- Scientific Journals of the Maritime University of Szczecin

Scientific Journals
Zeszyty Naukowe
Maritime University of Szczecin
Akademia Morska w Szczecinie
2008, 13(85) pp. 45‐49
2008, 13(85) s. 45‐49
Multi-component composite model of the sea surface
for radar applications
Wieloskładnikowy model powierzchni morskiej
w zastosowaniach radarowych
Yury A. Kravtsov1, Andrzej Stateczny2
1
Space Research Institute, Russ. Acad. Sci., Moscow, Russia.
Akademia Morska w Szczecinie, Instytut Matematyki, Fizyki i Chemii
70-500 Szczecin, ul. Wały Chrobrego 1–2, tel. 091 4809329, e-mail: [email protected]
2
Akademia Morska w Szczecinie, Katedra Geoinformatyki
70-500 Szczecin, ul. Wały Chrobrego 1–2, tel. 091 4809464, e-mail: [email protected]
Key words: sea surface radar models, sea radars
Abstract
The article presents multi-component composite model of the sea surface which generalizes the standard twoscale model (small-scale gravity-capillary waves lying on the large-scale gravity waves). The suggested
model considers the non-resonant backscatter from large-scale breaking gravity waves and resonant backscatter from the steep wavelets of meso-scale spectrum (meso-waves). The multi-component composite model
differs from the standard two-scale composite model in that it involves the non-resonant components against
the background of “macro-breaking” large-scale waves, or in the form of “micro-breaking” steep mesowaves. The main goal of this paper is to stimulate further analysis of the angular, frequency and polarization
characteristics of the resonant and non-resonant backscatter mechanisms in order to distinguish between
them.
Słowa kluczowe: radarowe modele powierzchni morskiej, radary morskie
Abstrakt
Opisano wieloskładnikowy model powierzchni morskiej, który uogólnia standardowy dwuskalowy model
(drobnoskalowe grawitacyjnie-kapilarne fale, leżące na tle wieloskalowych fal grawitacyjnych). Zaproponowany model uwzględnia nierezonansowe rozproszenie od wieloskalowych załamujących się fal grawitacyjnych albo rezonansowe rozproszenie od stromych faleczek mezoskalowej długości (mezofale). Wieloskładnikowy model różni się od standardowego dwuskalowego modelu dodaniem nowych składników w postaci nierezonansowych elementów na tle „makrozałamujących się” wieloskalowych fal albo w postaci rezonansowych „mikrozałamujących się” stromych mezofal. Głównym celem artykułu jest stymulacja dalszej analizy
kątowych, częstotliwościowych i polaryzacyjnych charakterystyk rezonansowych i nierezonansowych mechanizmów rozproszenia w celu ich rozróżnienia.
Introduction
ripples and thereby forms the radar image of the sea
surface.
Though the two-scale model satisfactorily
describes many properties of the radar echoes at
sufficiently moderate grazing angles, exceeding
(10–15)°, it does not explain the characteristic features of microwave scattering from the large breaking waves, when white capping occurs, as well as
backscattering from the sea surface at low grazing
The two-scale composite model of the sea surface forms a basis for the modern theory of the
radar signal scattering from the sea surface [1, 2, 3].
In frame of the two-scale composite model, the
small-scale component is responsible for resonant
(Bragg) mechanism of scattering, whereas the
large-scale component modulates the parameters of
Zeszyty Naukowe 13(85)
45
Yury A. Kravtsov, Andrzej Stateczny
angles γ ≤ (10–15)°. It concerns above all the abnormal polarization ratio at low grazing angles: the
observed ratio of the cross-section σH at horizontal
polarization to that at vertical polarization σV often
exceeds a unit [4, 5, 6, 7]: χobserved=(σH / σV)observed>1,
while Bragg theory predicts very low polarization
ratio [1, 2, 3]: χBragg 〈〈 1. The phenomenon of the
large spikes (“super-events”) observed at low grazing angles, as well as the phenomenon of asymmetry between upwind and downwind cross-sections
[8] can not be explained by the resonant theory
either.
