases were results of previous storms and were going against the
wind, (b) S catter plot of event and wind directions, (c) Scatter plot
of event an d wave directions............................................................................ 88
5.8
Directional spread of the event propagation direction as a function of
wind speed, calculated as th e standard deviation of the event direction.
89
Scatter plot of the mean Doppler velocity and th e radial component
of the event s p e e d .............................................................................................
91
5.10 Histograms of event propagation speeds for trackable sea-spike events.
Plots correspond to (from top to bottom) data taken under develop­
ing, fully developed and decaying seas in May 3, May 4 and May 7
respectively. ......................................................................................................
92
5.11 Top: m ean event propagation speed vs wind speed. Bottom : mean
event propagation speed vs phase speed of the dom inant waves. The
regression fits only use d a ta records for developed seas ( “+ ” symbols).
“O ” and “A ” symbols are for developing and decaying seas. Slopes
of the fits are provided on the right...............................................................
93
5.12 Normalized mean event propagation speed vs velocity scales of break­
ing waves.
“O” , and “A ” symbols are for developed, developing,
and decaying seas, respectively......................................................................
95
5.9
5.13 Sea-spike coverage and density dependence on it,. Coverage is unitless, while density has th e units of m ~ 2 s~ l .
“O ” , and “A ”
symbols axe for developed, developing, and decaying seas, respectively.
The num bers on the right are the slopes of th e regression fits using
only the d a ta for developed seas..................................................................... 97
5.14 Event density for trackable events (minimum duration of 1 second).
“O ” , and “A ” symbols are for developed, developing, and de­
caying seas, respectively. T he number on the right is the slope of the
regression fit using only th e data for developed seas.................................
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99
5.15 Coverage and density dependence on u , and threshold levels.
“O ” , “A ” and
are for threshold levels of 0 dB, 3 dB, 6 dB and 9
dB above the threshold determined by P/a = 10- 4 , respectively. The
num bers next to the straight lines are the slopes. Only the data for
developed seas are used...................................................................................... 100
5.16 Coverage and density dependence on wind and duration cutoffs.
“O ” , “A ” and
are for all events, events longer than 1 second,
events longer than 1.5 seconds and events longer than 2.5 seconds,
respectively. The numbers next to th e straight lines axe the slopes.
Only th e d ata for developed seas are used.....................................................102
5.17 W hitecap coverage obtained from video recordings of the radar scene.
The regression fits used ail data points where whitecap coverage is
above 10-4 .
“O” , and “A ” symbols are for developed, develop­
ing, an d decaying seas, respectively.
103
5.18 Sea-spike power and mean sea-spike cross section.
“O ”, and “A ”
symbols are for developed, developing, and decaying seas, respectively.
The num bers in the plots are the slopes of the regression fit using only
the d a ta for developed seas................................................................................105
xv
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C
h a p t e r
1
In t r o d u c t io n
1.1
M o tiv a tio n
Ocean surface imaging using microwave radar provides im portant information
on the dynamics of the upper ocean and atmosphere boundary layers. Surface wave
energy and directional distributions can be obtained from radar backscattered power
or Doppler velocity images. Highly resolved surface images also allow scientists to
study transient features such as breaking waves and Langmuir circulations th at
play im portant roles in energy and mass transfers in the boundary layer.
Lab­
oratory studies and open-ocean experiments have shown that the wave breaking
process has a distinct microwave backscatter signature whose characteristics are
consistent with radar sea-spikes, a phenomenon often observed by high-resolution,
low-grazing microwave radars. The interest in sea-spikes originally grew out of the
radar com m unity’s concern for their effects on the detection of near-surface targets,
where an optim al design of a ship-bome search radar requires knowledge of the
statistical properties of the clutter. However, w ith the recent and growing use of
microwave radar in the remote sensing of oceans, it becomes especially necessary
to understand not only the physics of sea-spike scattering, but more im portantly,
the connection between sea-spikes and surface waves, wind conditions, and other
oceanic param eters.
Most previous studies of sea-spikes have been performed in laboratory wavetanks with a few exceptions taking place on the open ocean. These observations
are not always consistent with each other and several different scattering models
for low-grazing-angle ocean backscatter have been proposed to explain the varying
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results. This diversity of experimental results and models has probably contributed
to the confusion in the interpretation of radar rem ote sensing data. A system atic
approach to th e study of open-ocean backscatter at low-grazing angles is therefore
warranted.
An X-band FOcused Phased Array Imaging R adar (FOPAIR) has been devel­
oped by the Microwave Remote Sensing Laboratory (MIRSL) to study ocean surface
waves and other dynamic processes occurring at the air-sea boundary. B ackscattered
power and Doppler velocity images using both vertical and horizontal polarizations
were obtained at near grazing incidence along with video recordings of th e ocean
surface during the Marine Boundary Layer Experiment (MB LEX) in th e spring
of 1995 in California coastal seas.
In this dissertation, I will present physical
characteristics of sea-spikes using MB LEX data, and compare them with scattering
model predictions. Radar sea-spikes are then compared to the visual observations
of breaking waves. Using the imaging capability of FOPAIR, spatial and tem poral
properties of sea-spikes are also derived and related to surface wave and wind
parameters. T he extensive radar sea-spike data presented here will help us b etter
understand the physical mechanisms of backscatter a t low grazing angles. T he close
correlation between radar sea-spikes and wind suggests new ways of utilizing radar
in rem ote measurements of surface wind and waves.
1.2
R e v ie w o f L iterature
The theory of electromagnetic wave scattering from a slightly rough surface was
first developed by Rice [1] using the small perturbation method. It was shown th at
rough surface scattering has a resonant nature similar to the interaction of light with
a crystal lattice as discovered by Bragg [2]. The experimental support for th e small
perturbation theory (SPT) first came from Crombie’s observation of sea echos a t HF
band [3], and later at L, C and X bands [4]. As the radio frequency increases, the
ocean surface can no longer be considered as a superposition of a flat surface and a
2
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small roughness. A composite surface theory (CST) was developed simultaneously
in the sixties by Wright [5] in the US and Bass [6, 7] in the USSR in which the
flat surface is replaced by a Iarger-scale rough surface whose correlation length is
much longer than the radio wavelength. Since then, CST has been very successful
in explaining ocean-backscattering observations for incidence angles from 20 to 70
degrees [8]. However, as the incidence angles approached grazing, it soon became
apparent that CST was inadequate to account for the large horizontally polarized
backscatter, as well as for the high Doppler velocities accompanying them [9, 10] for
higher microwave frequency (X band and up) systems.
T he sea-spike is a constant phenomenon in high-resolution, low-grazing, ocean
observing radars.
The term is used to describe sharp transient features whose
backscatter intensity approaches that of a hard target.
The Doppler velocities
associated with sea-spikes are typically on the order of several m eters per seconds for
X-band systems, much higher than the prediction for Bragg resonant scatterer [11].
T he HH sea-spike backscatter is often stronger than the corresponding W backscat­
ter, contrary to the CST prediction [10, 11]. Several models have been developed
to explain the observed characteristics of sea-spikes, notably the wedge-scattering
model [9, 12], accelerating plume model [13], and the m ulti-path and Brewster
dam ping model [10,14]. Each has limited success in explaining experim ental results.
Despite the poor understanding of the physics of sea-spike scattering, mea­
surem ents of sea-spikes have been used to study breaking waves and white-caps.
Laboratory studies have confirmed that breaking waves are directly related to the
occurrence of sea-spikes [10, 15,16,17]. A field experiment by Jessup has shown th at
60% of the sea-spikes caused by breaking waves can be detected when a microwave
radar is looking into the waves at moderate incidence [18]. Phillips has dem onstrated
th at the probability of breaking waves depends cubically on the friction velocity if
a saturated wind-wave spectra is assumed [19]. Based on this, he further deduced
3
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th at the backscatter intensity as well as the frequency of occurrence of sea-spikes
also depend cubically on friction velocity, and proposed counting sea-spikes as a
measure for friction velocity and wind speed [20].
Wave-energy dissipation due to breaking is shown to correlate with microwave
backscatter and acoustical radiation [21]. Breaking-wave geometrical properties have
been m easured w ith imaging sonar systems [22] and optical cameras [23]. O ptical
instrum ents are also used to obtain oceanic whitecap coverage, and a power-Iaw
relation was found between whitecap coverage and wind speed [24, 25]. These results
will be com pared to their radar counterparts.
1.3
S u m m a r y o f C hapters
T he prim ary objectives of this dissertation are first to investigate the characteris­
tics of low-grazing-angle radar backscatter, in particular, the properties of sea-spikes,
and to com pare experimental observations with scattering models; secondly, to in­
vestigate th e geom etrical properties of sea-spikes and establish connections between
radar sea-spikes and wind and wave parameters.
C hapter II reviews the principles of focused phased-array operation and describes
the FO PA IR radar system, calibration techniques and the data processing m ethod.
A brief account of th e Marine Boundary Layer Experim ent, the participation and
deploym ent of FO PAIR on the FLIP research platform , and a sum m ary of radar
and environm ental d ata will also be given in this chapter.
At near-grazing incidence, Bragg scattering and Composite Surface Theory pre­
dict th a t horizontal-transm it, horizontal-receive (HH) microwave backscatter is more
than 30 dB weaker than vertical-transm it, vertical-receive ( W j backscatter. The
backscatter is also Doppler shifted by an amount equal to the phase velocity of the
resonant scattering waves. In chapter III, dual-polarized FOPAIR radar images will
be described in detail in light of Bragg scattering models. While features in VV
radar images are consistent with Bragg scattering, HH backscatter properties show
4
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distinctive features unexplained by th e Bragg model, b ut are consistent with the
observations of sea-spikes.
Although sea-spikes behave much like hard targets, th e criteria for sea-spike
detection differs from th a t for a hard target because of th e inherent nature of an
im aging radar and the unknown statistics of sea-spikes. In chapter IV, the issues of
sea-spike detection are first discussed before the characteristics of backscatter inten­
sity and Doppler velocity of sea-spikes are presented. The HH backscatter intensity
o f sea-spikes is consistently higher than th at of W , and th e Doppler spectrum
shows th a t sea-spikes are moving at velocities much faster th an the resonant waves.
Colocated video images of the sea surface taken simultaneously with the radar data
are used to classify sea-spikes according to their corresponding surface features.
This comparison shows th a t the m ajority of sea-spikes can be correlated with either
actively breaking waves (whitecap) or steep waves. For developing and developed
seas in m oderate to high sea states, some 30% of sea-spike events can be identified
w ith surface whitecaps. Classification of sea-spikes shows th a t sea-spikes caused by
breakers are slightly stronger in am plitude and faster in Doppler than sea-spikes
caused by non-breakers, however their distributions are highly overlapped. Several
LGA scattering models are reviewed and compared with th e measurements.
T he spatial and tem poral properties of sea-spikes can be derived from the tim e
series of radar images, and axe compared to wind and surface wave scales in chapter
V. It is shown that sea-spikes tend to propagate in the direction of the local wind.
Sea-spike coverage, a quantity similar to whitecap coverage defined for optical instru­
m ents, follows a power-law relation to wind speed and friction velocity. Sea-spike
Doppler velocity and propagation speed derived from the movement of the scattering
centers scale with breaking wave velocity based on downward acceleration variance.
R adar results therefore show new possibilities in the rem ote sensing of ocean surface
5
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wind and wind stress, and provide evidence th a t wave breaking tends to occur in
the high frequency band of the wind-wave spectrum .
C hapter VI concludes this dissertation by a brief discussion of LGA scattering
models an d suggests new possibilities for the rem ote sensing of wind an d waves using
FOPAIR.
6
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C
h a p t e r
R a d a r Sy st e m
and
2
F ie l d E x p e r i m e n t
In this chapter, background on the principles of focused phased array imaging
and the FOPAIR system and its operation will be given. More detailed analysis
can be found in [26]. In the spring of 1995, FOPAIR was employed in th e Marine
Boundary Layer Experiment. The objectives of MB LEX, the experim ental setup,
data collection, and environmental conditions is described in this chapter.
2.1
R ev iew o f Im agin g P rin cip les
Imaging radars can be implemented with either mechanically scanned antennas
or electronically scanned phased arrays.
High azimuthal resolution can only be
achieved through a radiating aperture with dimensions many times the radio wave­
length. Phased array systems have the distinct advantages th a t no large movable
antenna is necessary and that scanning can be achieved very rapidly. For these
reasons, phased array systems are preferred when building rem ote sensing radars
th at look at scenes such as the ocean, surface that have short correlation tim es.
2.1.1
B eam form in g
The far-field of an aperture is defined as the distance beyond which th e elec­
tromagnetic waves radiated from the antenna can be approxim ated as plane waves.
The antenna aperture excitation distribution and the far-field radiation have an
approximate Fourier Transform relation, i.e.
/ Lf
2
E { y ) j ^ ™ 9dy,
(2. 1)
L/2
where J(9) is the far-field complex radiation pattern due to the aperture field E(y),
L is the aperture length, and A is the radio wavelength. The far-field boundary
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Ftfar is commonly defined such, that a spherical wave radiated from a point source
at distance R / ar will arrive at the aperture w ith a maximum phase error of 7r / 8. and
is given by
R far = 2 y .
(2.2)
The cross-range resolution at far-field is given by
6b =
olj,
(2.3)
where a is determ ined by the aperture illumination p a tte rn E(y).
For uniform
excitation, a is 0.88, however, a value 1 is often used in approxim ate calculations.
T he azimuthal resolution a t range R is therefore
ra = ROb ~ R -r ^ R / ar— = 2L .
Lt
(2-4)
Lj
Evidently it is not always possible to achieve a targeted azim uthal resolution at
specific ranges and to satisfy the far-field criteria at the sam e time.
2 .1 .2
F ocusin g
In the radiating near field, which is defined as the region from a few aperture
dimensions to the far-field boundary, the aperture excitation and the radiation
pattern are not related by a Fourier Transform since th e wave
frontcannot be
approximated as planar. It is, however, possible to focus the aperture and
achieve
the far-field condition at specific ranges. The radiation p attern of a focused array
at the focal range is essentially the same as the far-field p attern [27].
Figure 2.1 shows the geometry for a linear, broadside array focusing in the Fresnel
region at range R a. If the amplitude change due to the range variation along the
arc can be neglected, the radiated field on the arc due to array excitation is
N- 1
J(/2o,6) = ] T
(2.5)
t= 0
where G{(6 ) is the field pattern of the ith element located a t y,-, £(y,) is the excitation
of that element, and k is the free-space wavenumber. For arrays using identical
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Array
Figure 2.1. Focused phased array geometry. T he array is along th e Y-axis. T he arc
represents the range interval to be focused on.
9
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antenna elem ents, (7,(0) can be taken out of the sum m ation. The range from the
point (R 0 , 0 ) to an arbitrary location along the array is
R{y,0) = \J R \ + y 2 For R 0 ^> y and for small
2
R ^ y sin 0a.
(2.6)
6
R (y ,6 ) = R o - y 0 +
(2.7)
For a uniformly spaced array w ith elemental spacing d, equation 2.5 becomes
J ( R 0 , 0) = e~jkR°G{0) V E(d(i - ^ ) ) e /A:^ - f )ge- i f e ~ ))2.
i=Q
.
Clearly, if a quadratic phase term equal to e
3
(2.8)
W —g »2
*R° is applied across th e array, the
source distribution and aperture excitation again have a Fourier Transform relation
at range R 0, i.e.
w-i
„
J(Ro, 0) = e -jkRoG(0) ^ E(d(i - y ) ) e J'*rf(,' - £ )®.
(2.9)
t= 0
Except th e term s outside the summation, which can be easily removed without
affecting th e results, equation 2.9 is simply a discrete form of equation 2.1. Using
Fast Fourier Transform (FFT), J(Ro,0) is sampled at N evenly spaced points in
[—7r, 7r] in its fundam ental argument if) = kdO, which translates into N evenly spaced
points in [—
2.2
in azimuth space 0 .
