JOURNAL OF GEOPHYSICALRESEARCH,VOL. 102,NO. Cll, PAGES25,251-25,267, NOVEMBER 15, 1997
An improved compositesurface model for the radar backscattering crosssectionof the ocean surface 2. Model responseto surface roughnessvariations and the radar imaging of underwater bottom topography RolandRomeiserandWerner Alpers Institutftir Meereskunde,UniversitiitHamburg,Hamburg,Germany
Abstract. In the companionpaperwe havepresentedan improvedcompositesurfacemodel for the calculationof normalizedradarbackscatteringcrosssections(NRCS) of the ocean surface.The proposedmodel accountsfor the impactof the full two-dimensionaloceanwave spectrumon the radarbackscatterand was shownto reproducemeasuredabsoluteNRCS valuesfor a variety of radarconfigurationsandwind speedssatisfactorilyafter some reasonabletuning of the input oceanwave spectrum.This paperfocuseson the modulationof the NRCS in the presenceof spatiallyvaryingsurfacecurrents.First, the sensitivityof the NRCS to intensityvariationsof differentoceanwave spectralcomponentsis investigated. Then the hydrodynamicmodulationof the wave spectrumover underwaterbottomtopography in tidal watersis computedin differentways, andthe resultingradarsignaturesare discussed. The compositesurfacemodel yieldscomparableradarsignaturesat high (10 GHz, X band) and low (1 GHz, L band) radarfrequencies,which is in muchbetteragreementwith experimentalresultsthan the predictionsof a first-orderBragg scatteringmodel. On the other hand,measuredvariationsof the NRCS at high radarfrequenciesappearto be still underestimated in somecases,which may be due to shortcomings of our descriptionof the wave-currentinteractionby conventionalweak hydrodynamicinteractiontheory.Possible improvementsof the theoryare discussed,and requirementsfor future experimentsare formulated.
1. Introduction
The fact that underwaterbottom topographicfeaturesbecome, under certain environmental conditions, visible on ra-
dar imageshas attractedthe interestof scientistsfor more than 20 years.The phenomenonwas first describedby P. de Loor
andHenningsthecurrentmodulation is described by a continuityequation,the wave-current interaction by weakhydrodynamicinteraction theoryin the relaxation timeapproximation [Longuet-Higgins and Stewart,1964; Whitham,1965;
Bretherton,1970; Keller and Wright, 1975;Alpersand Hasselmann,1978;Hughes,1978; Plant, 1982], andthe interacand coworkers in the Netherlands [de Loot and Brunsveld van tion betweenradarsignaland seasurfaceby Braggscattering Hulten, 1978; de Loot, 1981], who had noticed signaturesof theory[Wright, 1968; Valenzuela,1978]. Followingthis apunderwatersandwaveson K• band (36 GHz) real aperturera- proach,thebackscattered poweris assumed to be proportional dar (RAR) images taken in 1969 from an aircraft over the to the wave height spectral density of the short "Bragg" North Sea. Later, similar signatureswere also found on radar waves,that is, of oceanwavesof a wavelengthcomparableto images obtained from other systemslike the SeasatL band the radarwavelength,andan analyticexpression for the inten(1.2 GHz) syntheticapertureradar (SAR) [Fu and Holt, 1982; sity variationsof thesewavesis obtained.It predictsthat the Lodge, 1983]. Since the penetrationdepth of microwavesin relativedeviationof the backscattered powerfrom its equilibseawateris only of the order of millimetersto centimeters,the rium valueis proportionalto the local currentgradientandto bottom topographyat depthsof tensof meterscan be imaged the so-calledrelaxationtime of the Bragg waves, which is a only via surfaceeffects.The imagingmechanismis a two-step measureof the tendencyof the wavesto returnfrom a stateof process:First, the spatialvariationsof the water depth lead to enhancedor reducedenergyto equilibriumstate. a modulation of the tidal flow. The resulting surface current On the basisof suchconsiderations,one would expectthat gradientsgive rise to hydrodynamicmodulationof the surface theradarsignatures of a givensurfacecurrentfeaturearemost roughnesswhich can be detectedby radar. pronounced at low radarfrequencies whichcorrespond to low First quantitativemodelsfor radar signaturesof underwater Braggwavenumbers, sincetherelaxationtimeof oceanwaves bottom topographywere presentedby Alpers and Hennings decreasesstrongly with increasingwavenumber[Hughes, [1984] andby Shuchmanet al. [1985]. In the modelby Alpers 1978; Plant, 1982; Caponi et al., 1988]. However, a strong