All the attempts to describe the totality of facts
observed at low grazing angles involve the nonBragg objects on the water surface, which principally can not be described by the Bragg theory.
Such non-Bragg scatterers are presented mostly by
large-scale breaking waves containing “boiling
water” component, characteristic for white capping
area, and steep and sharp-crested elements characteristic for the initial stage of wave breaking [9, 10,
11, 12].
In the series of publications [13, 14, 15, 16, 17,
18, 19, 20], the hypothesis was put forward that
besides large-scale breaking waves, the sharpcrested waves of meso-scale spectrum, which are
significantly lower and shorter compared to the
large-scale breaking waves, may contribute much to
phenomena observed at low grazing angles. Contribution of the sharp-peaked meso-waves was described in [13, 14, 15, 16, 17, 18, 19, 20] in the
form of “three component” composite model of the
sea surface, which involves the third component
(sharp-peaked meso-waves) into standard two-scale
model and thereby allows describing the non-Bragg
phenomena observed at low grazing angles.
A semi-empirical model of the sea surface, proposed by the Kudryavtsev et al. in [21, 22, 23],
takes into account large-scale breaking waves.
Kudryavtsev’s model represents the sea surface as
combination of two types of surfaces: a “regular”
(non-breaking) wavy surface, described by the
standard two-scale model, and strongly perturbed
breaking zones, characterized by the enhanced
roughness, radar scattering from the “regular” surface and the breaking zones are considered to be
statistically independent. Thus, Kudryavtsev’s
model presents a cross-section per unit of sea surface as a sum of two terms:
σ S = (1 − q)σ Sregular + qσ Sbreaking
correspondingly, and q is the fraction of the sea
surface, covered by breaking waves.
The experimental finding by Ericson et al. [24],
and a model approach proposed by Phillips [25],
Kudryvtsev et al. [21, 22, 23] have assumed that the
radar scattering from an individual breaking zone
can be presented as specular reflections from very
rough wave breaking patterns. Free constants of
Kudryavtsev’s model were chosen so that it fits
available radar measurements of polarization ratio
and upwind-downwind asymmetry [23].
In line with [26], this paper describes the multicomponent composite model, which unites the merits of the three component composite model, suggested in [13, 14, 15, 16, 17, 18, 19, 20], and semiempirical composite model, studied in [21, 22, 23].
The basic elements of the multi-component
composite model are presented in sect. 2. Sections
3 and 4 briefly describe contributions of whitecaps
and sharp-peaked elements into observed radar
cross-section. Section 5 discusses different phenomena, described by the multi-component composite model.
Multi-component composite model
of the sea surface
The two-scale composite model deals with ripples of sufficiently small amplitudes, superimposed
at large-scale gravity waves [1, 2, 3]. The latter
modulates the signal, scattered by ripples, in two
ways: by direct hydrophysical influence on a ripples spectrum and by showing the ripples at different aspect angles due to large gravity wave tilting.
The main shortcoming of the commonly accepted
two-scale composite model is its inability to describe phenomena observed at low grazing angles.
This shortcoming can be efficiently overcome by
inserting non-resonant components into traditional
two-scale composite model. The discrete sharpcrested elements responsible for non-resonant scattering by meso-waves were involved into two-scale
model in the papers [13, 14, 15, 16, 17, 18, 19, 20].
The extended composite model represents the
total radar cross-section σS of the element of radar
resolution S as a sum of the two terms:
σ S = σ SBragg + σ SnonBragg
(2)
The first term in equation (2) corresponds to the
standard two-scale composite model, which describes contribution of small-scale ripples, modulated by large-scale gravity waves. This term can be
presented as
(1)
Here σ Sregular and σ Sbreaking characterize the
“regular” breaking components of the sea surface
46
Scientific Journals 13(85)
Multi‐component composite model of the sea surface for radar applications
σ SBragg = ∫ σ 1Bragg d s
Contribution of whitecaps
(3)
The dynamics of processes inside whitecaps is
so complicated that nobody, according to the author, dares to suggest any reasonable radar model
for the sea surface. The simplest, if not primitive,
model for the whitecaps might involve a set of incoherent scatterers, which are presumably of the
egg-like form with a typical radius a ≥ λ. Then
individual cross-section is σ k ~ π ak2 . Assuming
that the scatterers that are densely packed (the average distance b between them is of order 2a ), the
non-resonant cross-section (4) for whitecaps can be
σ Swhitecap ~ N π a 2 ,
where
estimated
as
S
where dimensionless quantity σ 1Bragg is a resonant
cross-section per a unit surface.