S u m m a ry o f Radar S y ste m
The Focused Phased Array Imaging Radar was developed by Q uadrant Engineer­
ing, Inc. in th e early nineties to study ocean surface waves and transient features
[28]. The original system used only vertical polarization and was able to image
surface waves and obtain directional wave-number spectra in good agreement with
in-situ measurem ents [29]. The observations of nonlinear features in W images and
10
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wavenumber-frequency spectrum of coastal seas [30] prom pted the modification of
FOPAIR into a dual-polarized system. A brief description of the modified FO PA IR
hardware, calibration and d ata products is given below.
2 .2 .1
H ardw are
Figure 2.2 shows a block diagram of the FOPAIR radar system. It operates at
X-band (10 GHz) and consists of two sequentially sampled, 64-element receiving
antenna arrays, one vertically polarized and one horizontally polarized. Each array
employs a co-polarized pyramidal horn transm itter to illum inate the entire field-ofview to be imaged. A frame of radar d a ta is obtained by sequentially activating
the receiving array elements on a pulse-by-pulse basis. Azim uthal resolution of 0.5°
is achieved with an aperture of 3.42 m within the array’s 32° field-of-view, while
range resolution o f 1.5 m is achieved using either a short pulse of 10 ns or pulse
compression. Peak transm itted power is 200 W, boosted to an effective peak power
of 40 kVV if pulse compression is used. The backscattered signal is demodulated into
baseband I and Q channels, linearly sampled with a 12-bit high-speed digitizer at
up to 400 MHz, and stored on disk or tapes.
In theory, FO PA IR is capable of providing polarim etric ocean surface images.
In practice, however, since the radar receiver is time-shared between vertically and
horizontally polarized antennas, the radar is often operated in an interleaved mode,
i.e. alternating W
and HH scans, to reduce the data bandw idth and increase the
d a ta record length.
2 .2 .2
C alib ration
Accurate control of phase and am plitude distribution across the array is abso­
lutely necessary to produce focused radar images. Phase and am plitude errors due
to different cabling lengths and antenna pattern variations can be calibrated out by
looking at a point target.
11
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RFIn
1:2 Switch
1:64
RFIn
Switch Control
Short Pulse
or Chirp
Switch,
Network
RFO ut
64 Bement
H Receiver
Array
Radar
Trigger
Circulator Switch
VXmit
Digitizer
Control/Data
HXmit
Data
Disk Array
TWTA
System
Control/Data
Switch Control
Timing &
Control
Switch Control
1:64
Switch< „ ,
Network
Control
Tape Drive
Data
Computer
Switch Control
R F In
Figure 2.2. FOPAIR system block diagram.
12
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64 Bement
V Receiver
Array
Ideally, a point target calibration is performed by placing a point target such as
a trihedral corner reflector w ith a known radar cross section in the broadside of the
array at a range th at will be imaged. Theoretically, the complex received signal is
given by
VSCO = e -y* W ~ ^ )a, * = 0, 1, ...N.
(2.10)
The m easured values Vm contain both the changes due to the relative positions of
the target and array elements, and the changes due to phase and am plitude errors.
The calibration coefficients are given as
KcoraCO = j ® r , i = 0,1, ...A
(2.11)
for N array elements. The backscattered signals are multiplied by the calibration
coefficients before beam focusing is performed.
To properly compare W an d HH radar images, it is necessary to align them so
th at the radar images are colocated. For the experiments discussed here, the W
and HH antennas were configured end-on-end, and perfectly colocated images are
not possible, as shown in figure 2.3. To best align the images, a com er reflector was
placed along the center of the W and HH array at a range of 135 m in a grass field.
The com er reflector’s position is deliberately set to the broadside of both W and
HH antennas so th a t the field-of-views will be shifted in such a way th a t the corner
reflector appears at the center of both images. The maximum offset between W
and HH images is about 1 pixel and can be safely neglected.
Due to the physical size of th e FOPAIR antennas, a point-target calibration is
often difficult to perform, especially during the course of an open-ocean experim ent
like MB LEX where a comer reflector could not be m ounted stably in the rad ar’s fieldof-view. After MBLEX, FO PA IR was calibrated at th e University of Massachusetts
using the procedure described above. The radar system was positioned on top of
a 25-m eter-tall building overlooking an athletic field where a corner reflector was
13
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Figure 2.3. Calibration and alignment of W /H H radar images. Scales are exagger­
ated.
14
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set up. This calibration was not only intended to align the radar images, but also
to obtain the relative gain between the W
and HH channels so th at radar cross
sections could be compared. To reduce possible polarization dependence of the
com er reflector itself, it is mounted on a pivot so that it can be rotated around the
array broadside. D ata were then averaged over 360 degrees.
2 .2 .3
D a ta P ro cessin g
The unfocused complex backscattered signal is digitized and stored on tape.
Due to the large volume of the data, focusing and beamforming are accomplished
after each experiment using a workstation in the laboratory. Post-processing also
offers the flexibility to study different focusing techniques, adaptive beamforming
and beam synthesis tim e effects.
Once uploaded onto the workstation, th e raw complex voltage is first multiplied
by the calibration coefficients, then the quadratic phase corrections, and Fourier
Transformed from aperture space to beam space. To facilitate Doppler measure­
m ent, FOPAIR is usually operated in a pulse-pair mode in which each radar frame
is actually two scans separated by a short interval r , i.e., for dual-polarization
operation, the time sequence of data acquisition is (V, V), (H, H), (V, V), (H,
H), ......., where each parenthesis is a radar frame, while w ithin each parenthesis,
co-polarized scans are r apart. The resulting focused complex voltage signal is then
averaged for 0.25 seconds to reduce speckle. Three image products are accumulated:
backscattered power, Doppler velocity, and the coherence of th e complex backscatter. Letting V(t) and V ( t + t ) represent the complex images in a given pair, the
products are
p , <iy<or> + < lj3 L tr)P>
15
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(2. i 2)
where P, v, and p are backscattered power, Doppler velocity, and coherence re­
spectively and < > denotes averaging over a short tim e interval (0.25 s for 4 Hz).
In equation 2.13, A is the radio wavelength, and
t
is the inter-image delay. The
coherence, p, is an indicator of the uncertainty of th e Doppler velocity estim ate and
is often used as a measure of Doppler bandw idth [31]. When it approaches unity,
the uncertainty is small, implying a narrowband-type scattering during the time
interval. W hen it is low, uncertainty is large, implying either a very broad Doppler
bandw idth or inadequate signal-to-noise ratio when backscattered power levels are
low.
For distributed scattering, the backscatter decreases as r -3. The backscattered
power is corrected for this range dependence as well as the azim uthal antenna
p attern . The final power image is thus proportional to the normalized radar cross
section cr°.
2.3
M B L /F L IP E x p erim en t
2.3 .1
E x p erim en t O b jec tiv e
Sponsored by a m ultitude of government agencies, including the Office of Naval
Research, the National Science Foundation, and th e Mineral M anagement Services,
the M arine Boundary Layer Experiment was designed to achieve a b e tte r under­
standing of the atmospheric, surface, and oceanic processes governing the air-sea
fluxes of momentum, heat, moisture, and gas, and to develop b etter models for gen­
eralized environmental conditions. A m ajor objective of MBLEX is to understand
the in term itten t and turbulent processes in th e boundary layer, and perturbations
at th e surface. A high-resolution imaging radar capable of measuring microwave
backscatter and Doppler velocity, and of updating images at close to video frame
16
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rate can both provide inform ation on the surface-wave field and capture transient
surface features such as breaking waves, which play a very im portant role in air-sea
m om entum and gas exchanges.
To this end, FOPAIR participated in Phase II of MB LEX in th e spring of
1995. From A pril 14 to May 14, FOPAIR was installed on the Research Platform
Floating Instrum ent Platform (R /P FLIP), which was moored at 36.6°N, 122.5°W,
approxim ately 27 miles west of Monterey, California. FLIP is a special ship-like
instrum ent. It resembles a subm arine with a bow and a bridge like a regular ship.
The subm arine section is about 80% of the ship’s length, and consists o f water and
cement com partm ents. W ithout its own propulsion, FLIP is usually towed to a
destination by a tug boat. It is then “flipped” vertically, with the bow pointing
to the sky while most of its length remains submerged. Because of the sm all cross
section a t th e “neck” and th e large submerged mass, FLIP interferes minimally
with the surface waves and currents, therefore, it serves as a very stable open-ocean
research platform .
2.3.2
F O P A IR Setup
During the MBLEX Phase II deployment, the FO PA IR antenna was attached to
a boom on the starboard side of FLIP approximately 12 m above the m ean water
level. T he radar was aimed in th e direction of the keel of FLIP, nom inally North
(see figure 2.4). The area of ocean surface imaged by FO PA IR is a 24° sector lying
between 150 m and 246 m, corresponding to grazing angles between 4.2° and 2.8°
respectively.
2.3 .3
D a ta Sum m ary
After overcoming several difficulties during the tow from San Diego to the ex­
periment site west of Monterey Bay, which included repairing a broken boom and
waiting for a suitable condition to “flip” the FLIP, FO PA IR became one of the first
17
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FOPAIR Antenna
yEggtrrffl^ hu ji ill- l f f l S
Figure 2.4. FO PA IR configuration on FLIP during MBL experiment. FLIP is in
the “flipped” or vertical mode.
18
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operational instrum ents on board on April 24, and was continuously in operation
until May 9. Radar imaging d ata was taken approximately every hour except during
late nights and early mornings when rest became absolutely necessary. Each data
rim was typically 7 or 10 minutes in duration, depending on th e fram e rate used
(30,000 frames were taken for each run at either 64 or 48 Hz). This translates into
half of the capacity of FOPAIR data storage. The last run of each day usually
consisted of 60,000 frames. D ata was off-loaded to 8-mm tapes after each run.
All but a few d ata runs were operated in an “interleaved” m ode where the W
and HH images were taken alternately, at a combined frame rate of 48 or 64 Hz (24
or 32 Hz for each polarization). All d ata were acquired at a p rf of 100 kHz and in
pulse-pair mode with an inter-scan delay r of 2.5 ms. These translate into an image
formation time of 0.64 ms during which it is assumed th at the m otion of the ocean
surface is effectively frozen, and a Doppler velocity Nyquist interval of ±3.0 m /s.
Several data sets were taken simultaneously with a sector scan sonar developed
by Jerom e Smith and colleagues at th e University of California, San Diego and a
single-beam C-band radar from the New Zealand National In stitu te of Water and
Atmosphere Research, Ltd. A calibration data set was taken during which a small
ship was in the radar’s field of view. The data set serves as a reference when radar
images are compared with simultaneous video images.
A video camera was mounted at the left end of the radar receiver array, looking
toward the broadside of the antenna. Video data were taken during radar data
acquisition runs whenever there was sufficient ambient light.
Interestingly, the
camera has automatically controlled exposure and aperture which actually gives
it b etter sensitivity than the hum an eye.
Meteorological d ata such as wind speed, direction, air and w ater tem perature
measurements were either taken using FL IP ’s on-board instrum ents, or by other
researchers whose primary objectives were the dynamics of these parameters. In
19
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figure 2.5, wind speed and direction at 16 m above the m ean surface are plotted
along with the significant wave height for MBLEX Phase II.
During the course of MBLEX, a variety of meteorological conditions were en­
countered. From April 27 to April 30, winds were predom inantly from the South
and Southeast, with speeds varying from under 5 m /s to approximately 10 m /s.
Winds shifted on May 2, and remained consistently from the N orth and Northwest
until May 7. During this period, wind speed developed gradually from under 5 m /s
to about 14 m /s on May 4 and May 6, and slowed down on May 7. Since FOPAIR
was pointed towards the nominal North, excellent upwind d ata was obtained during
this period th a t included the radar observations of the development, m ature and
decay of wind waves.
FOPAIR d ata runs are marked in the bottom plot of figure 2.5. The data records
analyzed in this dissertation axe marked as
, “O ” and “A ” for upwind developing
seas, upwind developed seas, and upwind decaying seas, respectively. In addition,
four representative d a ta sets taken on April 28, May 3, May 5, and May 7 are used
in the comparison with video data, and are marked as A, B, C and D in the plot.
Most of the MBLEX research data and meteorological d ata obtained on FLIP
were stam ped with a Global Positioning System (GPS) tim e code which was syn­
chronized with the FOPAIR data acquisition clock. T he FOPAIR clock signal was
also inserted into the video data through a time-code insertion module.
Thus,
comparisons between the wind vector and wind stress data, sonar, and video with
FOPAIR were facilitated.
20
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Wind Speed
15
10
5
ot_
118
120
122
124
126
128
Ju lia n Day
Wind Direction Relative to North
360
_
cn
a)
270
-o 180
90
118
120
122
124
126
128
126
128
Ju lia n Day
S ignificant Wave Height
5 |-
4h
3 |-
2h
oL
118
120
122
124
Ju lia n Day
FOPAIR Data Collection
iM H tiiim 11
iiim in in
im
rnmnr inuinwii
i
D ata ta k e n
118
120
122
124
126
n n t n i i i i 11
iiiuniui ti
128
Ju lia n Day
Figure 2.5. Wind and wave conditions during the MBL phase II experiment
(courtesy of S. Miller of UC Irvine) and FOPAIR data collection tim es. Winds
were m easured at 16.5 m above the mean surface, and the direction is given relative
to N orth. Significant wave height H 1 / 3 is calculated as four times the RMS surface
height. FOPAIR data collection times are marked as circles and other symbols in
the bottom plot. The arrows m ark four radar data sets th at will be com pared with
video data.
21
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C
h a p t e r
3
I n t e r p r e t a t io n o f R a d a r Im a g e s
Dual-polarized FOPAIR images obtained in M BLEX are presented in this chap­
ter.
First, a brief review of the Bragg scattering theory will be given. Sample
radax backscattered power and Doppler velocity images, Doppler spectral density,
and surface wave wavenumber and frequency spectra derived from radar images
are described in detail using representative cases of both upwind and downwind
observations. Evidences of a non-Bragg scattering mechanism and sea-spikes are
emphasized in both radar images and Doppler spectra.
3.1
B ra g g S c a tte r in g M odel
The scattering of sound waves by a small periodic surface was investigated by
Lord Rayleigh using a perturbation method which was later applied to the scattering
of electrom agnetic waves by a perfectly conducting random rough surface by Rice
[1], The first-order normalized radar backscatter cross section is given by [32]
<r° = l6irk*\gp(do)\2if>(0,2ko sinfl0),
(3.1)
where k0 is th e radio wavenumber, gp the polarization dependent reflection coeffi­
cient, 0 o the incidence angle, and
the two-dimensional surface height wave-vector
spectrum given by
V>(K x , K y) =
1 7 “(x, y, t ) j ( x + u , y + v, t)etKxUelK»vdudv,
(3.2)
where K x, K y are surface wavenumber in X and Y directions, 7 is the surface height,
and the over-bar denotes an ensemble average. For a fixed incidence angle, <r° is
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
proportional to th e surface height roughness spectrum evaluated at (0, 2Aro s in 0Q).
The radar range direction is assumed to be in th e Y-direction in the equations above.
The first-order scattering coefficients are given by
= (e ~
+ sifl2 0°) ~ sin2 go]cos2 Oq
(e cos 6 a + y /e — sin2 0 o ) 2
.
( e — 1) cos2 0O
9h h (Po) = ---- ---------= = = = (cos 6 0 + v e —sin 0O)
/g gN
.
(3.4)
for W and HH backscatter respectively.
For radio wavelengths shorter than L-band, the sea surface can no longer be
considered as slightly rough. Wright developed a composite surface model where
the surface is divided into facets and each facet is a slightly rough surface w ith a
certain orientation. Facets are assumed to be independent of each other, and can
tilt not only in the plane of incidence, but also out of the plane of incidence. Radar
backscatter is the incoherent sum of returns from many facets, given by
<r°
= 167tA?o J
\gp(8 o,a,<f>)\2 r(;(2 ko<f>cos0 o, 2 ko sin 6 ')P (a , <f>)dad<f>,
(3-5)
where a and <f>are in- and out-of-plane angles, and P (a, <f>) is the joint probability
density function of surface tilt. For small tilt angles
9
9
v v ( 0 o,oc,<f>) = g v v ( 6 )
hh(Qo, a , <j>) = gffH(0 ) H
6
'=
6 0
COS v
(3.6)
gvv(0 )
+ a.
