Kobe University Repository : Thesis

学位論文題目Tit le

Analysis of the Cloud Observat ions by Radar and Lidar(レーダ、ライダによる雲の観測・解析)

氏名Author 岩崎, 杉紀

専攻分野Degree 博士（理学）

学位授与の日付Date of Degree 2001-03-31

資源タイプResource Type Thesis or Dissertat ion / 学位論文

報告番号Report Number 甲2264

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PDF issue: 2020-01-20

博士論文

AnalysisoftheCloudObservations

byRadarandLidar

(レーダ､ライダによる雲の観測 ･解析)

Suginorilwasaki

TheGraduateSchoolofScienceandTechnology ,

KobeUniversity,Nada,Kobe657-8501,Japan

Contents

1 Generalintroduction

2 Anomalousbackscatteringenhancementbynon-sphericalicecrystals

fTorlidarobservation

2.1 Introduction‥ ‥ ‥ .,..

2.2 Mechanismofbackscatteringenhancement.

2.2.1 ComparisonbetweenGOandKDforrectangularsurface.

2.2.2 CriterionfortheapplicationofGO .

2.3 Analysisofthelidarbackscatteringbypristinehexagonalcrystals.

2.3.1 Caseforsphericalparticle .

2.3.2 Casefor2D-column.....

2.3.3 Casefor2D-plate,

2.3A Casefor3D-columnand3DIPlate...

2.3.5 Discussion...

2.4 Summary

2.5 Appendix

2.5.1 Receivedpowerlbrarectangulartargetrandomlyorientedinhori-

zontalplane.

3 AnalysISOflidarbackscatteringenhancementforpristinehexagonalice

crystals

3.1 Introduction......

3.2 Seatteringbyrectangularparticles‥

3.2.1 Definitionofsymbolsanddiffractionpattern

8

(X)0

0

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4

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6

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.33

.33

3.2.2 ScatteringbytherectangularparticleswithRⅩedorientation. .34

3.2.3 Scatteringbytherectangularparticlesrandomlyorientedinhori-

zontalplane.

3.3 Scatteringbyhexagonalcrystals

3,4 Summary ,

.36

.37

.38

4 AnalysISOflidarreturnsfrom rectanglesandhexagonalicecrystals4.1 Introduction.

4.2 Scatteringmodel.

4.2.1 Scatteringbyarectangularparticlewitha丘Ⅹedorientation ‥

4.2.2 Scatteringbyarectanglerandomlyorientedinhorizontalplane ‥

4.2.3 Distancedependenceofthereceivedpowerbyhexagonalcrystals‥

4.3 Summary ..- .- - - - .

5 Cloudobservationbylidar,95GHzcloudprofi1ingradarand13.8GH2;

precipitationradar

5.1 Introduction.

5.2 Descriptionofourlidar,95GHzcloudradarand13,8GHzprecipitation

radarsystem‥

5.3 Cirruscloudsobservedbylidarand95GHzcloudradar‥

5_4 Cloudsandprecipitationobservedby95GHzand13.8GHzradars .

5.5 Summary .

6 Air-borneobservationby95GHzcloudradar

6.1 Introduction‥ ,

6.2 Theoryforcloudsobservedby95GHzcloudradaronboardaircraft‥ ‥

6.3 Results‥ .

6.4 Summary .

7 ListorPublications

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73

Chapter1

Generalintroduction

Thisthesisisdedicatedtounderstandthemicro-physicalpropertiesofthecloudparti-

clesbyusingactivesensors,suchaslidar,95GHzcloudradarand13.8GHzprecipitation

radar.SuchknowledgesareimportanttoincreasethepotentialofGeneralCirculation

Models(GCM)andleadstoacceleratethereliabilityfortheforecastoffutureclimate

changes.Thatis,itiswidelyrecognizedthattheverticaldistributionofthecloudparticles

andtheirinteractionwithaerosolsremainaskeyproblems.Thisisbecauseitisimpossi-

bletoderivesuchkindofmicro-physicsbyusingpassivesensorsonsatellite,wherethese

sensorsmeasureintegratedvalues.Onlyactivesensorscanprovidesuchinformations.