Copyright1997by theAmerican Geophysical Union. Papernumber97JC00191. 0148-0227/97/97JC-00191
$09.00
dependence of the radarsignatures of underwater bottomtopographyon radarfrequencyis not evidentin experimental results.Thus good agreementbetweenpredictionsof the modelby Alpersand Hennings[1984] andmeasurements has beenfoundonly at relativelylow microwavefrequencies like 25,251
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ROMEISER AND ALPERS' IMPROVED COMPOSITE SURFACE MODEL
1 GHz (L band), while observedmodulationdepthsat higher frequencieslike 10 GHz (X band) are underestimated by the modelby as much as 2 ordersof magnitude. Several authorshave shown that better agreementbetween model results and measurementscan be obtainedif not only the modulationof the shortBragg wavesbut the impactof the full ocean wave spectrumon the radar backscatteris taken into account.Examplesfor modelswhichincludethe effectof longer waves are the compositesurface model by Lyzenga and Bennett [1988] and the more fundamentalmodel by Holliday et al. [1986, 1987]. Again, the hydrodynamicmodulation of the surfacewave spectrumis describedby weak hydrodynamicinteractiontheoryin both models.Compositesurface modelshave been demonstratedto predictsimilar radar signaturesat L and X band for surfacecurrentpatternsover internal waves, which appearsto be in agreementwith experimentalresults.However, aside from conceptionalshortcomingsregarding,for example,the explanationof upwind/ downwind differencesof the normalizedradar backscattering crosssection(NRCS), they have normally not been validated for the quantitativereproductionof measuredabsoluteNRCS values or their actual variations.
Such models are not neces-
sarily suited for practical applicationslike the inversionof measuredradar signaturesof underwaterbottom topography into depthmaps. In the companionpaper [Romeiseret al., this issue] we have presentedan optimizedcompositesurfacemodelfor the computationof absoluteNRCS values.The proposedmodelis based on Bragg scatteringtheory like the models by Plant [1986], Donelan and Pierson [1987], and Lyzengaand Bennett [1988]. However, it combines for the first time some im-
portantfeatures:The physicalmeaningof all contributionsto the NRCS accordingto the model can be easily understood. Upwind/downwinddifferencesof the NRCS are explainedon a physicalbasis.The predicteddependenceof the NRCS on the polarizationof the radar is not in perfectagreementwith measurements, but it is clearlymore realisticthanpredictions of the fundamentalBragg scatteringexpressions as given by Valenzuela [1978]. Finally, some dedicatedoptimizationof the oceanwave spectrumthat entersinto the model has resulted in the fact that measured absolute NRCS
values for a
urementsof modulatedwavespectrahavenot beencarriedout duringmostexperimentalcampaigns. In the following section, a brief review of the proposed compositesurfacemodelis given.Thena quantitativeanalysis of the compositionof the NRCS is cardedout. In section3, the theory of the hydrodynamicaspectsof the imaging mechanismof underwaterbottom topographyis described. The simulatedradarsignaturesof underwaterbottomtopography are discussed in section4 andcomparedwith existingradar images.A summarizingdiscussionand someconclusions are then given in the last section.