(3.7)
(3.8)
Although CST is the most appropriate model for high-frequency microwave
radars, for high-resolution systems such as FOPAIR, the resolution cell is small
enough that a single facet is sufficient to describe the scattering surface.
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The
polarization dependence of <x° is plotted in figure 3.1 as a function of incidence
angle. T h e Bragg backscatter contribution to a° for HH is m ore than 30 dB weaker
th an th a t for W for incidence angles above 85°.
For a time-varying surface such as ocean surface, Bragg scattering waves also
induce a Doppler shift in the backscattered signal. In the absence of significant
ocean currents, this Doppler shift equals the phase velocity of the resonant surface
waves. For low frequency radars, this Doppler shift is manifested as a pair of sharp
spikes in Doppler spectra, as reported by Crombie [3]. For microwave radars, this
Doppler shift is broadened by surface tilt and other hydrodynamic modulations such
as straining and advection of capillary waves. For X-band radar looking at near
grazing, th e resonant surface waves have a phase speed of 24 cm /s with wavelength
of 1.5 cm.
3.2
Im a g e C haracteristics
3 .2 .1
V ertica l Polarization
Figure 3.2 shows sample FOPAIR images obtained on May 3, 1995, corresponding
to case B as marked in figure 2.5. T he radar was looking upwind at a developing sea
under a 10 m /s wind coming from the Northwest (upper left com er of the image).
The top images were obtained with vertically polarized radiation, the bottom with
horizontally polarized radiation. T he images have been averaged over 0.25 seconds
(unless otherwise noted, all radar images in this dissertation are averages over 0.25
seconds), and transformed into Cartesian ground coordinates. R adar power images
were corrected by the antenna patterns as well as the cubic range roll-off1, and are
proportional to the normalized radar cross section.
1Non-Bragg scatterers may follow a R~4 dependence, i.e. they behave more like point-targets
then area-extensive targets. However, in order to make a meaningful comparison between Bragg
and non-Bragg scattering intensity, they are both corrected for R~3
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Incidence Angle Dependence of a 0
1.5
H—poi
V—pol
<
tf
>
I
0.5
0.0
0
20
40
60
80
Incidence an g le (d e g r e e s )
>
x
o
-10
-2 0
o
|
-3 0
0
M
1 - 40
o
-5 0
0
20
40
60
80
Incidence an g le (d e g r e e s )
Figure 3.1. Bragg scattering coefficient (top) and polarization ratio (bottom )
dependence on incidence angle using small roughness model.
25
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V Power (dB)
V Velocity ( m /s )
V C oherence
i-0 iso
180
0.0 160
-1 5 1 6 0
-4 0 -2 0
0
20
40
-4 0 -2 0
H Power (dB)
0
20
40
-4 0 -2 0
H Velocity ( m /s )
0
20
H C oherence
240
220
oO’ 2001
c
1.0
0.8
0.6
1-0 180
18 0 1
0.4
160
0.0 160
-1 0 1 6 0
0.2
0.0
-4 0 -2 0
0
20
Azim uth (m )
40
-4 0 -2 0
0
20
Azimuth (m )
40
-4 0 -2 0
0
20
40
Azim uth (m )
Figure 3.2. R adar images for an upwind look, developing sea. Top: vertically polar­
ized radar images. B ottom : horizontally polarized radar images. T he backscatter
is normalized to th e m ean V backscatter.
26
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From left to right in figure 3.2 are the backscattered power, Doppler velocity
and coherence images, respectively. The W
images show distributed scattering
consistent w ith Com posite Surface Theory where both <r° and Doppler velocity are
m odulated by larger-scale waves. At an average 3° grazing angle, shadowing effect is
expected to occur and is quite evident in the low backscatter and coherence values
im m ediately behind the wave crests in these images. T he m axim um backscatter
typically occurs on th e wave crests, and is often about an order of magnitude
stronger th an th e mean backscatter. The mean Doppler velocity for the V image
is about 55 cm /s and th e coherence is typically above 0.8, except in the shadowed
regions. Although the overall image shows wave features as would be expected from
a distributed Bragg scatterer, it is interesting to note th a t there are some discrete
strong scatterers, often accompanied by Doppler velocities exceeding 2 m/s.
Figure 3.3 and 3.4 show radar images for a developed and a decaying sea (cases C
and D in figure 2.5) following the developing case. As in th e developing case, the W
power and velocity images show predominantly distributed Bragg scatter. As the
sea becam e more developed, th e apparent wavelength of th e dom inant surface waves
increases, and the shadowing effect became more severe, as indicated by the larger
area of weak backscatter and low coherence in these images. The velocity values
in the shadowed regions show a random distribution, indicating th at the radar is
imaging its noise floor. The discrete scattering events appear to be stronger, and
moving faster as th e wind picks up.
Figure 3.5 shows a case for downwind look with wind coming from the South at
10 m /s (case A in figure 2.5). The Doppler velocity now is m ostly negative in W
image since the capillary waves are now traveling away from the radar. Other image
features are consistent with those of upwind looks, and th e strong scattering events
near th e wave crests still persist, but appear to be slightly weaker.
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V Power (dB)
V Velocity ( m / s )
V C oherence
240
(m )
220
Range
200
180
160
-4 0 -2 0
0
20
-4 0 -2 0
40
H Power (dB)
0
20
40
H Velocity ( m / s )
-4 0 -2 0
0
20
40
H Coherence
240
Range
(m)
220
200
200
15
10
180
5
0
- 5 160
160
-10
-4 0 -2 0
0
20
Azimuth (m )
40
-4 0 -2 0
0
20
Azimuth (m )
40
-4 0 -2 0
0
20
Azimuth (m )
Figure 3.3. Radar images for an upwind look, developed sea.
28
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
V Power (dB)
V Velocity ( m /s )
240
220
220
'
V Coherence
■
Range
(m )
240
200
200
5
180
° s 180|
160
-151601
-1 0
-2 0
-4 0 -2 0
0
20
40
-4 0 -2 0
H Power (dB)
0
20
40
-4 0 -2 0
0
20
40
H Coherence
H Velocity ( m /s )
240
220
220
200
200
Range
(m)
240
1.0
0.S
180
180
0.6
0 .4
160
160
-4 0 -2 0
0
20
Azimuth (m )
40
160
•
-4 0 -2 0
0
20
Azimuth (m )
40
0.2
0.0
- 4 0 -2 0
0
20
Azimuth (m )
Figure 3.4. Radar images for an upwind look, decaying sea.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
V Power (dB)
V Velocity ( m /s )
V Coherence
240
220
220
200
200
n
Range
(m )
240
180
1.0
0.8
0.6
180
0.4
160
160
-15160
-4 0 -2 0
0
20
40
-4 0 -2 0
0
20
40
-4 0 -2 0
0
20
40
H Coherence
H Velocity ( m /s )
H Power (dB)
0.2
0.0
240
240
220
220
220
Ronge
(m)
240
200
,0 2001>
0.5
5
0 180 \
-5
180
- is ’eot
-4 0 -2 0
0
20
Azimuth (m )
40
180
1.5160
0.2
-
0.5
-
1.0
-
-4 0 -2 0
0
20
Azimuth (m )
40
1.0
0.8
0.6
0.0
-1 0
160
200
0.4
o.o
-4 0 -2 0
0
20
Azimuth (m )
Figure 3.5. R adar images for an downwind look, developed sea.
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
3.2.2
H orizontal Polarization
T h e bottom panels in figure 3.2 to 3.5 are HH images corresponding to the W
images in th e top panels. Compared to W images, HH images show little distributed
scattering except the isolated strong scattering centers. Since th e predicted Bragg
backscatter for horizontal polarization is about 30 dB below W backscatter at this
incidence angle [32], and is well below FOPAIR’s dynamics range, only localized,
non-Bragg scatterers contribute to the echo. The background in the HH power
image represents the noise floor of the radar. The velocity image shows random
variations in areas of little o r no scattering, consistent with a uniformly distributed
phase for w hite noise. The coherences are generally low, except for the discrete
scattering events.
As m anifested in the HH radar power images, the horizontally polarized radar
backscatter is dominated by the discrete scattering centers, or “sea-spikes” , a term
invented to describe the spiky returns observed in low-grazing, horizontally polarized
m arine radars. Because of th e random phase of the noise, the Doppler velocity of
sea-spikes cannot be easily discerned in the HH Doppler image, however, as will
be shown later, sea-spikes ten d to move at speeds much higher th an the mean W
Doppler or th e phase speed o f the resonant Bragg waves.
3 .2 .3
R a n g e-T im e Im ages
Two dimensional radar images provide information on the instantaneous spatial
variations of th e backscatter field. More insight can be gained by incorporating
the tim e history of the radar backscatter. Using the tim e series of the center beam
(corresponding to a vertical column in the middle of the radar image), the range-time
contours of backscatter and Doppler are shown in figure 3.6 for the developing case
corresponding to figure 3.2 (case A). Again, the textures of the W and HH images
are q u ite distinct: both W
power and Doppler contours show relatively smooth
31
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W Power (dB)
100
W Doppler ( m / s )
100 ,
150
100
150
HH Power (dB)
240
HH Doppler ( m / s )
. .r.jg>
100
.J _2
V i ~3
150
Time (s)
Figure 3.6. Range-tim e contours of backscatter and Doppler corresponding to case
B shown in figure 3.2. Both W and HH power are normalized with respect to the
mean W backscatter.
32
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transitions between wave crests and troughs, while the HH power image is again
dom inated by sporadic scattering events.
It is interesting to note that two slopes can be detected in W
images: a steep
slope corresponding to the phase speed of the dominant waves, and a lesser slope
th at corresponds approximately to a speed of half of the phase speed of the dom inant
wave. For linear gravity waves, the group velocity of a narrow-band wave packet
is half of the phase speed of the wave packet. This second slope appears to be the
group feature of th e waves. Note th at the strong HH scatterers tend to occur a t the
wave crests and follow the group structures.
3.3
D op p ler S p e c tr a
To compare FO PA IR radar imagery w ith the results of other investigators, it
is useful to examine the Doppler spectrum of the backscatter. This is the typical
output format of coherent scatterometers used in many ocean scattering studies.
Because of the large d a ta bandwidth associated with the imaging radar, it is not
feasible to obtain a highly resolved Doppler spectrum at each pixel location; only a
mean Doppler velocity is recorded. However, because there exists both an instanta­
neous power estim ate and a mean Doppler velocity estim ate at each pixel location,
one can construct a power-weighted Doppler velocity histogram by binning powers
by their corresponding Doppler velocities. Accumulated over a large num ber of
pixels (exploiting both area and tim e averaging), this histogram is analogous to the
mean Doppler spectrum one might obtain, for example, by averaging periodograms.
In figure 3.7, Doppler spectra for cases A, B, C and D are plotted. Each spectrum
is an accumulation over all pixels in an 8- or 10-minute d ata record. The solid and
dashed curves show the Doppler spectra for vertical and horizontal polarizations
respectively.
33
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Case A — downwind
~
Case B — upwind young sea
5
:=
5
a
tn
-3
-2
-1
1
0
-3
2
-2
Velocity ( m / s )
0
1
2
Velocity ( m / s )
Case C - upwind developed sea
7
-1
Case D — upwind decaying sea
.rrr*-
.........
,
V
6
~
5
.-=
4
a
5
3
ula- o2
1
o b i= .
-3
-2
cn
-1
0
1
-3
2
Velocity ( m / s )
-2
-1
0
1
2
Velocity ( m / s )
Figure 3.7. Doppler spectral density for cases A, B, C and D. Solid curves are W
spectra, dashed curves are HH spectra.
34
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3.3.1
V ertical Polarization
A com m on feature among th e W Doppler spectra is the spectral peak location,
which is relatively constant am ong all the W spectra. These spectral peaks are
displaced from zero Doppler by about 50 cm /s. Since th e Bragg resonant wave has
a phase speed of 24 cm /s and th e wind-induced surface currents range from 2 to 5
percent of th e wind speed, the W
Doppler peak location appears consistent with
the Bragg scattering model.
The W
spectral width, however, varies with th e sea state. Young, developing
seas usually have narrower spectra than developed seas. This is consistent w ith the
larger orbital velocity variances for developed seas. It is also interesting to note
that although developed seas usually produce greater Doppler width, the spectral
peaks are lower than with developing seas. This further confirms that W scattering
is Bragg in nature, since the backscattering intensity is determined by th e surface
resonant wave spectral strength, which is most likely saturated with both young
and developed seas, while the Doppler velocity is m odulated by larger waves th at
spread the Doppler spectrum. For decaying seas, th e intensity of the backscatter is
much weaker th an th at for young and developed seas, due to the reduced energy in
the capillary waves as the winds diminish.
The W spectra becomes m ore asymmetric as the sea grows, as seen in th e larger
spectra tails in figure 3.7. This asym m etry can be attrib u ted to two prim ary factors:
(1) the M odulation Transfer Function [33] and shadowing effects which accentuate
contributions from the forward faces of the advancing waves while inhibiting contri­
butions from the rear faces and (2) contributions due to non-Bragg scatterers near
wave crests which tend to have higher velocities.
35
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3.3 .2
H orizontal Polarization
T he spectral peaks for horizontal polarization (dashed curves in figure 3.7) occur
a t considerably higher velocities. For young seas, the spectrum is generally confined
to a range of velocities around 1.8 m /s. For developed seas, spectral peaks can be
as high as 2.5 m /s. T he spectral w idth for HH is broader th an the corresponding
VV w idth, and grows with the sea state. There is significant folding of the Doppler
sp ectru m for more developed sea conditions shown in Case C.
T he higher Doppler frequency values for HH backscatter indicates that the HH
scattering mechanism is quite different from th at for the W scattering. This agrees
w ith the previous observations th at HH radar images consist of sporadic scattering
centers, while W
3 .4
images consist of a distributed Bragg scatterer.
E v id en ces o f N on -B ragg S ca tterin g
T he dom inant scattering mechanism for W backscatter is Bragg resonant scat­
tering. This is shown as the distributed scattering features in both W power and
Doppler velocity images, in the Doppler spectral density where the spectral behavior
is consistent with Bragg scattering, and in K -f spectra where the dispersion shell
is observed [29], Although there are indications of non-Bragg scattering in W
backscatter, its contribution to the total backscatter tends to be masked by the
d istrib u ted Bragg scatter.
T h e non-Bragg scattering is most obviously manifested from the discrete scat­
tering events in HH radar-power images. Although features in the HH Doppler
images axe difficult to distinguish due to the random phase distribution of the noise,
the m ean HH Doppler spectral density shows that the relevant scatterers move at
velocities much higher than the phase speed of the Bragg resonant surface waves.
T he range-tim e diagrams indicate th a t these scatterers tend to move with wave
groups.
36
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T he non-Bragg scattering centers observed in HH backscatter images appear
to be consistent with the observations of “sea-spikes”, a term used to describe
high-resolution low-grazing radar backscatter impulses often observed in horizontally
polarized m arine radars.
In the following chapters, analysis will emphasize the
physical properties of sea-spikes, their comparison with visual surface features, and
their spatio-tem poral characteristics and relations to wind and wave parameters.
37
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C
h a p t e r
4
P hysica l P r o p e r t ie s o f S e a S pik e s
In the previous chapter, evidences of non-Bragg scattering were presented. In
particular, HH backscatter at low grazing angles is dom inated by sea-spikes, spatially
discrete, sporadic and impulsive scattering events. Sea-spikes have long been asso­
ciated w ith surface wave breaking and energy dissipation [10, 18, 21]. Information
on the radar backscatter properties, such as the am plitude distribution, Doppler
characteristics and polarization dependence, of sea spikes will not only help us un­
derstand th e physics of the scattering mechanism behind the sea spike phenomenon,
but will also shed light on the properties of wave breaking and th e use of radar as
a tool to m easure wave breaking.