The second term in equation (2) summarizes the
contributions of non-resonant scatterers within the
resolution element S:
σ SnonBragg = ∑ σ knonBragg
(4)
k
σ knonres being a cross-section of the k-th scatterer.
This term embraces contributions of both sharpedged waves and “boiling-water” surface inside
white capping areas in frame of Kudryavtsev’s
model.
According to Bragg theory [1, 2, 3], at low grazing angles the resonant cross-section for horizontal
polarization is significantly smaller compared to the
one for vertical polarization: σ SBraggH 〈〈σ SBraggV ,
whereas at moderate grazing angles, the quantity
σ SBraggH and σ SBraggV might be comparable with
N ~ S whitecap / b 2 is an estimate for the total number
of scatterers inside the resolution element. As
a result, the total non-Bragg cross-section happens
to be proportional to Swhitecap:
σ SnonBragg ~ S whitecap π a 2 /( 2a) 2 ~ S whitecap
In general, this regularity might be presented in
the form
each other: σ
~σ
. In contrast to Bragg
scattering, at low grazing angles the non-resonant
cross-section for horizontal polarization might exceed
that
for
vertical
polarization:
σ SnonBraggH > σ SnonBraggV . At the same time,
BraggH
S
BraggV
S
σ Swhitecap ≈ KS whitecap
(6)
implying that the proportionality coefficient K takes
into account the effects of shadowing, of multiple
scattering, of absorption in the foam cover and others. As a result, the factor K happens to be dependent on radar wavelength and on viewing angle.
Polarization dependence will appear, when the
Brewster effect is taken into account, as was analyzed in [27, 28, 29, 30, 31, 32, 33]. Upwinddownwind asymmetry stems from the shadowing
effect. Spikes arise, when intensive gravity wave
breaks inside resolution element.
σ SnonBraggH becomes comparable with σ SnonBraggV at
moderate grazing angles: σ SnonBraggH ~ σ SnonBraggV .
Depending on meteorological conditions, viewing angle, polarization and frequency of electromagnetic waves, the Bragg or non-Bragg mechanism might prevail. This explains the great diversity of the ocean images, observed by groundbased, ship-borne and aerospace-borne radar at
different angles of observation and in different frequency bands.
There are at least two classes of scatterers,
which may contribute to the non-resonant mechanisms of scattering. The first class is presented by
sharp-peaked waves, whose edge curvature radius
is less than a radar wavelength. Sharp-peaked profile is characteristic both for the initial phase of
“macro-breaking” phenomenon, that is large gravity wave breaking, and for “micro-breaking” of
comparatively short and low waves of meso-scale
spectrum. In contrast to “macro-breaking”, the latter practically does not produce foam and water
spray. The second class is “boiling water” inside
the whitecaps, accompanying “macro-breaking”.
Let us consider briefly both kinds of scatterers.
Zeszyty Naukowe 13(85)
(5)
Contribution of sharp-crested meso-waves
Analysis of experimental data, undertaken in the
papers [13, 14, 15, 16, 17, 18, 19, 20], has revealed
the important role of the sharp-crested meso-waves.
Their characteristic lengths (30–50 cm) and heights
(10–20 cm) are intermediate between those of
small-scale (a few centimeters) and large-scale
(meters and longer) components of the wave spectrum. Due to their relatively small height, mesowaves usually break ‘silently’, that is without producing foam and spray [34, 35]. The meso-waves
are typically seen as characteristic dark “wrinkles”
on the water surface (corresponding photos are
presented in [36]).
