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Optical and radar observations of steep and breaking waves of decimeter range (,,mesowaves") on the sea surface: electrodynamical and hydrophysical interpretation


· Kravtsov Yu.A., Bulatov M.G. , Raev M.D., Sabinin K.D., Sharkov E.A., Space Research Institute, Russ. Acad. Sci., Moscow, Russia · Kudriavtsev V.N., Nansen Center, StPeterburg, Russia · Klusek Z., Institute of Oceanology, Polish Acad. Sci., Sopot, Poland · Stateczny A. Maritime University, Szczecin, Poland


· Conte nt
· · · · · · 1. Introduction: 2. Optical observations of mesowaves 3. Radar obse rvations 4. Radar models of the Sea surface 5. Proble ms to solve 5.1 Hypothetic mechanis ms of the sharp c rests forming · 5.2. Direct hydrophys ical wavespectrum me as ure me nts · 5.3. Influence of mesowaves on wind-Sea inte ractions · 6. Conclusion


1. Introduction: what are mesowa ves? why mesowaves?
· Wave spectrum
Why meso waves ( waves of decimeter range) are of special interest? Because they are sharpcrested! Gravity-capillar waves

Gravity waves
Wa velength 100m 10m 1m 10cm

1cm


Steep and sharp-crest waves of decimeter range are of special interest, because they have sharp crest and therefore might be responsible for: · Strong spikes on radar images of the Sea surface · Enhanced energy and mo me ntum transfer from the wind to water surface · Manifestations of the internal waves on the SAR ocean images


2.Optical observations
2.1. Gdansk Bay (IO PAN, Z.Klusek)


2.2. Pacific 1


2.3. Pacific 2


Pacific 2


2.4 ,,Microbreaking" or ,,microscale breaking waves"
· Nature, 1993; · Sharkov, 1996-1998: aircraft photo

images, containing both ,,macrobreakings" (white caps) and ,,microbreakings", that is mesowaves breaking without foam and sprays · Measurement Sci. Technol., 2006


· 2.5. Photo registration of ,,microbreakings" (breaking wit hout foam and sprays) simultaneously wit h radar observations (Kwoh et al., 1980; Paper in Nature, 1993, and many other publications)


3. RADAR OBSERVATIONS
3.1. RADAR OBSERV AT IONS ON T HE BALT IC SEA (RADAR OF T HE TRAINING SHIP ,,NAWIGATOR XXI", SZCZECIN MARITIME UNIVERSITY ) Szczecin Maritime University training ship "Nawigator XXI" is equipped in radar system by Kelvin Hughes Company (KHC) (wavelenght about 3 cm). KHC radar has sufficiently high resolution: about 1.5° in azimuthally direction and 10 m in radial direction.


An example of the Baltic Sea image in conditions, when the sea surface was free of white caps. The image contains iscrete echoes, which might be accepted for false targets.

1.5 km


3.2. Radar observations on t he Black Sea (Mobile radar by the Space Research Instit ute, Russ.Acad. Sci., Moscow)

1.0 km


3.3. Airc raft radar image of the inte rnal waves manifestations on the Sea Surface (JUSREX'92: Joint US and Russia radar experime nt 1992, Space Res. Inst. ,Rus.Acad.Sci.)
H V

12 km


· 3.4. Satellite SAR (Synt hetic Aperture Radar) images of the Ocean: visual manifestations of the oceanic internal waves
· Sabinin et al. Int. J. Remote Sensing, 2002; Physics Uspekhi, 2003;

· site of the Space Res. Instit ute: www.asp.iki.rssi.r u)


4. RADAR MODELS OF THE SEA SURFACE 4.1. Two scale composite model Two scale composite model is commonly accepted for interpretation of microwaves scattering by the rough water surface. The two scale composite model deals with small scale gravity-capillary waves ("ripples") by few cm of wavelength, lying on the large scale gravity waves of wavelength longer than 3-5 m.


TWO SCALE COMPOSIT E MODEL: "RIPPLES" ON THE LARGE GRAVITY WAVE
Ripp le amlitude A Wa ve len gth lambda

Resonant (Bragg) theory is valid only if the amplitude of rippl es A i s small as com pared with the ra dar wavel ength lambda: A<

T he two s cal e model s atis factory describes the m ain pr oper ties of the r adar ec ho. Howev er, at l ow grazi ng angl es 10°-15° s ome phenomena hav e been obs erved, which pri ncipally c oul d not be ex plai ned by the res onant theory of sc atteri ng. It c oncer ns abov e all the abnormal pol arization ratio: the observ ed ratio of the cr oss-s ecti on at horiz ontal pol arization to that at ver tical pol arizati on often exc eeds a unit, w hile Bragg theory predicts very low pol arization ratio [Bass, F uks 1979; Ry tov , Kr avts ov, Tatarskii 1989]:


.

H V



ob s e r v e d

> 1,



H V



Br a g g

< < 1,


At second, the radar echoes at low grazing angles demonstrate large spikes or "superevents", which are not explainable by the Bragg theory The same is true for the obser ved asymmetry bet ween upwind and downwind radar cross-sections .


4.2. EXTENDED COMPOSIT E MODEL OF THE SEA SURFACE, UNITING THE BRAGG AND NON- BRAGG MECHANISMS OF SCATTERING

· Two ma in reasons for non-Bragg scattering · 1) Large scale breaking waves ( white caps) · 2) Sharp-crested mesowaves of decimeter scale,


The characte ris tic le ngths (40-60 cm) and heig hts (10-20 cm) of mesowaves are inte rmediate between those of s mall-scale (a few centimete rs ) and large-scale (mete rs and longe r) components of the wave spectrum. Sharp-crested mesowave

10-20 cm

40-60 cm


Fragment of the sea surface with sharpcrested mes owa ves.