The physical properties of sea spikes will be investigated in this chapter. VVe
will begin with a discussion of th e sea-spike identification issues th a t are pecu­
liar to FO PA IR, then present th e measurements of sea-spike Doppler velocity and
polarization characteristics.
By comparing sea-spike events with visual surface
features, sea-spikes are classified into four categories corresponding to white-capping,
steep waves, mixed, and no surface features, and their Doppler and polarization
characteristics are presented. T he results are discussed in the light of several LGA
scattering models.
4.1
Id e n tifica tio n o f Sea-Spikes
As is evident in the radar images, the HH backscatter is dom inated by noise
pixels. T he traditional approach to target detection is based on a tradeoff between
the probability of detection Pd and the probability of false-alarm P/a- It is therefore
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
necessary to have some knowledge of the backscatter distribution of the target
and the noise distribution. Since coherence images are calculated with power and
Doppler images, we will first discuss th e possibility of using coherence as a means
to select sea-spike pixels.
4 .1 .1
C oherence M e th o d
The coherence m easurem ent p is related to the signal-to-noise ratio. It is expected
th a t noise pixels generally will have low coherence values while strong scattering
targets will have high coherence, provided that their Doppler bandwidth within
each pixel is small com pared to the pulse-pair interval. A histogram of p is shown
in figure 4.1 (solid curve) for d ata record 95050308. T he m ajority of noise pixels
are distributed between 0.1 and 0.8. A secondary peak can be detected around
p = 0.9, but is m asked by the broad noise distribution. T he dashed curve in the
plot is a power-weighted coherence distribution, where the secondary “peak” in
the solid curve is th e dom inant peak, indicating th a t, although the noise pixels
comprise the m ajority of th e pixels, th e backscattered power is highly concentrated
near p = 0.9. A coherence value of 0.8 appears to be an appropriate value to divide
the noise-dominated pixels from the signal-dominated pixels.
A major problem w ith coherence-based detection is th a t, although most of the
energetic scatterers will be selected, th e number of noise pixels identified as seaspikes often far exceeds the number of true sea-spikes. In other words, P ja will
be so high that the accum ulated statistics will be biased towards those of noise,
especially under low sea states or low wind conditions when there are few seaspikes. For measurements th a t are inherently power-weighted, such as the Doppler
spectrum and its m om ents, this contam ination is not as severe because noise power
is generally lower th an sea-spike power. However, when other quantities such as the
polarization ratio or th e frequency of sea-spikes are of interest, the results will be
severely contaminated.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.2x10 5
0.050
Histogram of c o h e r e n c e
P ow er^istriBbtion
0.040
8.0x10 4
Count
0.030
4
4.0x10
2.0x10
0.020
4
0.010
4
0.000
0.2
0.4
0.6
0.8
1.0
Covariance
Figure 4.1. Coherence histogram and power-weighted histogram distribution.
40
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Power Density
1.0x10 5
A second, more fundam ental problem associated with using coherence is the
difficulty in quantifying the coherence w ith Pfa and Pj.
For a signal-to-noise
ratio much greater than unity, the coherence is related to the bandw idth of the
backscattered signal by [31]
p = e- 8(™W*)2,
(4.!)
where er„ is the Doppler bandw idth, r the pulse-pair delay and A th e radio wave­
length. On the other hand, th e coherence for a noise signal should approach zero
if the noise bandwidth is large compared to 1/ r . However, the coherence estimates
obtained using equation 2.14 will be non-zero even for white noise because the
number of samples averaged is finite (6 to 8 samples). Therefore, although coherence
is a qualitative measure of signal-to-noise ratio, the convoluted relationship between
them prevents a simple and direct correspondence between coherence and Pi or Pfa4.1.2
Pow er M ethod
Target detection in surveillance radars usually uses a power threshold deter­
mined by balancing the probabilities of false-alarm and detection, as illustrated
in figure 4.2. Depending on the purpose of the radar, either minimizing Pfa or
maximizing Pi can be the more important factor. In either case, knowledge of the
statistics of the noise and backscatter is required.
For characterizing radar sea-spikes, the emphasis is placed more on isolating true
sea-spikes from false-alarms than on a high detection probability since the statistics
of the noise will undoubtedly contaminate or bias the statistics of the sea-spikes.
This differs from the m ilitary situations where a low probability of detection (of
enemy missiles and aircrafts) may result in serious consequences. Therefore, the
objective in sea-spike detection is to eliminate as m any false-alarms as possible, while
m aintaining a Pi that provides enough samples to produce converging statistics. To
do this, the statistics of the noise power should be obtained.
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.014
threshold
Noise PDF
0.012
0.0 1 0
u- 0.008
Q
Signal PDF
CL
0.006
0.004
0.0 0 2
0.000
0
10
30
20
40
50
60
Power
Figure 4.2. Illustrative plot of the relation between Pj, and P ja- Area under the
dashed curve to the right of Pthreskoid is P /a while area under the solid curve to the
right of Pthreshold is Pi-
42
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4.1.2.1
Noise Statistics
Noise voltages in the I and Q channels using linear detection usually follow
Gaussian distribution with zero mean. T he noise power for such a signal is Chisquare distributed. FOPAIR radar images were obtained by averaging over 6 or 8
frames, where each fram e consists of two closely spaced radar scans or a pulse-pair.
Since the noise bandw idth is much larger than 1/ r , the scans in the pulse-pair can be
considered independent of each other, therefore the num ber of noise power averages
is actually 12 or 16, giving noise power a Chi-square distribution with 24 or 32
degrees of freedom. To verify this, a histogram of noise power was plotted in figure
4.3. The histogram was obtained using d ata taken on May 1, 1995, when th e wind
was under 4 m /s, and the ocean was dead calm w ith virtually no capillary waves.
Both VV and HH rad ar images showed low coherence and contained no backscatter.
A Chi-square distribution with 32 degrees of freedom is also plotted in the figure
as the solid curve. T he agreement between the measurement and the prediction is
indeed very good.
4.1.2.2
Determination o f Power Threshold
In the above verification of noise statistics, the radar power images were not
adjusted for range roll-off and the antenna pattern because the noise signal is not
affected by these effects. However, radar signal backscattered from the ocean surface
is modulated by both cubic range roll-off and the antenna pattern. To properly
compare scattering events at various ranges and azim uth angles, it is necessary to
compensate for these modulations. It can be reasonably assumed th at for upwind
and downwind observations, sea-spikes are uniformly distributed in azim uth within
the field-of-view of the radar. Once the correction is applied, the backscattered
power distribution a t each pixel position should therefore be the same. In other
43
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Probability Distribution of Noise
>s
0.8
JD
O
X3
O 0.6
CL
<D
>
-2 0.4
E
D
O
0.2
0.0
0.000
0.010
0.020
0.030
0.040
0.050
Noise power (relative unit)
Figure 4.3. Cum ulative probability distribution of noise for data record 95050104.
“O ” are measured values and the solid curve is a x 2 distribution with 32 degrees of
freedom.
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
words, a single power threshold can be applied to radar images to obtain a uniform
probability of detection.
By applying the range and azimuth corrections to backscattered power images,
the noise power is also raised by various amounts, depending on the pixel position
in the radar image. This is a problem peculiar for imaging radars such as FOPAIR.
It is not possible to achieve uniform P4 and P ja across radar image because it is
not possible to adjust the radar power images such th at uniform distributions of
noise power and backscatter can be obtained. To resolve this problem, a power
threshold is determ ined based on a worst-case probability of false-alarm Pfa, 0, that
is determined by the pixels having the highest mean noise level, i.e., pixels at the
outermost azim uth and range positions. T he result is a uniform Pd and a variable
Pfa not worse th an P/a,0 -
4.L2.3
Backscatter Distribution
Trizna has proposed that HH backscatter at LGA can be modeled as a Weibull
distribution w ith two modes - the low-power mode corresponds to Bragg backscatter
while a high-power mode relates to sea-spikes [34]. To estim ate the distribution of
HH backscattered power, pixels whose coherence is above 0.8 are used. A sample
distribution calculated from a data set taken for an upwind look, developing sea is
plotted in figure 4.4. As discussed earlier, high-coherence itself does not eliminate
all the noise pixels, especially at the lower power levels. Due to FOPAIR’s limited
sensitivity, the extrem ely weak HH Bragg backscatter cannot be detected. Therefore
only the high end of the histogram is significant.
The HH backscatter power levels in figure 4.4 are normalized to the mean VV
backscatter which serves as a reference for Bragg backscatter level at a 3° incidence
angle. The upper tail of the histogram shows a K-like distribution.
The mean
HH backscatter level is 7.4 dB above the mean W backscatter level and the 90%
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Histogram of HH B ackscatter Power
1000
Mean HH power:
7 .3 9 dB :
00
c
3
o
o
-10
-5
0
5
Pow er (dB)
10
15
20
Cum ulative Probability Distribution
1.0000
0 .1 0 0 0
0 .0 1 0 0
CL
0 .0 0 1 0
0.0001
-10
-5
0
5
Pow er (dB)
10
15
20
Figure 4.4. Top: histogram of the HH backscattered power using all pixels with
p > 0.8 for a d ata set taken during May 3, when the radar was looking upwind at
a developing sea. Bottom: cumulative probability distribution. 0 dB on abscissa
corresponds to an HH backscatter level equal to the mean W backscatter level.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
confidence interval is found to be -1.9 dB to 14.3 dB from the cumulative distribution
function.
4.2
S ea-S pik e P r o p e r tie s
The Doppler velocity and polarization characteristics of sea-spikes are presented
in this section through four representative cases corresponding to (A) down-wind
observation, developed sea, (B) upwind observation, developing sea, (C) upwind
observation, developed sea, and (D) upwind observation, decaying sea, and are
marked in figure 2.5 of chapter 2. The signal-to-noise ratios for these four data
records are all above 10 dB and were taken during daylight. Consequently they can
be compared with the video d a ta in a following section.
4.2.1
D o p p ler S p e c tr a
The Doppler spectra shown figure 3.7 in chapter 3 were obtained using all radar
image pixels. The HH spectral-peak Doppler was found to be much higher than the
VV peak Doppler. Visual inspection of radar images showed th at the sea-spikes in
HH images are often present in W images. By applying a power threshold to HH
power images, sea-spike pixels are selected, and their Doppler spectra are calculated
as a power-weighted Doppler velocity histograms as in chapter 3.
Figure 4.5 shows Doppler spectra for cases A, B, C and D using p = 0.8 as a
filter. While the HH Doppler spectra shapes were relatively unchanged compared
to the Doppler for all pixels (see figure 3.7), much of th e energy has been removed
from the W spectra, which now appear more similar to the HH spectra. The mean
velocities of W spectra are still systematically lower th an those of HH, indicating
that there is still residual Bragg scattering within the resolution cells containing
non-Bragg scatterers or sea-spikes.
Pixels selected using coherence alone still contain a large number of false-alarms,
which for VV backscatter are dominated by Bragg scatter. To effectively eliminate
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C ase A
2.0
c
a<0
1.5
CJ
1.0
— V,
— H,
— V,
— H,
C ase B
p threshold
p threshold
power threshold
power threshold
2.0
c
©
1. 5
a
aGL 1.0
(A
a
03
CL
CO
0.5
0. 5
/>\
0.0
- 3
- 2
- 1
0
1
2
-3
- 2
- 1
0
1
V elocity ( m / s )
V elocity ( m / s )
Case C
C ase D
2.0
c
1.5
oCD
CJ
1.0
03
CL
CO
0. 5
/»
0.0
-3
-2
-1
0
2
3
-3
V elocity ( m / s )
-2
-1
0
1
V elocity ( m / s )
Figure 4.5. Doppler spectra of sea-spikes for four representative cases: (A) downwind
look, developed sea, (B) upwind look, developing sea, (C) upwind look, developed
sea, and (D) upwind look, decaying sea.
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
false-alarms and reduce the influence of Bragg scattering, a power threshold corre­
sponding to a worst-case Pja = 10-4 was applied to HH images1 and the resulting
Doppler is shown as th e thicker curves in figure 4.5. While the HH spectral shape
still remains relatively unchanged, th e W
spectral peaks approach those of HH.
T he num ber of pixels selected by this power threshold is approxim ately half of th at
selected by p = 0.8, but the total spectral energy for HH is little changed, indicating
th a t the noise pixels are effectively elim inated.
Scatter plots for W and HH sea-spike Doppler velocities are shown in figure 4.6.
A lthough some velocity bias is still present, the two velocities approach each other
a t higher speeds. This confirms th at sea-spikes are present in both W
and HH
radar backscatter and their non-Bragg properties are often masked by the dom inant
VV Bragg scattering.
4 .2 .2
P o la riza tio n C haracteristics
T he polarization ratio, 7 = <Tffff/o-yV, is one of the critical param eters to be
tested for LGA scattering models. Open-field experiments have reported th at 7
often exceeds unity (0 dB) for sea-spikes [9, 11], but wave-tank studies of breaking
waves had not reported such values until very recently [17].
W hile ratios of Doppler spectra can provide an indication of polarization ratios
for non-Bragg scatterers, they only compare powers at a common Doppler velocity.
Scatter diagrams of V velocities vs. H velocities for the upper half of signal pixels
in figure 4.6 indicate th at some velocity bias is still present. By aligning the VV
and HH radar images, pixel-by-pixel comparisons of the backscatter can be made.
Figure 4.7 shows histograms of the polarization ratio 7 for sea-spike pixels. The
m ost probable polarization ratio is found to be in the neighborhood of 6 dB for
upwind observation of young and developed seas, several dB higher for decaying
lIn the following, sea-spike pixels will be selected by applying a power threshold corresponding
to a worst-case Pja of 10-4 unless otherwise noted.
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Case A
Case B
5
4
t/J
\
E
tn
E
3
2
0
......
-5 - 4
-3 - 2 - 1 0
V, ( m / s )
1
1 0
Case C
1 2
3
V. ( m / s )
4
5
4
5
Case D
5
4
(n
\
E
c/i
E
3
2
0
XftAni
0
1
2
3
V. ( m / s )
4
5
1 0
1
2
3
V. ( m / s )
Figure 4.6. W and HH sea-spike Doppler velocity scatter plots for four represen­
tative cases: (A) downwind look, developed sea, (B) upwind look, developing sea,
(C) upwind look, developed sea, and (D) upwind look, decaying sea.
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Case A
5
m ,= 5.87 dB
m2= 5.34 dB
4
c
Case B
5
m 2= 5 .70 dB :
4
3
3
c
3
O
o 2
3
O
o
m ,= 6.18 dB :
2
1
OF
-10
10
30
20
Polarization ratio (dB)
c
m2= 5.61 d B :
4
3
c
3
O
3
O
CJ
CJ
2
0
10
10
20
30
Case D
5
m ,= 6.08 dB :
4
0
Polarization ratio (dB)
Case C
5
/■ ■■■
20
m ,= 9 .63 dB
m2= 9 .22 dB
3
2
10
30
Polarization ratio (dB)
20
30
Polarization ratio (dB)
Figure 4.7. Polarization ratio ( y ) histograms for sea-spike pixels for four represen­
tative cases: (A) downwind look, developed sea, (B) upwind look, developing sea,
(C) upwind look, developed sea, and (D) upwind look, decaying sea. m i and m 2 are
the mean and median polarization ratios.
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
seas, and slightly lower for downwind observation. Thus, for the sea-spikes observed
here, the polarization ratio exceeds unity most of th e tim e. Because of the residual
influence of W -p o la riz e d Bragg backscatter w ithin th e resolution cells, polarization
ratios reported here probably underestim ate th e polarization ratio of the non-Bragg
component of scattering. This might partially explain th e higher polarization ratios
observed in the decaying-sea case where Bragg backscattering levels are lower. T he
observed polarization ratio and its implications about likely scattering mechanisms
are discussed in detail in a later section.
4.3
Sea-Spike C la ssifica tio n and C om p arison w ith W h itecap s
Sea-spikes have long been associated with whitecaps and breaking waves. VVave-
tank studies have shown th at onset and actively breaking waves generate radar
backscatter spikes [10, 17, 35]. Jessup showed th a t, at m oderate incidence angles,
breaking waves and strong radar backscatter are well correlated, although spatial
and temporal lags on the order of 1 m eter and 1 second exist.