47
Yury A. Kravtsov, Andrzej Stateczny
Polarization ratio. Strong influence of the
Brewster phenomenon on polarization ratio was
revealed in [27, 28, 29, 30, 31, 32] as applied to
microwave scattering from the steeping and breaking large-scale gravity waves. According to [27, 28,
29, 30, 31, 32], in the vicinity of the Brewster angle
the Fresnel reflection coefficient from the sea water
at vertical polarization happens to be significantly
smaller as compared to that at horizontal polarization, what results in noticeable suppression of the
radar echo at vertical polarization.
The Brewster mechanism of vertical polarization
damping holds also for microwave scattering from
sharp-crested meso-waves. According to calculations, performed in [20] and [37] on the basis of
geometrical theory of diffraction, the polarization
ratio χnonBragg at low grazing angles reaches sometimes 5–10 dB, whereas the resonant polarization
ratio χBragg is small enough.
Super-events. Sea spikes, i.e. spikes in the temporal records of backscattered signal (“super
events” in the terminology of [6, 7]) are the most
prominent at horizontal polarization and less visible
at vertical one. What is important, the amplitude of
radar signal spikes at horizontal polarization can be
significantly higher, sometimes by 10 dB, than at
vertical one. It was found in [34, 35] that radar signal spikes are not often associated with the whitecaps, registered by video records simultaneously
with radar signal, so that radar spikes are mostly
not accompanied by visual breaking.
It looks somewhat surprising that the echo signals from the sharp-peaked wave might be of significant strength, up to
Due to the concave shape of the wedge front
side, the incident electromagnetic wave experiences
multiple diffractions, which can be described in the
framework of the geometrical theory of diffraction.
The incident wave excites, first of all, the wedge
wave Ee, which diverges from the wedge sharp
crest. The wedge wave Ee, in turn, brings about
multiplicity of waves Ees, Eess, Eesss and so on, reflected from the footnote in a specular way. The
primary electromagnetic wave, incident on a concave front side of a meso-wave, may produce also
multiply specular reflected wave Es, Ess, Esss, ...., as
well as the wedge wave Ese and its byproducts Eses,
Esess and so on. Every term among the listed wave
fields can be treated as a channel of multiple diffractions, as it was presented in the recent papers
[36, 37].
The most important features of multiple diffractions at curvilinear wedge are presented by the
four-channel model, which includes the following
four terms:
E = Ee + Ees + Ese +Eses
(7)
The first term is an edge wave, mentioned
above. This wave returns to the radar antenna after
the single act of diffraction at the curvilinear wedge
crest. The second term ues, excited by the edge
wave, returns to the radar antenna after specular
reflection from the wedge foot. The third term use is
a wave, which firstly is reflected from the wedge
foot and then diffracted at the wedge sharp crest.
By virtue of reciprocity theorem, double diffracted
wave fields ues and use are coherent to each other:
Ees = Ese
(8)
These two terms are responsible for the enhanced backscattering phenomenon, caused by
multi-path (multi-channel) scattering, similar to
backscattering from “macro-breaking” waves, studied in [27, 28, 29, 30, 31, 32, 33], only with ‘white
capping’ wave field instead of the edge wave.
The fourth term in equation (7) corresponds to
a triple diffraction: first specular reflection occurs
from the wedge foot, which is followed by a diffraction, by the sharp crest and by the second reflection from the wedge [37].
σ nonBragg ≈ L2c
(9)
where Lc is a “coherent” crest length, which obeys
to Fresnel criterion (phase difference should not
exceed π).
According to (9), coherently illuminated wedge
crest of Lc ≈ 1 m by length provides crosssection σ Sedge ≈ 1 m2. Even larger cross-sections
might be produced by the specular reflections from
a concave front of a meso-wave: the ‘specular’
cross-section, even if very rarely, could reach the
value σ Sspecular ≈ 10 m2. Of course, the random factors are able to deteriorate the smooth form of the
curvilinear wedge and thereby to reduce the effect
of coherent scattering, but this does not exclude the
possibility of super-events completely.
Upwind-downwind asymmetry. Another fact,
incompatible with the Bragg theory, is an observed
asymmetry between upwind and downwind
Phenomena described by the multi-component composite model
With the sharp-crested meso-waves incorporated
as additional elements of the sea surface, the threecomponent composite model is able to describe
a wide circle of phenomena at low grazing angles
and simultaneously to clarify the role of the sharpcrested meso-waves at large grazing angles.