The extended c omposit e model of the sea surfac e incorporates macrobreaking w aves and micr obreaking mesowav es into standard two scale model :

Two scale composite model (Bragg scattering) + breaking waves and mesowaves (non-Bragg scattering) => extended composite model of scattering


T he extended m odel repres ents the total r adar cr oss-s ecti on of the area S as a s um

S = (1- q)

Bra g g S

+ q

n on Bra g g S

= (1- q)

Bra g g 1

ds + q
k

n on Bra g g k

The f irs t ter m in th is equa tion rds sc r ibes co ntr ibu tion of th e r ipp les , e e 1is treated here as a resonant (Bragg) crossd im ens ion less quant ity sect io n pe r a un it surf ace. The sec ond te rm su mmar izes the co ntr ibu t ions o f mes owaves w ith in the reso lut io n e lem ent S, kn o n Bra g g be ing a cross-s ect ion o f the k-th mesowave. Thus, t he scatt er mo de l, w av es extended c ompo nent mode l co mb ines c ont inu ous res onant ing from sma ll sca le r ipp les, lik e in sta ndar d two sca le compos ite a nd d iscre te no n-res onant ref lect ions fr om th e ind iv idu a l breaking and m es owaves.


4.3. MICROWAVE DIFFRACTION AT SHARP-CRESTED MESOWAVES The most important features of multiple diffractions at curvilinear wedge are pr esented by the four/five channel model. The four-channel model includes the foll owing four terms:

ufour= ue + ues + use +use

s


Single scattered edge wave ue Triple scattered wave use ,,Edge" wa ves generation

s

Coherent double scattered waves ues = use


At last, when specular reflection comes into play, specular term us will appear in the total wave field. Then four channel model converts into five channel model

ufive= ue + ues + use +u

ses

+u

s

Transition from fou r-chan nel to fiv e-channel model might be perfo rmed on the basis of the UNIFORM THEORY OF DIFFRACTION, which generalizes GEOMETRICAL THEORY OF DIFFRACTION for light-shadow bounda ries.


4.4. PHENOMENA, DESCRIBED BY THE EXTENDED COMPOSITE MODEL A. P olarization ratio
Brewster phenomenon is well known in optics: for vertical polarization of electromagnetic wave at definite angle, which is named Brewster angle, all the energy completely passes through the interface of two dielectrics, and reflection coefficient turns

out to be zero.


Brewster Phenomenon
Polarizat ion-d ependent reflect ion:

H

R=1

V
R<1


In microwave range Brewster phenomenon plays an important role. Strong influence of the Brewster phenomenon on polarization ratio was pointed by Trizna et al (1991). According to Trizna, at low grazing angles the Fresnel reflection coefficient from the sea water at vertical polarization is at 5-7 dB smaller as compared to that at horizontal polarization, what results in significant suppression of the radar echo at vertical polarization.


B. Superevents
Sea spikes (superevents) of backscattered radar signal are most prominent at horizontal polarization and only rarely are visible at vertical one. The amplitude of a sea spike at horizontal polarization can be much higher, sometimes by 10 dB, than its amplitude at vertical polarization. Superevents in no way can be explained by the Bragg theory. It looks quite surprising that most of the sea spikes are not accompanied by visual breaking.


Echo signals at horizontal polarization mi be of significant strength. On the basis Geometric Theory of Diffraction (GTD) radar cross-section of the wedge crest of by length can be estimated as :

ght of the

Lc



non - resonant H

L

2 c


It means that c oher entl y illumi nated w edge cr est of Lc =1 m by l ength provides unex pectedly high r adar cr oss-s ecti on:



H

1m

2

which is at least 100 times gr eater as c om par ed with the res onant (Bragg) r adar cross-section and is comparabl e with cro ss- section of a boat or small yacht. The pro blem is to eliminate the radar refl ection s from mesowav es by digital methods, u sing algorithms of moving target s distin guishing.


5. Hydrophysical aspects
· 5.1. Hypothetic mechanis ms for sharp crested meso waves for ming
Sharp-c rested mesowaves hypothetically might be soliton-like solution of the hydrodynamical equations in the presense of the shear wind and the s hear wate r curre nts, induced by gravity wave.


Influence of the shear wind
Wind profile


Influence of the shear currents
According to visual observations, sharpcrested meso waves arise predominantely at the front side of a gravity wave:
sharp-c rested meso wa ve

Shear currents


Hypothetic effect of differential surface wave transfer by shear current, which might be responsible for sharp peak forming
· Shear current profile Ushear= U0exp(-Kz) Su fface wa ve vertica l profile vx(z)= vx(0)exp(-kz)

z

Differential shear transfer velosity Vt
rans=

=U0[k/(k+K)] = U0 for short surface waves, k>>K = U0(k/K)<

· Total velocity Vtot (k)= Vphase(k) + Vtrans(k)= =(g/k)1/2 + [k/(k+K)]U0
Plato, allo wing dispersiveless propag ation of the sharp (high frequency) crest

wave number k


5.2. Possible role of sharp-crested mesowaves in t he wind-sea interaction
· Sharp-crested mesowave s may act like a small sails and thereby may contribute into Jeffrey echanism of wind wave s production. That is why sharp-crested mesowave s might be of great practical interest as a factor, determining dynamics of the wind waves. Unfortunately , the authors did not find any me ntioning of contribution of the s harp-c rested waves into fetch phe nome na.


· 6. Conclusion
· 1) Optical and radar data are presented, evide ncing the inportant role of sharpcrested meso waves in for ming discrete redar echoes from the sea surface. · 2) Hydrophysical mechanis ms for sharpcrested meso waves for ming as well as their role in wind-sea interaction are not clarified until no w.