Kalmykov reported th a t for low-grazing angles, radar backscatter is related to
wave breaking in th e open ocean. However, there are currently no simultaneous W
and HH high-resolution radar and surface video d a ta to allow systematic and direct
comparison between sea-spikes and oceanic whitecaps for near grazing incidence.
The following analysis is an attem pt at such a study.
To determ ine if th ere is a relationship between scattering signatures and surface
geometries, radar images were compared to simultaneous video recordings of the
surface. The prim ary intent of this analysis is twofold: first, to determine if visually
different surface features show measurably distinct Doppler or polarization-ratio
properties, and second, to determine to what extent the radar signature is a m etric
of visual white-capping or wave breaking.
52
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4.3.1
Comparison Procedure
During the experim ent, both the video recordings and the radar data were
synchronized using an ERIG tim e code generator th a t stam ped th e video and radar
images with the current tim e. For each radar d ata record, a sam ple of 100 video
images was extracted using a frame grabber. Since the precise moment when the
video images were extracted could not be controlled with the available equipment,
the tim e stamps on the digitized video images were used to retrieve th e corresponding
radar images.
R adar sea-spike images were compared w ith video images, and scattering events
were classified into four categories: (I) white-capping exclusively present, (II) “steep”
wave feature present b u t no white-caps, (III) a combination of white-capping and
steep waves, and (IV) no features evident. Categories I and II are unambiguous,
while Category III was included to account for spatially large sea-spike events cor­
responding to long-crested, partially breaking waves. The aim was to discriminate
unambiguously between strictly white-capping and steep waves w ith the expectation
th a t the properties of Category III would fall somewhere in between. Once catego­
rized, radar image pixels for these event types were examined to infer Doppler and
polarization-ratio properties.
Given the 32°x24° field-of-view of the video cam era and the 640x480 pixel res­
olution of the frame grabber, the angular sam pling resolution of the video image
is approximately 0.05°/pixel. Based on this information and th e nominal height
of the array above the m ean water level, and using the horizon as a reference, the
radar range vs. azim uth image is mapped onto the video elevation vs. azimuth
image. The azimuthal resolution of FOPAIR is 0.5°, a factor of 10 lower than the
video sampling resolution. In elevation, however, the video angular resolution maps
to range resolutions of 1.6 m and 4 m at ranges of 150 m and 246 m respectively.
These are comparable to or slightly lower than the radar range resolution.
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T here axe a few lim itations inherent to this kind of comparison which need
to be mentioned. First, at near-grazing incidence, pixel-by-pixel classification is
extremely difficult due to the inevitable misregistration between the radar and
video images caused by the undulating sea surface (the assum ption of a flat sea
surface m ust be made in order to transform between radar and video coordinates).
Since misregistration is most severe at near-grazing incidence, this demands that
classification be performed manually on an “event-by-event” basis, where an event
is a group of contiguous sea-spike image pixels. To make the m anual classification of
the pixels reasonable, it was also necessary to place a modest threshold on the spatial
extent of events - only those events whose spatial extent exceeded two contiguous
pixels were considered. Though these conditions may seem somewhat arbitrary, they
discard only those events for which visual comparison is not straightforward while
retaining most of the to tal H polarized signal power (about 85-90%). We believe
this to be a tractable criterion, which is as inclusive as possible.
4 .3 .2
S a m p le R adar and V ideo Im ages
R adar and video images are compared for Cases A, B, C and D studied in the
previous sections. These four cases well represent the diverse conditions that axe of
interest: upwind and downwind observations, and developing, m ature and decaying
seas a t various wind speeds. These cases have good signal-to-noise ratios, and data
were taken during daylight when the ocean surface was clearly visible and good
video images could be obtained.
Figure 4.8a shows a video image taken simultaneously w ith the radar image
shown in figure 3.2 for developing seas on May 3, 1995 (Case B). The time code
inserted near the bottom of the video frame allowed the retrieval of th e corresponding
radar images. The rectangle in the video frame marks the approxim ate location of
the radar footprint given the viewing geometry and assuming a flat sea. As discussed
in chapter 3, the wind had been blowing for over 20 hours from the Northwest, but
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
little development of seas occurred, possibly due to an opposing swell. The wind
speed a t the time of the radar images was 10 m /s, just at the onset of significant
sea development with frequent white-capping.
Figures 4.8b and 4.8c show a stretched version of the boxed area and a color
composite of the radar power images transformed into the video’s coordinate system.
V scattering is represented by green intensity, H by red. W here they are of compa­
rable intensity, the colors combine, yielding yellow. Here, it is relatively easy to see
evidence of non-Bragg scattering events th a t one can associate with visual surface
features such as white-caps or steep wave features. Some m isregistration between
radar image features and their apparent sources in the video image is inevitable as
the sea is never truly flat. This is particularly an issue in higher sea states.
Figures 4.9 shows radar and video images for more developed seas on May 5
(Case C), where three breakers can be easily identified with three sea-spikes in the
radar image. The corresponding radar images in ground coordinates were shown
in figure 3.3. Notice the discrepancies in th e locations of the radar sea-spikes and
whitecaps - for this case, the significant wave height was over 3 m, subtending an
elevation angle of about 1° at a range of 180 m (20 video pixels).
Similar images for decaying seas (Case D) are shown in figure 4.10. The radar
images in ground coordinates axe shown in figure 3.4. For this case, surface white­
caps were practically non-existent, however radax sea-spikes still appeared, though
at a lesser frequent rate than that for young and developed seas. The sea-spikes
correlate well with the darker areas in the video which is most likely due to the
sharp crested waves th at reflect lights in an unisotropic fashion.
Case A corresponds to downwind observation of a developed sea. The images axe
shown in figure 4.11 and 3.5. As in the upwind developed cases, sea-spikes appear
to correlate to surface whitecaps or steep crested waves.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(C)
Figure 4.8. Video image corresponding to the radar images in figure 3.2 for upwind
look of a developing sea (Case B). (a) shows the overall ocean surface and the
horizon, where the boxed area indicates the radar footprint, (b) is a stretched
version of th e boxed area in (a), (c) shows a color-composite of the radar images
where the H backscatter is coded in red and V backscatter in green. T he yellow
area signifies strong H and V backscatter. Radar images are transform ed into video
coordinates.
56
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
(a)
(b)
Figure 4.9. R adar and video images for an upwind look, developed sea (Case C). (a)
Stretched video images; (b) Color-composite of radar images in video coordinates.
(b)
Figure 4.10. Same as figure 4.9 for an upwind look, decaying sea (Case D).
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Figure 4.11. Same as figure 4.9 for a downwind look, developed sea (Case
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3.3
Sea-Spike Classification
Results of the classification, of sea-spikes based on radar and video d a ta for four
representative cases are shown in figure 4.12 and listed in table 4.1. Stacked bar
charts in the figure show th e fractional contributions of each class. T he table lists
the num ber of events classified for each case, and the mean power, Doppler velocity,
and polarization ratio statistics. For the young and the developed seas (cases B
and C ), video and radar comparison show th at categories I and III, corresponding
to to tal or partial white-capping, together account for about 30 percent of the
observed sea-spike events, while steep waves account for approximately 60%. For
the decaying sea (case D) there were virtually no white-caps despite th e presence
of large waves. In this case, to tal or partial white-capping accounted for about 3%
of the observed spikes while steep features accounted for 92%. For th e downwind
look (case A), a somewhat larger percentage of th e sea-spike events, about 40%, can
be associated with actively breaking waves. Though both the number of spikes and
their intensity are significantly lower than for upwind looks, the viewing geometry
appears to suppress the influence of steep waves.
These percentages are based solely on event counts with no regard to their
intensity. If events are weighted by their areal coverage, the percentages increase
somewhat. If events are weighted by their corresponding powers, actively breaking
waves can be associated w ith a modest m ajority of power in cases A, B, and C even
though they account for a m inority of events. In decaying seas, steep waves still
dom inate the sea-spike signature.
T he Doppler properties of classified sea-spike events are summ arized in fig­
ures 4.13 to 4.16. Here, Doppler spectra and polarization ratio histogram s were
com puted individually for each class. From an exam ination of the Doppler signatures
it is relatively easy to discrim inate between the velocity distributions of categories
I and II. The Doppler shifts for white-capping events are generally higher than for
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S e a —Spike Event Classification
S e a —Spike V Power
S e a —Spike H Power
Category I
Category II
C ategory III
C ategory IV
Figure 4.12. Sea-spike categories and their percentages in terms of events, pixels, and
to tal V and H power. Category I: white-caps and active breaking waves, Category
II: steep wave features, Category III: active breaking waves and steep waves both
present, Category IV: no obvious features.
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Table 4.1. Sea-spike classifications. < Pv > and <
> are the backscatter power
norm alized to the mean V-Pol Bragg backscatter level for V and H sea-spikes. Vv
and Vh axe Doppler centroids, < 7 > is th e mean polarization ratio, and C p is the
phase speed of the dom inant gravity waves.
file
category
95042810
case A
I
II
III
IV
I
II
III
IV
I
II
III
IV
I
II
III
IV
95050308
case B
95050504
case C
95050704
case D
number
of events
37
69
25
2
64
413
162
49
115
376
173
56
2
161
11
29
< Pv >
(dB)
10.5
8.5
10.3
7.9
9.1
7.0
8.4
5.9
8.9
6.0
7.7
5.2
11.6
9.1
10.2
6.2
<Pk >
(dB)
14.9
14.0
15.6
13.8
14.3
13.3
14.7
12.4
14.5
11.9
13.6
12.0
16.9
18.0
19.6
16.8
Vv
Vk
(m/s) (m/s)
-1.39 -1.54
-1.25 -1.50
-1.54 -1.82
-1.39 -0.79
2.24
2.40
1.37
1.81
1.99
2.42
1.17
1.56
3.00
3.31
1.73
2.16
2.67
3.08
1.96
2.37
2.89
2.88
1.72
1.90
2.14
2.43
1.14
1.25
<T>
(dB)
5.0
6.1
4.9
7.0
5.4
6.2
6.2
6.8
5.7
6.0
5.5
6.9
5.5
9.3
8.8
11.4
Cp
(m/s)
5.35
6.57
13.05
12.01
steep waves as one might expect, although th e two distributions overlap significantly.
T he D oppler spectra for category III falls between the I and II spectra as expected.
This is tru e for both V and H polarizations.
It was our expectation th a t actively breaking waves and steep waves might
show noticeably different polarization ratios.
Comparing the polarization ratios
for scatterers in categories I and II, however, no consistent differences in the mean
polarization ratios are found th at can be attrib u ted other than m easurem ent errors
(see tab le 4.1). The distributions for both types are again highly overlapped, as in
the case w ith the Doppler signatures. Based upon these observations, it appears that
polarization ratio is less sensitive to the category of scatterer than is Doppler velocity.
The absolute powers of the events do provide discrimination between categories I
and II for both vertical and horizontal polarizations. Table 4.1 shows a difference
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
V Doppler Spectra
H /V Histogram
...
H Doppler Spectra
Category I
--Category II
---Category II
40 ;
density
=> 0.05
30
(0
|
0.04
Jl
c
o
u0 0.03
<
Spectra
Category I
Category II
3 20
cn 0 .0 2
10 •
Spectra
density
ij. hl
- 5 - 4 - 3 - 2 -1 0 1
- 5 - 4 - 3 - 2 -1 0 1
Velocity ( m /s )
Velocity ( m / s )
- 2 0 - 1 0 0 10 20 30
Ratio (dB)
V Doppler Spectra
H Doppler Spectra
• I I I'll ....
H /V Histogram
I I I I
I— Category III
-Category IV
Category III
0.06 ----Category IV
(IV negilible)
0.05
£
0.04
® 0.04
c
0.03
5o 0.03
A 20
0.02
CO
0.06
40
0.05
-Category III
Category IV
30
0)
0 .0 2
J 1
10
0.01
0.01
0.00
0.00
- 5 - 4 - 3 - 2 -1 0
Velocity ( m /s )
1
- 5 - 4 - 3 - 2 -1 0
Velocity ( m / s )
1
- 2 0 - 1 0 0 10 20 30
Ratio (dB)
Figure 4.13. Sea-spike event classification summary for Case A.
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
H/V Histogram
H Doppler Spectra
V Doppler Spectra
Spectra
density
Category I
. . . . Category II
0.60
>s
§
o 0.40
0.40
o
0.20
”
200
•
o
oQ>
100
0.20
0.00
Velocity ( m /s )
10 1 2 3 4-5
Velocity ( m /s )
2 0 - 1 0 0 10 2 0 30
Ratio (dB)
V Doppler Spectra
H Doppler Spectra
H /V Histogram
.
5
...........
tmnwupnmimiiw
IWH>HIHIW|IIIIIIIIHIIIIIIHHIMIIIIIHWW
Category III
— Category IV
Category III
---Category IV
Category III
.----Category IV
0.60 - (IV negilible)
density
300
0.60
tn
c
0
T3>
0.00
Spectra
■ Category I
•— Categpry II
0.60
300
0.40
c 200
3
o
<n
c
*0o)
0.40
o
oV
a.
0.20
in 0.20
0.00
0.00
■1 0 1 2 3 4
Velocity ( m / s )
5
100
Hn
-1 0
1 2
3 4
Velocity ( m /s )
5
- 2 0 - 1 0 0 10 2 0 30
Ratio (dB)
Figure 4.14. Sea-spike event classification summary for Case B.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Category I
• --Category II
---Category II
density
H /V Histogram
H Doppler Spectra
V Doppler Spectra
Category I
Category II
400
■5* 0.40
300
Spectra
c
a
o
200
9 0.20
100
0
U.fmJ
0 1 2
3 4 5
Velocity ( m /s )
0
V Doppler Spectra
1 2 3 4 5
Velocity ( m /s )
2 0 - 1 0 0 10 20 30
Ratio (dB)
Doppler Spectra
H /V Histogram
..... .........................|" m w rpr
Spectra
density
0 .50
i
i
Category III
---Category IV
(IV negilible)
F*■■I.............j .......... ■■r
-Category III
Category IV
Category III
Category IV
0.40
0 .40
0 .30
u
0.20
®
200
0.20
in
0.10
0.00
0
1 2
3 4 5
Velocity ( m /s )
0
1 2 3 4 5
Velocity ( m /s )
- 2 0 - 1 0 0 10 20 30
Ratio (dB)
Figure 4.15. Sea-spike event classification summary for Case C.
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d ensity
T linmimtm
— Category I
---Category II
0 .1 5 (I negilible)
Spectra
H /V Histogram
""I......I......I...."'I......
H Doppler Spectra
,
.
V Doppler Spectra
—Category I
;— C ategory I
— C ategory II
120 — Category II
100 (I negilible):
0.15
tn
c
V
0 .1 0
■ °
o
0 .1 0
o0)
_
c
80
J
60
40
™ 0.05
0 .0 5 •
20
■A......
0.00
-1 0 1 2 3 4 - 5
Velocity ( m / s )
0.00
-1 0 1 2 3 4 - 5
Velocity ( m /s )
V Doppler Spectra
..... ...... ...... ...... ...... .... .
H Doppler Spectra
— Category III
— C ategory IV
0.15
>N
tf)
c
*° 0.10
o
100
I
V
80
60
40
01 0.05
J
- 1 0 1 2 3 4 5
Velocity ( m /s )
H /V Histogram
...... ...............................
----- Category III
120 ----Category IV
Count
Spectro
density
---- Category III
— Category IV
• (III 8c IV negilible)
- 2 0 - 1 0 0 10 20 30
Ratio (dB)
^ ..........
0.00
- 1 0 1 2 3 4 5
Velocity ( m / s )
20
0 ...................................
- 2 0 - 1 0 0 10 20 30
Ratio (dB)
Figure 4.16. Sea-spike event classification summary for Case D.
65
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in. the mean o f about 3 dB between steep- and breaking-wave spikes. However the
distributions for both are highly overlapped.