2. Review and Analysis of the Proposed Radar
Model
The proposedcompositesurfacemodel hasbeendescribed in detail in the companionpaper [Romeiseret al., this issue]. We shall now give a brief summaryof its main featuresand then focusthe discussionon somedetailsof the composition of the NRCS accordingto the model. 2.1. Composite Surface Model Theory
According to resonantBragg scatteringtheory [Wright, 1968' Valen•uela, 1978], the normalizedradarbackscattering crosssection0- of a facet at the oceansurfaceis proportional to the wave height spectraldensity of the so-calledBragg waves which are in resonancewith the electromagneticsignal. In the general caseof a slightly tilted Bragg-scatteringfacet, one finds that 0- and the backscatteredpower vary with the
slopesSpands, parallelandnormalto the radarlook direction.An expectation value{0-) of theNRCS of a realisticsea surfacecan then be calculatedby expandingthe local NRCS up to secondorder in the surfaceslopesand averagingover the illuminatedarea in spaceand time. In additionto the zeroth-order term, some terms of second order in the surface
slopessurvivethe averagingprocedure.The resultingexpectation value can be written
as
= o'(ø)+
UlO-- 10 rn/s
1.3
oll ;>
ß
• 0.9 Solid:
Dashed:{50
_ X HH 45øDown
u10- 10 m/s----
ß
a
Solid' Dashed:{50
0.8
b
0.8
100
200
300
400
500
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0
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-10 Depth Profile
• = 1.0m/s----
-2o
-20
-30
f Depth Profile •=1.0 m/s ----
-30
0
100
200
300
400
x [m]
500
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800
ß
0
100
200
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700
x [m]
Figure 15. Examplesof simulatedradar signaturesof the scenarioof Figure 14 as obtainedfrom the full compositesurfacemodel (solid lines) and from a basicBraggmodel (dashedlines) for an incidenceangleof 45ø and a downwindpointingantenna:(a) L band(1 GHz) HH; (b) X band(10 GHz) HH.
800
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ROMEISERAND ALPERS'IMPROVED COMPOSITESURFACEMODEL
0.9
0.9
Solid: 10 m/s
0.8 l
•...
0.7-
Dashed' 5 m/s
L Band
0.7-
O.6-
0.5-
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0.3-
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a I
0.0
•
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t
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X Band
O.6-
0.1-
Solid: 10 m/s
0.8 l
•
60
I
•
70
0.1-
b
0.0
'
80
10
I
20
•
I
30
O [deg]
•
I
40
i
I
50
i
I
60
t
I
70
•
80
O [deg]
Figure 16. TheoreticalmodulationdepthM of the NRCS over the subsurfacefeatureshownin Figure 14 as functionof incidenceangle 0 for wind speedsumof 5 m/s (dashedlines) and 10 m/s (solid lines) and for HH andVV polarization:(a) L band;(b) X band.
in spatiallyvarying currentfields than the zeroth-ordercontribution.
This
results in the fact that more than 90%
of the
modulation of the total NRCS can sometimes be attributed to variations Some
of the second-order information
on
terms.
the
directional
variation
of
the
modulation depth can be derived from Figure 18, which shows the ratio between the modulation depthsobtainedfor the azimuthal
look directions
downwind
and cross-wind.
Es-
pecially at low wind speedsand VV polarizationthe modulation depth at L band appearsto be much more sensitiveto directional changesthan the modulation depth at X band. This is a result of the fact that the second-order
contributions
spatiallyvaryingwind correctionthat affectsthe equilibrium wave height spectrum. Thus the presenceof significantradar signaturesin cases
wherethe azimuthalradar look directionis perpendicular to the directionof the currentgradients is a purecomposite surface model effect which cannot be explained within the frameworkof a simple Bragg scatteringmodel. However, from a look at Figures3 and6 onemay expectan evenmore specialeffect: The contributionsto the NRCS which are asso-
ciatedwith "normal"surfaceslopeshave been found to be negative under certain conditions, while contributionsassoci-
of the
ated with "parallel" slopes are always positive. From the NRCS are much less significant at L band than at X band, qualitativepoint of view it would be possiblethat square while the zeroth-orderterms for the cross-wind(cross-stream) slopevariationsof waves in a given directioncan lead to relook directionexperienceonly a very weak modulationvia the versedradar signaturesat different azimuthallook directions,
16.0
16.0
- Solid: 10 m/s
14.0
Dashed: 5 m/s
14.0
L Band
- Solid:10m/s Dashed: 5 m/s•
,Ban•H X H 10.0
12.0
12.0
10.0
8.0
8.0
6.0
6.0
4.0
4.0
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0.0
' 10
20
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O [deg]
i
I
60
•
I
70
•
- b
VV
0.0
80
10
20
30
40
50
60
70
O [deg]
Figure 17. Sameas Figure16, but showingthe corresponding increase of the modulation depthwhen switching froma basicBraggmodelto theproposed composite surface model,M/Mo.
