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. Kravtsov
1, Andrzej Stateczny
21 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: kravtsov@am.szczecin.pl 2Akademia Morska w Szczecinie, Katedra Geoinformatyki
70-500 Szczecin, ul. Wały Chrobrego 1–2, tel. 091 4809464, e-mail: astat@am.szczecin.pl
Key words: sea surface radar models, sea radars Abstract
The article presents multi-component composite model of the sea surface which generalizes the standard two-scale model (small-two-scale gravity-capillary waves lying on the large-two-scale gravity waves). The suggested model considers the non-resonant backscatter from large-scale breaking gravity waves and resonant backscat-ter 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 meso-waves. 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). Zapropono-wany model uwzględnia nierezonansowe rozproszenie od wieloskalowych załamujących się fal grawitacyj-nych albo rezonansowe rozproszenie od stromych faleczek mezoskalowej długości (mezofale). Wieloskładni-kowy model różni się od standardowego dwuskalowego modelu dodaniem nowych składników w postaci nie-rezonansowych elementów na tle „makrozałamujących się” wieloskalowych fal albo w postaci rezonanso-wych „mikrozałamujących się” stromych mezofal. Głównym celem artykułu jest stymulacja dalszej analizy kątowych, częstotliwościowych i polaryzacyjnych charakterystyk rezonansowych i nierezonansowych me-chanizmów rozproszenia w celu ich rozróżnienia.
Introduction
The two-scale composite model of the sea sur-face 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
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 fea-tures of microwave scattering from the large break-ing waves, when white cappbreak-ing occurs, as well as backscattering from the sea surface at low grazing
angles γ ≤ (10–15)°. It concerns above all the ab-normal 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 graz-ing angles, as well as the phenomenon of asymme-try 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 non-Bragg objects on the water surface, which princi-pally 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 charac-teristic 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 sharp-crested 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. Contri-bution of the sharp-peaked meso-waves was de-scribed 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, pro-posed 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” sur-face and the breaking zones are considered to be statistically independent. Thus, Kudryavtsev’s model presents a cross-section per unit of sea sur-face as a sum of two terms:
breaking regular ) 1 ( S S S qσ qσ σ = − + (1) Here regular S σ and breaking S σ characterize the
“regular” breaking components of the sea surface
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 multi-component composite model, which unites the mer-its of the three component composite model, sug-gested in [13, 14, 15, 16, 17, 18, 19, 20], and semi-empirical 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 phe-nomena, described by the multi-component com-posite model.
Multi-component composite model of the sea surface
The two-scale composite model deals with rip-ples 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 rip-ples spectrum and by showing the riprip-ples at differ-ent aspect angles due to large gravity wave tilting. The main shortcoming of the commonly accepted two-scale composite model is its inability to de-scribe 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 sharp-crested elements responsible for non-resonant scat-tering 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:
nonBragg Bragg S S S σ σ σ = + (2)
The first term in equation (2) corresponds to the standard two-scale composite model, which de-scribes contribution of small-scale ripples, modu-lated by large-scale gravity waves. This term can be presented as
∫
=
S
SBragg σ1Braggds
σ (3)
where dimensionless quantity Bragg 1
σ 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:
∑
= k k SnonBragg σnonBragg σ (4) nonres kσ being a cross-section of the k-th scatterer. This term embraces contributions of both sharp-edged waves and “boiling-water” surface inside white capping areas in frame of Kudryavtsev’s model.
According to Bragg theory [1, 2, 3], at low graz-ing angles the resonant cross-section for horizontal polarization is significantly smaller compared to the
one for vertical polarization: V
S H
SBragg σBragg
σ 〈〈 , whereas at moderate grazing angles, the quantity
H SBragg
σ and V
SBragg
σ might be comparable with
each other: V
S H
SBragg ~σBragg
σ . In contrast to Bragg
scattering, at low grazing angles the non-resonant cross-section for horizontal polarization might ex-ceed that for vertical polarization:
V S H
SnonBragg σnonBragg
σ > . At the same time,
H SnonBragg
σ becomes comparable with V
SnonBragg
σ at
moderate grazing angles: V
S H
SnonBragg ~σnonBragg
σ . Depending on meteorological conditions, view-ing angle, polarization and frequency of electro-magnetic waves, the Bragg or non-Bragg mecha-nism might prevail. This explains the great diver-sity of the ocean images, observed by ground-based, ship-borne and aerospace-borne radar at different angles of observation and in different fre-quency bands.