4 .3 .4
S u m m a ry
Although th e comparison between radar and video d a ta is rather crude, it is
probably the best th a t can be achieved given the different nature of the video
and radar d ata, and the available d a ta storage and video equipm ent. The results
of this analysis show th at about 30 percent of sea spikes are caused by actively
breaking waves, while the m ajority of the rest are caused by steep waves, incipient
breakers, and possibly micro-breakers th at cannot be observed in the video data.
Recent wave-tank studies have shown good correlation between radar sea-spikes and
violent breaking waves that generate bubbles [17]. Similar studies may also establish
connections between smaller-scale breaking and radar signatures.
4.4
D iscu ssio n
4.4.1
S ca tter in g M odels
The scattering mechanisms responsible for sea-spikes are not yet fully under­
stood, and a num ber of models have been proposed to explain the phenomenon.
While FO PA IR LGA measurements and the comparison w ith video presented in
this chapter do not necessarily rule out any model, one can speculate about model
relevance given the observations.
In their controlled wave-tank experim ents, Kwoh and Lake [15] used a wedge
scattering model to explain comparable W and HH backscatter levels observed for
incidence angles up to 67°. This type of model was also used by Lyzenga [12] as a
“correction” to Composite Surface Theory to explain discrepancies between models
and m easurem ents of cr° at large incidence angles. In both cases the wedge used was
horizontally oriented, akin to a Stokes wave profile with an internal angle /3 < 120°,
as illustrated in figure 4.17a. Using th e equivalent current m ethod, backscatter cross
66
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sections for perfectly conducting wedges can be calculated [12]. The ratio between
HH and W backscatter for a wedge lying flat is plotted in figure 4.18 as a function
of /3 for a num ber of grazing angles. W hile this type of model successfully predicts
average behavior a t moderate incidence angles, it cannot produce the polarization
ratios exceeding unity found at near grazing incidence.
Kalmykov and Pustovoytenko [9] used a different “nose-on” wedge scattering
model (figure 4.17b) to explain polarization ratios at low grazing angles. T his model
can produce polarization ratios consistent with FOPAIR observations as shown in
figure 4.19, though it has been criticized as “highly contrived and unrealistic” [36].
The polarization ratio is quite sensitive to the choice of internal wedge angle and
would be an unlikely explanation for our downwind, downwave observations. How­
ever, for upwind, upwave observations, one cannot dismiss this potential scattering
geometry.
Parasitic capillary waves bound near the crests of steep waves have been observed
and proposed as a source of non-Bragg backscatter [37]. While Bragg resonance is
still responsible for the microwave echo, the scattering waves are not the “free”
capillary waves distributed over the long waves. Such scatterers can produce the
large Doppler shifts associated with the phase speeds of gravity waves and may
contribute to the observed V polarized signature. However, because the mechanism
is based on Bragg scattering, it cannot, by itself, explain the observed polarization
ratios.
An accelerating “plume” model was proposed by Wetzel [13, 36], in which the
scatterers are modeled as small cylinders with curvature radii on the order of the
radio wavelength cascading down the front of the larger gravity waves. Here, the
predicted HH backscatter is a sensitive function of the radii of the cylinders and
cylinder location on the front face of the long waves. At the peak of an unstable
67
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Observer
Observer
(a)
(b)
Figure 4.17. Geometries of wedge scattering, (a) Kwoh and Lake’s model, (b)
Kalmykov’s model.
68
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t
g _
1------ 1------ 1------[------ 1------ 1------ 1------ 1------1------ 1------ 1------ 1------ 1------ 1------ 1------ r
N um bers in p a r e n th e sis are nominal d e p r e ssio n a n g le
_!
I
I
L.
±
50
I
1
I
_l
L.
I
100
1
L.
150
Internal w edge angle (d e g )
Figure 4.18. Polarization ratio (7 =
) variation as a function of depression angle
and internal wedge angle for the wedge geometry depicted in figure 4.17a.
69
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1.0)
40
2.0)
3.0)
30
4.0)
CD
I 5-0)
TJ
>
\
X
10 .0 )
o
o 20
C
o
20.0)
o
M
o
o
CL
Num bers in parenthesis are nominal depression angle
0
100
50
150
Internal wedge an g le (d e g )
Figure 4.19. Polarization ratio variation as functions of depression angle and internal
wedge angle for wedge geometry depicted in figure 4.17b.
70
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Stokes wave (slope as 30°) for exam ple, HH backscatter can be 10 dB stronger than
VV backscatter with 3-cm-radius cylinders.
Recently, Sletten et. el. [14] showed that multi-path, scattering from a target
ju st above the ocean surface can result in stronger HH backscatter if the incidence
angle is in the vicinity of the Brewster angle, about 83° a t X-band. This enhanced H
backscatter is due to Brewster angle damping of the m ulti-path scattered V polarized
return. They showed th at if th e targets used in their study were replaced by a small
scattering source at a wave crest, such as a small bore or plume, then the same
effect could explain low grazing angle backscatter. H returns consist of the coherent
combination of single and m ultiple bounce echoes from th e scattering source. These
vary rapidly in and out of phase providing a wide echo dynamic range. The V
return consists primarily of th e single bounce echo, as th e multiple bounce echoes
are damped by the Brewster angle effect.
While the results presented here do not provide conclusive evidence, Brewsterangle damping in conjunction w ith either a plume or wedge scattering source pro­
vides a plausible explanation for the results. Despite th e difference in scattering
models, it is worth noting the sim ilarity in the pictures of scattering geometry given
by Sletten and by Kalmykov an d Pustovoytenko. As with most field measurements
in which conditions are not controlled, one can not rule out other scattering models.
Given a complicated sea surface, it is clear that sea-spikes are caused by a variety of
scattering mechanisms. While no single source can provide a consistent prediction,
a combination of several different mechanisms may.
4 .4 .2
Breaking W aves
Though virtually every investigation of high-resolution ocean-surface backscatter
has noted the importance of breaking waves in the horizontally polarized signature,
few have deliberately attem pted to correlate microwave echoes with white-cap events
using video imaging in the field. Lewis and Olin [38] used combined radar and video
71
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in their investigation of breaking waves in the near-shore zone. They noted an
obvious correspondence between the largest events and breaking, but also noted
a large num ber o f events not associated w ith visual breaking. Wave breaking in
shallow water, characterized by large curling breakers, is quite different than deep
water-wave breaking which is more “spilling” than plunging.
Jessup [18] used combined scatterom eter and video measurements from a tower
to determ ine white-cap detection estim ates. At the moderate incidence angle they
employed, the “sea-spikes” they detected were likely dominated more by specular
events where (Th h I ^ v v ~ 1- They used a combination of power and Doppler
criteria to identify sea-spikes associated w ith white-caps, and with a space-time
window included in their comparison, they found they could detect 60-70% of
sea-spikes produced by waves that broke within a limited distance downwave of their
illum inated area. If they limited attention to coincident sea-spike and white-cap
events, detection probabilities were substantially lower.
It is found here (for the limited number of cases studied) th at the m ajority of
the observed sea-spikes axe not associated w ith white-caps, though breaking waves
are responsible for more than half of the sea-spike power. Since FOPAIR images
an extended area, it would be inappropriate to include a similar space-tim e window
about the radar measurements to improve detection statistics. T hat is, at any given
tim e the radar echo consists of echoes due to both actively breaking waves and
steep waves th at may or may not eventually break. If a state of local equilibrium
can be assumed, then the average number of incipient breaking waves (waves th at
will break) and of actively breaking waves should be equal. Thus, one might reason
th a t a fraction of the sea-spike events due to steep waves that is equal to the fraction
of events due to white-caps will likely evolve into white-caps themselves (note th at
the number of events due to steep waves is consistently more than double th a t due
to total plus partial white-capping). Counting these events as detections would,
72
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however, yield an estim ate of breaking event density (or white-cap coverage) too
high, by a t least a factor of two.
Given the comparable contributions of scattering power from categories I, II, and
III in cases A, B, and C, it is also apparent th a t th e mean velocity of white-caps
is likely underestim ated by the centroid of th e HH Doppler spectrum .
Lee [11]
described their LGA scattering measurements in term s of “slow” and “fast” scat­
terers as discerned from Doppler spectra. He associated the fast scatterers with
non-Bragg scattering from gravity waves. Assuming the mean velocity of the fast
scatterers was associated with the phase speed of breaking waves, he inferred their
wavelength and found them to be short gravity waves well beyond the spectral peak.
This raised the question: if the H-polarized backscatter is due primarily to breaking
waves, then what are the m ost likely waves to break in a given wave spectrum ? The
results presented in this chapter indicate th a t the HH Doppler spectrum includes
roughly equal contributions from actively breaking waves and from steep waves,
some of which are incipient breakers. Because th e “steep wave” spikes tend towards
lower Doppler velocities, their contribution to the Doppler spectrum m ay bias any
estim ates of the wavelength of breaking waves towards shorter waves. Sm ith [39]
and Frasier [30] both inferred the group velocity of non-Bragg scatterers, and hence
the m ean wavelength of the wave group responsible for the scattering, by analyzing
dispersion properties of the backscatter. This m ay be a more reliable technique for
estim ating the breaking wave portion of the spectrum as it does not rely on absolute
velocity measurements, but rather their average space-time distribution. However,
it cannot distinguish between events associated with breaking or with steep wave
features either. Both types of events are similarly m odulated by the group structure
of the wave field and will appear together in a dispersion diagram.
Based on these results, the picture that develops of low grazing angle backscatter
is th a t the radar is essentially sensitive to a different portion of the evolution of
73
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breaking events th an is the human eye. T hat is, the radar is sensitive to both the
precursor (steep waves) and the active breaking portion of a white-cap, while the
optical cues are the white-cap itself and also the residual foam and bubbles left over
following th e event (from which the microwave echo is often negligible).
Though th e radar/video comparison has been restricted to the larger events,
the substantial overlap in both the power distributions and the Doppler velocity
distributions for steep wave spikes and for white-caps indicate th a t attem pting to dis­
criminate between the two is not straightforward and perhaps not even worthwhile.
One cannot detect a reasonable range of breaking scales w ithout also detecting
steep wave features, at least using the param eters of power, polarization ratio, and
Doppler velocity. It is perhaps more realistic to consider a simple param eter like
sea-spike density or sea-spike coverage based solely on a power threshold. Though it
may be consistently higher than separate estimates of white-cap coverage, it might
scale with wind speed or wind stress in the same way.
Phillips [20] argued as
much on dimensional grounds, predicting a cubic dependence on the number of
sea spikes w ith wind stress. Such a dependence was also observed by Jessup in
his moderate-incidence-angle tower-based measurements using his detection crite­
rion [18]. Investigating these relationships for FOPAIR/M BLEX measurements is
the goal of the next chapter.
74
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C
B
h a p t e r
5
r e a k in g w ave p r o p e r t ie s a n d e n v ir o n m e n t a l
PARAMETERS
5.1
Introduction
Breaking waves on the ocean surface are an im portant component of air-sea
interactions. They limit the height of ocean waves, mix surface waters, transfer
energy from th e wave field to currents, and enhance the fiuxes of heat, mass,
and m om entum through the generation of turbulence and entrainment of air [40].
Because wave breaking is a nonlinear and interm ittent process, direct measurement
of wave breaking in th e field is extremely difficult. For this reason the development
of optical, acoustical, and microwave rem ote sensing methods is desirable.
Breaking events have long been considered a source for microwave backscatter
especially for horizontally polarized radiation at near-grazing angles [36].
“Sea-
spikes” observed at high incidence angles (or low grazing angles) are attributable
both to actively breaking waves and to scattering features (wedges, bores, plumes)
bound near th e crests of steep waves. A number of radar studies of wave breaking
in the laboratory have attem pted to identify the specific mechanisms for scattering
and to m easure the dependence of the microwave signature on breaking strength.
Kwoh and Lake [15] attributed discrete bursts of backscatter from short gravity
waves at m oderate to high incidence angles to “gentle” breaking. Banner and Fooks
[41] studied th e scattering properties of a stationary breaker in a laboratory wave
flume. They found the scattering consistent with Bragg scattering from disturbances
in the wave field due to the breaker.
Loewen and Melville [21] correlated both
microwave backscatter and acoustic radiation from mechanically generated breaking
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waves with wave slope and dissipation. These studies all employed CW radars
operating in a beam-filled mode. As such they were precluded from operating near
grazing incidence. More recent wave-tank measurements using pulsed radars [35, 42]
and ultra-wideband radars [43] have focused more on lower grazing angle (LGA)
backscatter from breaking wave surfaces.
While much can be learned from wave-tank investigations about the physical
mechanisms for scattering due to breaking, laboratory measurements cannot repli­
cate conditions typically observed in the field, where an entire spectrum of waves is
present. Many observations have focused on characterizing the am plitude distribu­
tion of sea clutter for the purpose of rejecting it in surveillance radar applications.
Comparatively few have attem pted to relate backscatter specifically to measures
of wave breaking. Lewis and Olin [38] used combined video and radar measure­
ments to study shallow water breaking waves from the shore. Keller [44] reported
characteristic Doppler signatures of breaking events from CW scatterom eters at
moderate incidence. Phillips [19] predicted a cubic dependence on the frequency of
occurrence of breaking events versus friction velocity, u ,, and in a subsequent paper
[20] suggested th at sea-spike events due to breaking might be exploited for remote
measurements of u». Jessup [18, 45] used a CW scatterom eter and boresighted
video to study both the detection of breaking waves and their dependence on
environmental param eters. They found an approximately cubic relation w ith u .
in the number of sea-spikes (observed at moderate incidence) due to breaking, in
agreement with Phillips’ prediction.
Point measurements such as those made at moderate incidence are restricted
to measuring only th e number and/or intensity of events. Since events generally
travel through the area illuminated by the radar, duration or size measurements are
limited by the radar’s azimuthal or range coverage. This is alleviated somewhat
with ranging radar provided the events travel along the direction of the radar beam.
76
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For obliquely traveling waves, scales are again limited by the width of the beam.
Ideally, 2D imaging radar is desirable for studying these transient events.
In the previous chapter, the radar backscatter characteristics of sea-spikes were
analyzed and presented.
Sea-spikes were also classified by their visual surface
features. This com parison showed th a t radar sea-spikes are closely related to both
active breaking waves and “steep” features on the surface. It was not possible to
determine w hether such features constituted breaking or microbreaking. Thus, the
extent to which th e low grazing angle microwave signature is a reliable m etric of
wave breaking in a field environment is still not known.
In the following sections, the spatial and temporal characteristics of sea-spikes
will be explored using the high-resolution imaging and high-speed updating capa­
bilities of FOPAIR, and will be related w ith boundary layer wind and surface wave
parameters. The results are discussed and compared with space-time measurements
of wave breaking using imaging sonars [22] and films [23], and Phillips’ models.
5.2
R a d a r D a t a a n d W in d a n d W av e M e a su re m e n ts
To simplify th e analysis, only upwind radar data taken from May 2 to May 7
are used. These records correspond to a period with consistent north and northwest
wind, ranging from under 5 m /s to over 14 m /s. Radar d ata records were divided
into three groups: the first group, marked by “O” in figure 2.5, consists of 14
records obtained during May 2 and early May 3 as wind was building up while
significant wave height (SWH) remained steady. An opposing swell from the South
was prevalent for this period, and may have inhibited the development of the wave
field. The second group, marked by
consists of 47 records obtained during
developed seas. T he third group, m arked by “A ”, consists of 5 records obtained on
May 7 as winds diminished.
The wind d ata used here are 5-minute averaged wind speed and direction mea­
sured 16.5 meters above the mean surface (u 16), and friction velocity (u«) provided
77
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by M iller and Friehe o f the University of California, Irvine [46]. T he friction velocity
is plotted against Uj6 in figure 5.1, and is seen to be linearly related to u i6. u ,
represents the stress on th e surface and is more representative of the force th at
generates capillary waves, it will be used in obtaining wind dependences of sea-spike
quantities.