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ROMEISER
AND
ALPERS'
IMPROVED
0.6
COMPOSITE
SURFACE
MODEL
25,265
0.6
- Solid: 10 m/s 0.5 -
Dashed: 5 m/s
L Band
0.2 -
0.2 _
_
_
_
X Band
0.1,
0.0 10
20
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0.0
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•
40
Dashed: 5 m/s
I
•
50
t
,
60
I
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80
6} [deg]
6} [deg]
Figure 18. SameasFigure16, but showingthe ratioof the modulationdepthsobtainedfor cross-windand downwindpointingradarantennas, Mcros.,./Mdown.
sincethe wavescanbe responsible for the "parallel"slopesin one caseand for the "normal"slopesin anothercase.This effect is not observedhere, sincethe variationof the negative terms is always clearly dominatedby the variation of the positivetermswhich doesnot changesign. Finally, Figure 19 showsthe upwind/downwinddifference of the modulationdepth,which is also a pure compositesurface model effect. As expected,the differencesare more pronouncedat X band than at L band, but a surprisingfact is that highermodulationdepthsare obtainedfor the upwindlook direction in case of a 5 m/s wind and for the downwind
look di-
5. Discussion
and Conclusions
In this paper we have carriedout severalanalysesin order to investigatethe theoreticalvariation of the normalized radar backscattering crosssection(NRCS) of the oceansurfacewith
the surface roughness.The optimized compositesurface model usedfor the NRCS calculationshas been presentedin the companionpaper [Romeiseret al., this issue], where it was demonstratedto reproducemeasuredabsoluteNRCS values for a wide range of radar frequencies,incidenceangles, azimuthalradar look directionsand wind speedsand for hori-
rection in case of the 10 m/s wind. However, the situation
zontal(HH) andvertical(VV) polarization. In thispaperthe
may be different if a more advancedsourcefunction for the hydrodynamicmodulationis used.
modelhasbeencombinedwith a modelfor the hydrodynamic modulationof the ocean wave spectrumby spatiallyvarying
1.4
1.4 1.3 --
Solid: 10 m/s
Dashed: 5 m/s
1.3
L Band
Solid: 10 m/s
Dashed: 5 m/s
X Band
.--'"
1.2
•....-"•'/'•' HI--I 1.1........... •___-__-_--_-_-_-'_-_'5_-_5_-__-_-_ ................ :_-_::_ .......
1.0
0.9 -
O.9
0.8-
0.8
0.7-
0.7- b
0.6 10
I 20
I
I 30
,
I 40
,
.I 50
0 [deg]
,
I 60
,
I 70
• 80
0.{5 10
•
I
20
,
I
30
,
I
40
,
I
50
,
I
60
,
I
70
6} [deg]
Figure 19. Sameas Figure 16, but showingthe ratio of the modulationdepthsobtainedfor upwind and downwindpointingradarantennas, Mup/Mdown.