48
Scientific Journals 13(85)
Multi‐component composite model of the sea surface for radar applications
16. KRAVTSOV YU.A., LITOVCHENKO K.TS., MITYAGINA M.I.,
CHURYUMOV A.N.: Radiotekhnika, Moscow, 2000, N1,
61–74.
17. CHURYUMOV A.N., KRAVTSOV YU.A.: Waves in Random
Media, 2000, 10(1), 1–15.
18. CHURYUMOV A.N., KRAVTSOV YU.A., LAVROVA O.YU.,
LITOVCHENKO K.TS., MITYAGINA M.I., SABININ K.D.: Advanced Space Research, 2002, 29(1), 111–116.
19. CHURYUMOV A.N., KRAVTSOV YU.A., LAVROVA O.YU.,
LITOVCHENKO K.TS., MITYAGINA M.I., SABININ K.D.: Intern. J. Remote Sens., 2002, 23(20), 4341–55.
KRAVTSOV YU.A.,
LAVROVA O.YU.,
20. BULATOV M.G.,
MITYAGINA M.I.,
RAEV M.D.,
LITOVCHENKO K.TS.,
SABININ K.D., TROKHIMOVSKII YU.G., CHURIUMOV A.N.,
SHUGAN I.V.: Physics-Uspekhi, 2003, 46(1), 63–79.
21. KUDRYAVESTV V., HAUSER D., CAUDAL G., CHAPRON B.:
Pt. 1. J. Geophys. Res. 108 No. C3, doi:
10.1029/2001JC001003, 2003.
AKIMOV D.,
JOHANNESSEN J.A.,
22. KUDRYAVTESV V.,
CHAPRON B.: Pt. 1. J. Geophys. Res. 110, C07016, doi:
10.1029/2004JC002505, 2005.
23. MOUCHE A.A., HAUSER D., KUDRYAVTSEV V.: J. Geophys.
Res. 2006, 111, C09004, doi: 10.1029/2005JC003166.
24. PHILLIPS O. M.: J. Phys. Oceanogr, 1988, 18, 1063–1074.
25. ERICSON E.A., LYZENGA D.R., WALKER D.T.: Radar backscattering from stationary breaking waves. J. Geophys.
Res. 1999, 104, C12, 29,679–29,695.
26. KRAVTSOV YU.A., STATECZNY A., BULATOV G.M., RAEV
M.D., SABININ K.D., KLUSEK Z., KUDRYAVTSEV V.N.: Optical and radar observations of steep and breaking waves of
decimeter range („mesowaves”) on the sea surface: electrodynamical and hydro-physical interpretation. IV Conference “Modern Methods of Earth Observations from
Space”, 13–17 Nov. 2006, Space Research Institute, Russ.
Acad. Sci., Moscow, Russia 2006.
27. TRIZNA D.B., HANSEN J.P., HWANG P., JIN WU.: J. Geophys. Res. 1991, 96 (C7), 12529–12537 ; TRIZANA D.B.
Proc. IGARSS`93 (Tokyo, Japan, 1993), 776–778.
28. MCLAUGHLIN D.A., ALLAN N., TWAROG E.M., TRIZINA
D.B.: IEEE Trans. Oceanic Eng., 1995, OE-20, 166–178.
29. WEST J.C., STURM J.M., SLETTEN M.A.: Proc. IGARSS’95,
Lincoln, Nebraska, USA, 1995, 2207–2209.
30. SLETTEN M.A., TRIZNA D.B., HANSEN J.P.: IEEE Trans.
Ant. Propag., 1996, 44 (5), 646–651.
31. TRIZNA D.B., CARLSON D.: IEEE Trans. Geosci. Remote
Sens., 1996, 34, 747.
32. TRIZNA D.B.: IEEE Trans. Geosci. Remote Sens., 1997, 35
1232–44.
33. SLETTEN M.A.: IEEE Trans Ant. Propag., 1998, 46, 45–56.
34. KWOH D.S.W., LAKE B.M.: IEEE J. Oceanic Eng., 1984,
OE-9(5), 291–308; J. Geophys. Res. 1988, 93 (C10),
12235–48.