Surface wave frequency spectra are calculated from the tim e series of the FOPAIR
VV Doppler m easurem ent [29]. From th e wave spectra, dom inant wave frequency
is estim ated. For th e developing cases, th e spectra show two peaks, a lower peak
corresponding to an opposing swell from a previous storm, and a higher peak due
to th e local wind. A normalized wave age is estim ated from Cp/ul6, where Cp is
the estim ated phase speed of the relevant dom inant waves (not th e swells). A wave
age close to unity m eans th at the waves axe “old” or the seas are developed since
the phase speed of th e dominant wave approaches the wind speed. On the other
hand, a wave age less th an unity implies th a t the wind is still driving the waves, as
in developing, or “young” seas. Figure 5.2 plots the wave age for the data records
studied.
5.3
S ea-S p ik e E v en t D e te c tio n and T racking
As discussed in th e last chapter, sea-spike detection is achieved by applying to
HH power images a threshold determ ined from a worst-case P /a of 10~4. For the
m oderate to high sea-states considered here, this power threshold identifies about
80,000 sea-spike pixels in a typical data record with 2,000 radar images with a 10
m /s wind. A bout 400 pixels are estim ated to be mis-identified as sea-spikes due to
therm al noise fluctuations. Therefore, for m oderate to high sea-states, this power
threshold effectively separates thermal noise and sea-spikes.
Following gain correction and thresholding, detected scattering events were col­
lected into 20-second space-time volumes for analysis. A sam ple volume of data
is shown in figure 5.3. An “event” is defined as a group of pixels exceeding the
78
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20
%+ +
cn
E
<0
0.0
0.2
0 .4
0.6
0.8
u. ( m /s )
Figure 5.1. Scatter plot of friction velocity u , and wind speed at 16 m ux6 above
the m ean surface.
79
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Wave Age
3.0
2.5
2.0
CO
3
o
a_
0.5
0.0
118
120
124
122
126
128
Julian Day
Figure 5.2. Wave age estim ates for the radar data records studied. “O ” , “+ ”
and “A ” mark developing, developed, and decaying seas respectively. T he “D’s”
correspond to the “O ’s” , but were calculated using th e phase speeds of dom inant
waves due to an early storm. All d ata were taken upwind looking.
80
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*
f
t
Figure 5.3. A space-time map where each blob represents a sea-spike event. The X,
Y and Z axes correspond to azimuth, range and time respectively. Only sea-spike
events th at persist longer than 1 second are shown.
81
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power threshold th a t is spatially or tem porally connected. W ithin each volume,
individual events are uniquely labeled and their statistics are accum ulated. Among
the geom etrical properties th a t can be directly measured are th e duration, area,
propagation distance and directional orientation of scattering events. In addition,
the m ean Doppler velocity and backscattered power of events can be measured.
To reliably determ ine the directional properties of events, it is necessary th a t they
persist long enough to be tracked. A large num ber of small events are detectable
but are of too short a duration to be reliably tracked. For an event propagating at 3
m /s, the distance traveled in one radar image interval (0.25 s) is only 0.75 m. Since
the radar resolution cell is 1.5 m in range and approximately 2.1 m in azim uth at
200 m range, propagation distance and direction for events shorter than 1 s cannot
be reliably estim ated.
A trackable event is therefore a sea-spike event whose duration is at least 1 s.
For each tim e slice of a trackable event, th e centroid of scattering (x ( t ) , y ( t )) is
estim ated using
(*(0 .y(<)) =
(5-D
where (xt-(i), ?/,-(£)) and PffH,i(t) are the position of the ith pixel in the tim e slice t
of a trackable event and th at pixel’s corresponding power. For trackable events, an
event direction <f>is defined as the direction th e scattering center travels, and is found
by fitting a vector to the scattering center’s trace. Event propagation speed, Vp, is
the speed the scattering center moves, and is estim ated by dividing the distance
traversed by the scattering center by the event duration.
In video and photographic studies of oceanic whitecaps, whitecap coverage is
defined as the fractional surface area covered by foam, bubbles and any objects th at
are optically white. Ding and Farmer defined a similar quantity for the acoustic
signature of breaking waves measured by a passive imaging sonar [22]. To facilitate
later comparisons of microwave radar data, a sea-spike coverage, C, is defined as
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the fractional surface area covered by radar sea spikes. A sea-spike event density,
Q, is defined as th e number of sea-spike events per unit area per u nit tim e, and is
a m easure of the number of breaking waves passing a fixed point.
5 .4
G e o m e tr ic a l S ta tistica l P ro p erties o f Sea-Spikes
5.4.1
E v e n t D urations
Sam ple histograms of event durations for three cases corresponding to developing,
m ature, and decaying seas are plotted on linear-log scales in figure 5.4.
Mean
durations are reported for all events (m i) and for trackable events (m2). These
distributions show an increased num ber of longer duration events for the higher
wind speeds and sea states (longer tails in the PD F), however mean durations are
only weakly influenced by these events due to the consistently large num ber of
short duration events. Figure 5.5 shows mean event duration for all events and for
trackable events as functions of u ,. The wind speed and friction velocity dependences
of breaking wave parameters are generally expressed as power-laws, i.e. f ( u . ) = /?u“.
The slope of a straight line fit on a log-log plot yields the u« exponent a . Slopes for
all sea-spike events, trackable events and events longer than 1.5 and 2 seconds are
all on th e order of 0.25, indicating a weak dependence on wind speed. This result is
consistent w ith the value of 0.27 reported by Ding and Farmer for their acoustically
locatable events [22].
5.4.2
P r o p a g a tio n D irection
Propagation direction can only be determined for trackable events. By selecting
only events longer than 1 second, the m ajority of sea-spike events are discarded.
However, for typical upwind observations of developed seas, from 500 to 1000
trackable events are observed in a given data record, which is sufficient to give
reasonable directional estimates.
Figure 5.6 shows event-propagation directional
distributions for the same cases shown in figure 5.4.
The directions are given
83
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Histogram of Event Duration (JD 123.74)
10000
c
3
ou
c
1000
If )
100
It)
>
UJ
0
1
2
3
Duration (s)
4
5
6
Histogram of Event Duration (JD1 24.67)
10000
c
3
o
o
c
1000
100
<
>u
UJ
0
1
2
3
Duration (s)
4
5
6
Histogram of Event Duration (JD 127.71)
10000
3 1000
O
o
100
c
a)
>
C
o
UJ
0
2
3
Duration (s)
4
5
6
Figure 5.4. Breaking-event-duration distributions. Ti and r 2 are the mean durations
for all events and for trackable events. Plots correspond to (from top to bottom )
data taken under developing, fully developed and decaying seas in May 3, May 4
and May 7 respectively.
84
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3 .5
a = 0 .2 4
a = 0 .2 7
2.0
a = 0 .2 9
to
c
o
o
3
•a
a = 0 .2 0
0 .5
++
+:
0:
A:
□:
0.2
0 .2 0
all even ts
e v e n t duration ^ 1 .Os
e v e n t duration ^ 1.5 s
e v e n t duration ^ 2 .0 s
0 .3 0
0 .4 0
u. ( m / s )
0 .5 0
0 .6 0
0 .7 0
Figure 5.5. W ind dependence of mean breaking-event durations on log-log scale.
Slopes of the straight-line fits are the exponents to u , in a power-law relation
t = Ku*, and are provided on the right side.
85
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Histogram of Event Propagation Direction (JD12 3 .7 4 )
c
120
100
Event lon ger than 1s
'wfnd
Event longer than 1.5 s
— 1_ _ Event lon ger than 2 s
wove
D 80
oO
c
0)
>
UJ
40
20
100
150
0 event (°North)
200
Histogram of Event Propagation Direction (JD 124.67)
120
_
100
3
o
u
80
c
c
CD
>
UJ
40
100
$ event
150
(“North)
200
Histogram of Event Propagation Direction (JD125.72)
120
100
C
3
oU
c
wave
80
60
<D
>
UJ
50
100
150
0 event
200
(°North)
Figure 5.6. Sample directional distribution of trackable sea-spike events. The plots
correspond to d ata taken under developing (top), and developed seas (middle and
bottom ) in May 3, May 4 and May 5, respectively.
86
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relative to North. W ind direction and wave direction are also m arked in the figure.
Wave direction was estim ated from wave-vector spectra com puted from W velocity
im agery as in [29].
It is not clear from these plots how the directions of wind, waves, and sea-spikes
are related since th e directional distribution of events is rath er broad and wind
and waves were often aligned. On May 6, however, the wind directions deviated
from previous days by as much as 20°, while the wind speed remained relatively
high. Figure 5.7a plots tim e histories of wind, wave, and m ean event propagation
directions. Note th e excursion of wind direction from Julian day 125.5 to 126.5
and the subsequent change of the mean event propagation direction. Scatter plots
(figure 5.7b,c) of th e mean event direction vs the wind and wave directions show
clearly that sea-spike direction correlates more with the wind direction than with
the wave direction.
The standard deviation of the sea-spike event directions m ay serve as an estim a­
tor for the directional spread of breaking waves, and is plotted vs th e wind speed in
figure 5.8. Directional spread is seen to increase with the wind speed. However, it
is unclear how much of this spread is due to the wind speed increase alone because
it is probably more affected by the directional distribution of the wave and wind
fields.
5 .4 .3
Event P r o p a g a tio n Speed
Event propagation speed can be estim ated for trackable events from the distance
the event travels and its duration. Event speed is different from Doppler velocity.
It is the mean speed o f the feature while Doppler is the line-of-sight velocity of scatterers comprising the feature. To verify the consistency between the two measures,
figure 5.9 shows m ean Doppler velocity plotted against the line-of-sight component
of the event propagation speed. Given the fact th at the mean Doppler is an average
over the whole azim uth of 24°, and includes an inherent spread, the agreement
87
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180
160
- t
O 140
c
o
o 120
<u
wind direction
wave direction
ev en t direction
100
123
124
125
126
127
128
Julian Day
180
180
-C
o
|
160
~Z.
O
o
140
o
<D
'■a 120
c
■■5 1 2 0
c
a>
^
V
^
100
1 00 120 140 1 6 0 180
Wind direction ( “North)
100
100 1 2 0 140 1 6 0 180
Wave direction ( “North)
Figure 5.7. Wind, wave and event propagation directions. The angles are given
relative to North, (a) Tim e history of wind, wave and event directions. The
developing sea cases are not plotted since the dominant waves for those cases were
results of previous storms and were going against the wind, (b) Scatter plot of event
and wind directions, (c) Scatter plot of event and wave directions.
88
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Directional Spread o f Event Direction
50
45
30
6
8
10
12
14
16
U,6 ( m /s )
Figure 5.8. Directional spread of the event propagation direction as a function of
wind speed, calculated as the standard deviation of the event direction.
89
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between event speed and Doppler is good. Histograms of the event propagation
speed of trackable events are plotted in figure 5.10 for three different wind-speed
cases. These are somewhat analogous to a Doppler spectrum, though w ithout the
N yquist fold-over limitations of th at m easurem ent and without the power weighting.
Although the num ber of trackable events drops significantly for decaying seas, the
speed distribution remains similar to th a t of th e developed case.
T he mean event speed (of trackable events) is plotted against wind speed in the
top plot in figure 5.11. Regression on the d ata points for developed seas yields
a slope of 0.56, again similar to the value of 0.45 reported in [22]. Note th a t for
developing cases, mean event speeds tend to be below the regression fit, while for
decaying cases, they tend to be above th e fit. This is consistent with the observation
th at an opposing swell may have reduced the velocity of scattering features in the
developing cases, while for the decaying seas, the waves are traveling faster th an the
wind. The bottom plot in figure 5.11 shows the mean event speed plotted against
the phase speed of the dominant waves. The event speed is much smaller th an the
phase speed of the dominant waves, as is the mean Doppler velocity of sea-spikes.
5 .4 .4
B reak in g W ave Scales and S ea-S pik e V elocity
If sea-spikes are due to breaking waves at or near the crests of waves, then the
Doppler velocities of sea-spikes reflect th e velocity scales of breaking waves since
the particle velocities at the wave crests approach the phase speed of th e waves.
Similarly, if th e scattering features hold their shape and travel with th e breaking
waves, the event propagation speed should also approximate the phase speed of the
breaking waves. O ur observations of sea-spike velocity distributions are consistent
w ith dominant breaking scales much smaller than those of the dominant waves, as
has been observed by other investigators [11, 39, 30].
Snyder [23] evaluated a hypothesis th a t deep water white-capping is predictable
in term s of a threshold mechanism involving the vertical (downward) acceleration.
90
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3 .0
O', d evelop in g with op p osin g swell
+ : d ev elo p ed sea
A: d eca y in g se a
m
>>
cj
o 2.0
<
>u
jd
a.
CL
o
Q 1.5
1.0
1.0
2 .5
1.5
2.0
Radial co m p o n en t o f e v e n t s p e e d ( m / s )
3 .0
Figure 5.9. Scatter plot of th e mean Doppler velocity and the radial component of
the event speed.
91
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Histogram of Event Propagation Speed (JD 1 2 3 .7 4 )
400
Mean s p e e d :
2 .2 4 m / s
c 300
“
200
C
a>
ifi 100
o
2
4
8
6
10
12
14
Speed (m /s )
Histogram of Event Propagation Speed (JD 124.67)
400
Mean sp e e d :
2 .6 9 m / s
c 300
“
200
C
<D
ifi
100
o i
0
2
4
8
6
10
12
14
Speed (m /s )
Histogram of Event Propagation Speed (JD 127.71)
Mean sp e e d :
2 .4 9 m / s
c
3
O
o
c
>
UJ
Speed (m /s )
Figure 5.10. Histograms of event propagation speeds for trackable sea-spike events.
Plots correspond to (from top to bottom ) data taken under developing, fully
developed and decaying seas in May 3, May 4 and May 7 respectively.
92
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5
4
0 .5 6
3
T>
Ld
4
5
6
7
8
9
10
Wind sp e e d ( m / s )
20
15
5
4
.0.25
3
Ld
4
5
6
7
8
9
10
15
P h a se sp eed of dom in an t wave ( m / s )
20
Figure 5.11. Top: m ean event propagation speed vs wind speed. Bottom: mean
event propagation speed vs phase speed of the dom inant waves. The regression fits
only use d ata records for developed seas ( “+ ” symbols). “O ” and “A ” symbols are
for developing and decaying seas. Slopes of the fits are provided on the right.
93
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Ding and Farmer used this hypothesis as motivation to predict breaking speed using
the acceleration spectrum as a weighting function. For linear gravity waves, the
acceleration spectrum is related to the surface elevation and velocity spectra by
j4.(u/) = u;2V(u;) = w4S(u/),
(5-2)
where A(u>), V (u) and S (u ) are acceleration, velocity, and displacement spectra
respectively. The mean speed of breaking waves can then be defined as [22]
Cbr = 7-
f
c(u)A(u>)du,
/ 4 Jfwi
wi
(5.3)
where
Ml?
I A(w)du
(5.4)
Jut1
is the fourth moment of the elevation spectrum, and c(w) = g /u is the phase velocity
of gravity waves. The integration limits are set to the dominant wave frequency, wj,
and a high-frequency cutoff, u 2, imposed by instrum ent limitations. Tim e series of
VV Doppler velocity have been used to obtain velocity and acceleration frequency
spectra. Weighting by the acceleration spectrum emphasizes the influence of shorter
(slower) waves. The breaking wave scale velocity is calculated for each d a ta record,
and plotted against the mean event propagation speed in figure 5.12. The m ean event
speed is 60-80% of the breaking scale. Ding and Farm er reported that breaking-event
propagation speed was 75-95% of th at of the breaking scale. The lower values we
obtained may be explained by the fact that the upper limit of the frequency spectrum
of surface waves derived using radar Doppler measurement is limited by th e radar
resolution cell size, which is about 2 meters. The cell size determines th e Nyquist
wavenumber that can be sampled. Using the linear dispersion relation, th e Nyquist
frequency was found to be 0.62 Hz, corresponding to a phase speed of 2.5 m /s.
94
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0.8
x>
<u
§. 0.6
CO
c
CD
>
<D
§ 0.2
2
0.0
2.0
2.5
3.0
3.5
Cbr (m /s )
4.0
4.5
5.0
Figure 5.12. Normalized mean event propagation speed vs velocity scales of breaking
waves.