There are at least two classes of scatterers, which may contribute to the non-resonant mecha-nisms of scattering. The first class is presented by sharp-peaked waves, whose edge curvature radius is less than a radar wavelength. Sharp-peaked pro-file is characteristic both for the initial phase of “macro-breaking” phenomenon, that is large grav-ity wave breaking, and for “micro-breaking” of comparatively short and low waves of meso-scale spectrum. In contrast to “macro-breaking”, the lat-ter practically does not produce foam and walat-ter spray. The second class is “boiling water” inside the whitecaps, accompanying “macro-breaking”. Let us consider briefly both kinds of scatterers.
Contribution of whitecaps
The dynamics of processes inside whitecaps is so complicated that nobody, according to the au-thor, 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 in-coherent scatterers, which are presumably of the egg-like form with a typical radius a ≥ λ. Then individual cross-section is ~π 2
k
k a
σ . Assuming
that the scatterers that are densely packed (the aver-age distance b between them is of order2a), the non-resonant cross-section (4) for whitecaps can be estimated as whitecap~Nπa2 S σ , where 2 whitecap/ ~ S b
N 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: whitecap 2 2 whitecap nonBragg~S πa /(2a) ~S S σ (5)
In general, this regularity might be presented in the form
whitecap whitecap KS
S ≈
σ (6)
implying that the proportionality coefficient K takes into account the effects of shadowing, of multiple scattering, of absorption in the foam cover and oth-ers. As a result, the factor K happens to be depend-ent on radar wavelength and on viewing angle.
Polarization dependence will appear, when the Brewster effect is taken into account, as was ana-lyzed in [27, 28, 29, 30, 31, 32, 33]. Upwind-downwind asymmetry stems from the shadowing effect. Spikes arise, when intensive gravity wave breaks inside resolution element.
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 spec-trum. Due to their relatively small height, meso-waves usually break ‘silently’, that is without pro-ducing 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]).
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,
re-flected from the footnote in a specular way. The primary electromagnetic wave, incident on a con-cave 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 dif-fractions, as it was presented in the recent papers [36, 37].
The most important features of multiple diffrac-tions 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 en-hanced backscattering phenomenon, caused by multi-path (multi-channel) scattering, similar to backscattering from “macro-breaking” waves, stud-ied 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 dif-fraction, by the sharp crest and by the second re-flection from the wedge [37].
Phenomena described by the multi- -component composite model
With the sharp-crested meso-waves incorporated as additional elements of the sea surface, the three-component composite model is able to describe a wide circle of phenomena at low grazing angles and simultaneously to clarify the role of the
sharp-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 break-ing large-scale gravity waves. Accordbreak-ing 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 polariza-tion, 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 calcula-tions, performed in [20] and [37] on the basis of geometrical theory of diffraction, the polarization ratio χnonBragg at low grazing angles reaches
some-times 5–10 dB, whereas the resonant polarization ratio χBragg is small enough.
Super-events. Sea spikes, i.e. spikes in the tem-poral 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 sig-nal spikes are not often associated with the white-caps, 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 nals from the sharp-peaked wave might be of sig-nificant strength, up to 2 nonBragg c L ≈ σ (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
cross-section edge
≈
1
S
σ
m2. Even larger cross-sectionsmight 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 specular ≈
S
σ 10 m2. Of course, the random
fac-tors 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
effective cross-sections [8, 31]. In contrast to the resonant theory, which predicts independence of cross-section on wind direction, non-Bragg mecha-nisms are sensitive to the concave form of breaking waves and thereby to the wind direction. Therefore, generally downwind nonBragg upwind nonBragg| | S S σ σ ≥ (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 phenom-ena. The problem, which is still waiting for solu-tion, reveals the specific signatures, characteristic for the “macro-” and “micro-breaking”. These sig-natures might be quite helpful for distinguishing of “macro-” and “micro-breaking” contributions into the observed echo signal.
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Recenzent: prof. dr Aleksander Walczak Akademia Morska w Szczecinie