35. LIU Y., FRASIER S.J., MCINTOSH R.E.: IEEE Trans. Ant.
Propag., 1998, 46(1), 27–40.
36. KRAVTSOV YU.A., STATECZNY A.: II Internat. Congress of
the Seas and Oceans (ICSO), Szczecin, Poland, 2005, 119–
128.
37. KRAVTSOV YU.A., NINGYAN ZHU.: Wave Motion, 2005,
43, 206–221.
effective cross-sections [8, 31]. In contrast to the
resonant theory, which predicts independence of
cross-section on wind direction, non-Bragg mechanisms are sensitive to the concave form of breaking
waves and thereby to the wind direction. Therefore,
generally
σ SnonBragg |upwind ≥ σ SnonBragg |downwind
(10)
Conclusions
The analysis of empirical data undertaken in this
paper has shown that multi-component composite
model of the sea surface, which combines both
Bragg and non-Bragg mechanisms of scattering, is
able to explain majority of the observed phenomena. The problem, which is still waiting for solution, reveals the specific signatures, characteristic
for the “macro-” and “micro-breaking”. These signatures might be quite helpful for distinguishing of
“macro-” and “micro-breaking” contributions into
the observed echo signal.
References
1. BASS F.G., FUKS I.M.: Waves Scattering From Statistically
Rough Surfaces. Oxford: Pergamon, 1979.
2. RYTOV S.M., KRAVTSOV YU.A., TATARSKII V.I.: Wave
Propagation through the Random Media. In: Principles of
Statistical Radio Physics. Springer Verlag, Berlin, 1989, 4.
3. VORONOVICH A.G.: Wave Scattering from Rough Surfaces.
Springer Verlag, Berlin, 1994.
4. GUINARD N.W., RANSONE J.T., DALEY J.C.: J. Geophys.
Res, 1971, 76, 1525.
5. KALMYKOV A.I., PUSTOVOYTENKO V.V.: J. Geophys. Res,
1976, 81, 1960–1964.
6. LEE P.H.Y., BARTER J.D., BEACH K.L., HINDMAN C.L.,
LAKE B.M., RUNGALDIER H., SHELTON J. C., WILLIAMS
A.B., YEE R., YUEN H.C.: IEEE Trans. Ant. Propag, 1996,
44, 333–340.
7. Lewis R. L., Olin I. D.: Radio Sci. 1980, 15, 815-826.
8. KROPFLI R.A., CLIFFORD S.F.: Pros. IGARRS’94, Pasadena, CA, 1994, 2407–2410.
9. LYZENDA D.R., MAFFET A.L., SHUHMAN R.A.: IEEE
Trans. Geosci. Remote Sens, 1983, 21, 502–505.
10. LYZENDA D.R., SHUCHMAN R.A., KASISCHKE E.S., MEADOWS G.A.: IGARSS'83, New York, 1983, 7.1–7.10.
11. LYZENDA D.R, ERICSON E.A.: IEEE Trans Geosci Remote
Sens, 1998, 36, 636.
12. WETZEL L.: In: Wave Dynamics and Radio Probing of the
Ocean Surface, ed. O.M. Phillips and K. Hasselmann, Plenum, New York, 1986, 273–284.
13. KRAVTSOW YU.A., MITYAGINA M.I., CHURYUMOV A.N.:
Radio Phys. Quant. Electron., 1999, 42(3), 216–228.
14. KRAVTSOV YU.A., MITYAGINA M.I., CHURYUMOV A.N.:
Bulletin of Russ. Acad. Sci., Physics, 1999, 63(12), 1859–
1865.
15. KRAVTSOV YU.A., KUZ’MIN A.V., LAVROVA O.YU., MITNIK L.M.,
MITYAGINA M.I., SABININ K.D., TROKHIMOVSKY YU.G.: Earth Observation and Remote Sensing,
2000, 15, 909–926.
Zeszyty Naukowe 13(85)
Recenzent:
prof. dr Aleksander Walczak
Akademia Morska w Szczecinie
49