“O ”, and “A ” symbols are for developed, developing, and decaying
seas, respectively.
95
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5.4.5
Sea-Spike Event Coverage and D ensity
Oceanic whitecap coverage has long been studied using photographic and video
instrum ents. Power-law relations are often assumed between whitecap coverage and
wind speed typically measured at 10-m eter height (u l0). W ind speed exponents
have been found in the range 3.2 to 3.75 [25] for visual estim ates obtained from
film and video. For microwave imaging radars, an analogous quantity, sea-spike
coverage, can be defined. Since the physical mechanisms responsible for th e optical
and microwave signatures of breaking waves differ, th e absolute coverages measured
using these techniques will likely differ from each other. However, if they are rooted
in the same physical mechanism (i.e. wave breaking), one might expect common
dependencies on wind speed.
Sea-spike coverage is plotted against u . in the top of figure 5.13, and power-law
relations estim ated. It is interesting to note th at for th e earlier developing seas
(marked as “O ”), sea-spike coverage is higher than for developed seas a t the same
wind speed. This may be due to the earlier stage of development of the wave field and
in part to th e presence of an opposing swell, which probably made the wind waves
more unstable. If only d a ta records for the developed seas are used, an exponent of
2.16 for u . is obtained. Ding and Farmer defined an “active acoustic coverage” in
their passive acoustic measurements and found a wind speed exponent closer to 1,
a linear dependence [22].
Sea-spike event density is closely related to sea-spike coverage. However, since
each event m ay comprise many pixels, the event density as a function of wind is
expected to behave differently from that of coverage. T he bottom plot in figure 5.13
shows the event density vs friction velocity. The power-law fit shows a slope of
1.09 for friction velocity. Phillips developed a model for the number of sea-spike
events per u n it area per unit time based on a saturation wind-wave spectrum , and
predicted th a t event density will have a cubic dependence on friction velocity if the
96
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0 .1 0 0
<u
cr>
ou.
>
O
U
2.16
CD
CD
0.010
'c l
cn
o
(/)
A
cd
0.001
0.20
0.30
0.40
u. (m /s)
0.50
0.70
0.010
cn
c
a>
•o
c
<
>u
1.09
CD
CD
'o.
cn
o
CD
c/)
0.001
0.20
0.30
0.40
u. (m /s)
0.50
0.70
Figure 5.13. Sea-spike coverage and density dependence on u ,. Coverage is unit-less,
while density has the units of m ~ 2s~l .
“O ”, and “A ” symbols axe for
developed, developing, and decaying seas, respectively. The numbers on the right
are the slopes of the regression fits using only the data for developed seas.
97
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power threshold for sea-spike detection is set sufficiently high, or a suitable sea-spike
duration threshold is imposed [20]. To see if th e trackable events will follow a cubic
dependence on friction velocity, event densities for trackable events are plotted in
figure 5.14. The slope is now 1.65, still well short of the prediction. The num ber
of trackable events is much smaller than the to tal num ber of sea-spike events, as
expected, and the d a ta shows greater scatter th an using all events.
One possible explanation for the low wind exponent is that in Phillips’ model,
sea-spike backscatter is assumed to be independent of the radio wavelength. From
the physical point of view, a sea-spike can be due only to one of several possible
mechanisms: Bragg resonance, specular reflection, or edge diffraction. Since Bragg
scattering cannot produce the observed polarization dependence of sea spikes, only
the last two choices are possible. For specular reflection, the optical limit is assumed.
As long as the breaking surface scale is much larger th an the radio wavelength, the
backscatter will not depend on the breaking scale. However, if edge diffraction is
the physical scattering mechanism, the scales of the scattering features m ust be
comparable to the radio wavelength. This means th at the backscatter only occurs
in a certain band of the breaking scales, or a certain band within the saturation
spectrum . The expected backscatter due to edge diffraction would therefore be
lower than th at predicted by Phillips’ model.
Another possible explanation is that the power threshold used was not sufficiently
high, th at noise or possibly interference due to the FLIP structure biased the results.
To see the effect of varying threshold, sea-spike coverage and event density are
plotted in figure 5.15 using increasingly higher thresholds. As expected, the absolute
levels of coverage an d density drop as the threshold is increased. The u , exponent
for sea-spike coverage varies little as the power threshold is increased by 9 dB above
the level determ ined by P/a = 10~4. The exponent for event density, however, nearly
doubled, changing from 1.09 to 1.95. While th e coverage levels drop by about 10
98
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0.0010
1.65
>>
CO
c
CD
“O
c
CD
>
CD
_0J
n
o
U
o
0.0001
0.20
0.30
0.40
0.50
0.70
u. ( m / s )
Figure 5.14. Event density for trackable events (minim um duration of 1 second).
“O ” , and “A ” symbols are for developed, developing, and decaying seas,
respectively. The number on the right is the slope of the regression fit using only
the d a ta for developed seas.
99
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0.100
0.0100
2 .1 6
aj
O’
a
<
>u
CO
c
2.31
<u
-o
c
o
V
CD
>D 0.0010
<
<U
2 .4 7 -
0.010
'o.
cn
-
' c l.
tn
I
cu
2 .3 7
o
CO
0.0001
0.001
0 .3 0
0 .4 0
0 .5 0
0 .7 0
u. ( m / s )
0 .3 0
0 .4 0
0 .5 0
0 .7 0
u- ( m / s )
Figure 5.15. Coverage and density dependence on u , and threshold levels.
“O ”, “A ” and
are for threshold levels of 0 dB, 3 dB, 6 dB and 9 dB above the
threshold determ ined by P /a = 10~4, respectively. The numbers next to the straight
lines are the slopes. Only the d a ta for developed seas are used.
100
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dB for a threshold increase of 9 dB, the density levels drop only about 7 dB. This
is consistent with the observation th a t a single event sometimes splits into two or
more events as the threshold increases (see figure 4.9 for an illustration).
Phillips also suggested that duration and power thresholds are equivalent to
each other, and to a threshold on wavenumber. In figure 5.16, coverage and density
estim ates using different duration cutoffs are plotted against i t.1. For low wind
conditions, th e sea-spike coverage decreases quickly as the minim um event duration
is increased, probably because of the lack of longer events. Although the slopes for
density do not change as dramatically, the absolute densities drop by a factor of
100. Both quantities show significant scatter as the minimum duration is increased,
implying th a t duration is a much more restrictive filter than power. No convergence
of the u Mexponents for both coverage and density can be detected.
From video records of the ocean surface taken simultaneously with the radar
data during daylight, whitecap coverage can be estimated. For each radar record,
50 corresponding digitized video images (sampled at approximately 5 s intervals
over each rim) were analyzed. Grey-scales of the digitized video images show clear
distinctions between whitecaps and the background wave field. W hitecap coverage
was estim ated from a region of the video including the radar footprint corresponding
to an area of 13,800 m 2. The total accum ulated whitecap area was divided by
the total area over the 50 images. Figure 5.17 shows a scatter plot of whitecap
and sea-spike coverages.
Whitecap coverage values appear to be low compared
to the reported values of 1% or more for wind speeds over 10 m /s [22, 23], and
show large scatter. A power-law fit between whitecap and sea-spike coverages gives
a slope 3.76, further indicating th at the two behave very differently. The large
variation of whitecap coverage may indicate th a t whitecaps are not simply related to
lThe concept of a duration, however, can only be defined after an event is detected. The
duration threshold is therefore applied to sea-spike events detected using the power threshold from
P/a = 10- 4.
101
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0 .1 0 0
2 .1 6
2 .7 3
3 .1 7
<u
cr
oI .
<
>D
O
V
4 .4 2
0 .0 1 0
■tn
q.
0.001
0 .3 0
0 .4 0
0 .5 0
0 .7 0
u. ( m / s )
0 .3 0
0 .4 0
0 .5 0
0 .7 0
u. ( m / s )
Figure 5.16. Coverage and density dependence on wind and duration cutoffs.
“O ” , “A ” and
are for all events, events longer than 1 second, events longer than
1.5 seconds and events longer than 2.5 seconds, respectively. The numbers next to
the straight lines are the slopes. Only the d ata for developed seas are used.
102
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-2
<u
cr>
ou .
<
U
>
-3
o
++
o
CL
a
o
<u
-4
-5
0.001
0 .0 1 0
S ea spike c o v e r a g e
0 .1 0 0
Figure 5.17. W hitecap coverage obtained from video recordings of the radar scene.
The regression fits used all d ata points where whitecap coverage is above 10-4 .
“O ”, and “A ” symbols are for developed, developing, and decaying seas,
respectively.
103
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wind. O ther factors such as currents, air and sea tem perature, salinity and pressure
th a t would affect not only breaking and breaking scales, but also the persistence
of bubbles and foam, may play very im portant roles in w hitecap coverage. Using
visual whitecaps as estimates for surface wind and wind stress m ay be unreliable.
5.5
D iscu ssio n
T he statistics of the geometrical properties of sea-spikes and their dependence
on wind and wave parameters show clearly that sea-spikes are closely associated
with local surface wind and wind stress. The mean sea-spike duration is weakly
dependent on the wind speed and th e sea-spike travel direction appears to follow
the local wind direction. The dependence of sea-spike coverage on friction velocity
has a power-law exponent about 2.3 th a t is relatively constant as one varies the
power threshold. T he sea-spike event density, however, does not show a converging
dependence on friction velocity as the threshold level is varied. The exponent to
u , for sea-spike density shows an increasing trend (from 1.09 to 1.95 as th e power
threshold is raised by 9 dB, and from 1.09 to 3.14 as th e minimum duration is
increased to 2.5 seconds). Thus no conclusion can be reached a t this point as to
the validity of Phillips’ prediction o f the u? dependence of the sea-spike density for
low-grazing radar data.
The mean Doppler of sea-spikes and the propagation speed of sea-spike events
are both substantially lower (17% and 26% respectively) th an th e phase speed of
the dom inant waves, and somewhat lower (45-58% and 59-79% respectively) than
the breaking-velocity scale based on a downward acceleration variance [23]. The
scattering features responsible for radar sea-spikes at LGA appear to correspond to
surface waves of a few meters’ length, and are consistent w ith sonar measurements
[22],
Jessup reported th a t sea-spike backscatter cross section is cubically dependent
on friction velocity [45] at moderate incidence angle, in agreem ent with Phillips
104
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CL
CL
<tf
£
O
0 .1 0
Q.
<D
*Q .
(fl
*o
CP
«
C
o<D
0.01
0.2
0.3 0.4 0.5 0.6
u. (m /s )
0.3 0.4 0.5 0.6
u. ( m /s )
Figure 5.18. Sea-spike power and mean sea-spike cross section. “+ ” , “O ”, and “A ”
symbols are for developed, developing, and decaying seas, respectively. The numbers
in the plots are the slopes of the regression fit using only the d a ta for developed
seas.
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
predictions [20]. It would be interesting to see how sea-spike backscatter is related
to friction velocity at near grazing incidence. In figure 5.18, integrated HH sea-spike
backscattered power and mean HH sea-spike backscattered power are plotted against
um. W hile a slope of 2.5 for the total sea-spike power is found, the m ean sea-spike
backscatter - which is proportional to the m ean normalized radar cross section
- only has a very weak dependence on wind. This suggests th at the increase of
sea-spike backscatter in low-resolution radars such as scatterometers is due to the
increased sea-spike coverage. Although the LGA sea-spike data presented here do
not appear to follow Phillips prediction, the results do support Phillips’ suggestion
that a high-resolution imaging radar can be used to measure the surface wind field
by simply counting pixels instead of relying on its accuracy.
106
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C h a p t e r
6
C o n c l u sio n s
In this dissertation, I have attem pted to answer several questions on low-grazingangle ocean backscatter using FOPAIR MBLEX image data. The first question
addressed is what are the physical scattering features responsible for radar sea
spikes?
Secondly, how are radar sea spikes related to wave breaking and other
oceanic and environmental param eters?
The backscatter of sea spikes suggests that Bragg scattering models cannot
explain the sea spike phenomenon. Doppler spectra d a ta indicate that sea spikes
tend to move much faster th a n the phase speed of the resonant Bragg waves. The
fast moving scatterers are present in both W and HH backscatter. While in HH
they are the dominant scatterers, they tend to be masked by Bragg scattering in
W . An examination of the polarization ratio of the sea spike scatterers showed th at
HH spikes are 6 dB stronger th an W spikes. The large positive polarization ratio
implies that low-grazing-angle scattering models such as specular reflection, bound
capillary waves, or scattering from Stokes-wave-like wedges alone will not explain
the phenomenon. Plausible models include nose-on wedge scattering and m ulti-path
backscattering near the Brewster angle. Well controlled wave-tank experiments are
needed to further verify these models.
It has also been shown in this dissertation that low-grazing-angle radar sea spikes
are closely related to breaking surface waves. In young and developed seas under
m oderate to high wind conditions, some 30 percent of sea spikes are caused by
actively breaking waves, while the m ajority of the rest are associated with steep and
incipient breaking waves. Although no significant differences in sea spikes’ physical
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
properties exist between the classes o f sea spikes, in the m ean, the Doppler of th e
active-breaking spikes is higher than th e other classes. This implies that using th e
m ean Doppler of sea spikes to infer th e phase speed of breaking waves will lead to
an underestim ation.
T he relations between the sea-spikes and oceanic and environmental param eters
were the second area this dissertation explored. Sea-spikes were tracked utilizing th e
space-tim e tracking capability of FOPAIR. The results show th a t they are closely
related to the local wind and wave conditions: sea-spikes tend to move in th e
direction of the local wind at speeds approaching the phase speeds of the highest
downward accelerating waves, but considerably slower than the phase speed of th e
dom inant waves derived from surface height or velocity spectrum . Radar sea-spike
coverage is found to have a friction velocity dependence C = fin l-3, but no consistent
u , exponent is found for sea-spike event density. The lack of a cubic exponent to
u , for sea-spike density is probably due to the unique scattering mechanisms a t
low-grazing angles, and does not necessarily disagree with the predictions using a
satu ration wind-wave spectrum . Nonetheless, the very sensitive dependence of radar
sea-spike properties - both physical (radar backscatter, Doppler) and geometrical
(coverage, feature movement) - on wind and friction velocity should be further
explored for remote sensing applications.
Together with previous work on using the W radar image to obtain wavevectorfrequency spectra, it has been shown th a t a dual-polarization imaging radar such as
FO PA IR can provide a great deal of useful information about ocean surface waves,
surface wind conditions, as well as on the physics behind the scattering of radio
waves by ocean waves. T he research presented here will provide support for further
stu d y of electromagnetic scattering and radar remote sensing of the oceans using
such instrum ents.
108
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Referen ces
[1] Rice, S. O. Reflection of electromagnetic waves from slightly rough surfaces.
C om m . Pure and Applied Math., 4:351-378, 1951.
[2] Bragg, W. L. The diffraction of short electromagnetic wave by a crystal. Proc.
Cambridge Phil. Soc., 17:43, 1913.
[3] Crombie, D. D. Doppler spectrum of sea echo at 13.56 m c./s. Nature, 175:681682, 1955.
[4] Valenzuela, G. R. and Laing, M. B. S tudy of doppler spectra o f radar sea echo.
Journal o f Geophysical Research, 75(3):551-563, 1970.
[5] W right, J. W. A new model for sea clutter. IE E E Transactions on Antennas
and Propagation, AP-16(2):217-223, 1968.
[6] Bass, F. G., Fuks, I. M., Kalmykov, A. I., Ostrovsky, I. E., and Rosenberg,
A. D. Very high frequency radiowave scattering by a disturbed sea surface p a rt 1: scattering from a slightly disturbed boundary. IE E E Transactions on
A ntennas and Propagation, AP-16(5):554-559, 1968.
[7] Bass, F. G., Fuks, I. M., Kalmykov, A. I., Ostrovsky, I. E., and Rosenberg,
A. D. Very high frequency radiowave scattering by a disturbed sea surface p art 2: scattering from an actual sea surface. IE E E Transactions on Antennas
and Propagation, AP-16(5):560-568, 1968.
[8] Valenzuela, G. R. Theories for the interaction of electromagnetic and oceanic
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