80
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ROMEISER AND ALPERS: IMPROVED COMPOSITE SURFACE MODEL
surfacecurrentfields. The hydrodynamicmodel is basedon tion of the surfacecurrentgradients.This effect resultsfrom weak hydrodynamicinteractiontheory, where different op- the impact of second-ordertermsof the NRCS which depend tions for the sourcefunctionof the actionbalanceequation on the mean squaresurfaceslopenormal to the azimuthalrahave been tried. dar look direction. The other notable feature is an upAssumingthat the conversionof wave spectrainto NRCS wind/downwind asymmetry of the signatures and of the valuesby the proposedcompositesurfacemodelis correct,it modulationdepth,whichresultsfrom the asymmetrictermsof was possible to evaluate how the different sourcefunctions theNRCSwhichaccount for thehydrodynamic modulation of affect the theoreticalradar signaturesof existingunderwater the Braggwavesby all longerwavesand which causealsothe sand waves in coastalwaters.It was found that the simple upwind/downwindasymmetryof the absoluteNRCS. quadratic source function as given by (12) in combination We believe that the proposedcompositesurfacemodel has with Plant's [1982] expressionfor the relaxationrate leadsto quitegoodpotentialfor theoretical analyses associated with relatively good agreementbetween model resultsand meas- the radar imaging of underwaterbottom topographyin tidal urementsat low and high radar frequencies.However, while waters or of internal waves. It should be also well suited for the observedreductionof the NRCS in divergentcurrentre- an incorporationin inverse models for the determinationof gions is reproduced satisfactorilyby our model, the corre- surfacecurrentfields from radar measurements. Only the hyspondingincreasein convergentregionswhich has been ob- drodynamicpart of the modelsuiteneedssomeimprovement, servedat high radarfrequencies(X band"image1") cannotbe which must be based on additional dedicated measurements in explainedby any of the five sourcefunctions.Even if the re- future campaigns.The resultsof this studywill then be useful laxationrateis reducedby a factorof 10, theresulting modu- for a correcttheoreticalinterpretationof the measurements. lationof the surfaceroughness is not strongenough.Also, the relativelyweak linear sourcefunctionas given by (11) or the Acknowledgments. We wouldlike to thankD.R. Thompson, J.
sophisticatedsource function developedby Trokhimovski Vogelzang, A. Schmidt, and W.J. Plant for valuable discussions of thispaper.Furthermore, we aregratefulto V. [1993a,b] doesnot improvethe situationaslongasno addi- duringtheevolution tional modulation mechanisms are taken into account.
Irisovandto an anonymous second reviewerfor providingvaluable andconstructive comments. This work hasbeensupported by the
In our opinion,the mostpromisingapproach for obtaining EuropeanCommunityas a part of the Marine ScienceandTechnoloa strongerpositivemodulationin convergentcurrentregions gy (MAST) program under contractsMAST-0040-C and MAS2Agenturftir Raumfahrtangelegenheiten is the inclusionof wind modulationeffectsas proposed by CT94-0104,by theDeutsche 50 QS9014and50 QS9016,andby Trokhimovski[ 1993a, b], Romeiseret al. [1994], and Masten- (DARA),Bonn,undercontracts broek [1996] or the inclusion of modulation effects associated
theDeutscheForschungsgemeinschaft, Bonn,undercontractA188/2.
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depthmapshave normallybeen carriedout withoutpaying much attentionto this problem,althoughit has been known for sometime that accurateNRCS calculations requirecompositesurfacemodelswhich dependon the completetwodimensional surfacewavespectrumandits spatialvariations. In addition to the test calculationsfor existingimages, somemoregeneralmodelcalculationshavebeenpresentedin orderto discussthe dependence of the theoreticalradarsignaturesof underwaterbottomtopography on variousparameters. First of all, it was found that the compositesurface modelis capableof explainingcomparable modulationdepths at high and low radar frequencies,while a simpleBragg modelwould underpredictthe signaturesat high frequencies very much. Only at low wind speedslike 5 m/s the modulation depthsat low radarfrequenciesare clearlyhigher,while
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W. Alpers and Roland Romeiser, Institute of Oceanography, Universityof Hamburg,Troplowitzstr.7, 22529 Hamburg,Germany. (e-mail:
[email protected];
[email protected]) (ReceivedMarch 28, 1996, revisedJanuary9, 1997; acceptedJanuary22, 1997)