Thisisthefundamentaladvantagesofactivesensors.

Lidar(lightdetectionandranging)isoneofthemostsuitableactivesensorstoob-

servecloudandaerosolparticles.Itmeasuresthedistancebetweenscattersandalidar

system,andbackscatteredpowerbyscatters.Ourlidarsystemcanalsomeasurecross-

polarization.Itiswellknownthattheicecloudparticles,thatoftenexistatthealtitude

ofaroundlOkm,arenon-spherical.However,itisverydimculttocalculatescattering

signals,C.9.,backscatteringcoefncient,forsuchirregularlyshapedparticlesobtainedby

thelidarobservation(Seechapter2).Inthisthesis,wedevelopanewscatteringmethod

thatispossibletoretrievethebackscatteringcoe氏cientfromthelidarobservation.

Theconventionalcentimeterwavelengthsradars(radiodetectingandranging)donot

havesensitivitytodetectcloudparticles.Becausethosewavelengthsaremuchlonger

thancloudparticles,generallylessthan100FLm,theradarechofromtheseparticlesare

lessthanthedetectionlimit.Thisisthemainreasonwhyweneedmillimeterwavelengths

radars.Fromthetechnicalpointofview,sincetheirfrequencyisveryhigh,i.C.,95GHz,

W-band,itisverydifhculttodevelopcloudradars.Thereforeonlyfewcountries,such

asU.S.,U.K.,GermanyandJapanhavecloudradars.InJapan,onlyCommunications

ResearchLaboratory(CRL)succeededindevelopmentofthecloudradarcalledSPIDER

(SpecialPolarimetricIceDetectionandExplicationRadar)in1998甘 SPIDERcanme且-

3

sureco-andcross-polarizedbackscatteredradiancebylogdetectorandDopplervelocity

byIQdetector.Moreover,itisdesignedtobeabletoperformanair-borneobservation.

Consequently,itbecomes possibletoinstantlyobservecloudsatlargearea(～100km).

Receivedpowerbyradarandlidardependsontheseveralmicro-physicalpropertiesof

scatters亘 e.,size,numberconcentration,Shapeandalignmentofcloudparticles.How-

ever,therehavebeenonlyfewsynergyexperimentsbyusingtheseinstruments[2-5]･

Thisthesisconsistsofsixchapters,wherethefollowingpapersarecited,

.SJwasaki,andH.Okamoto,Anomalousbackscatteringenhancementbynon-spherical

icecrystalsforlidarobservation.,Appl.Opt,2000.,submitted.

●S.Iwasaki,andH.Okamoto,Analysisoflidarbackscatteringenhancementlbrpris-

tinehexagonalicecrystals･,InSingh,Itabe,Sugimoto(Eds)SPIE2000:Remote

SensingoftheAtmosphere,Environment,andSpace.,2000.,inpress.

.S.Iwasaki,andH.Okamoto,Analysisoflidarreturnsfromrectanglesandhexagl

onalicecrystals.,InSmithandTimofeyev(Eds･)IRS2000:CurrentProblemsin

AtmosphericRadiation,DeepakPublishing,2000.,inpress.

Inchapter2,weexaminethelidarbackscatterlngbylargenon-sphericalicecrystals

onthebasisofrayopticsl6]･Ournumericalcomputationsshowwhenlargeiceparticles

haveflatsurfacesanddistanceZbetweentheparticlesandareceiverislessthanlkm,an

anomalousbackscatteringenhancementcanbeexpectedcomparedwithsphericalcase,in

thelidarobservations.

Inchapter3,weanalyzelidarbackscatteringenhancementforpristinehexagonalice

crystalsbyusingFhunhoferdiffractionbasedonKirchhoff'sdiffractiontheory[7]･Those

numericalcomputationsshowthatreceivedpoweratthealtitudeZinthelidarequation

isproportionaltoZ-α,whereαisafunctionofZ,sizeandshapeofparticlesandisnot

necessarytobe2,whichistheslopeofsphere.Ourcalculationssuggestthathexagonal

icecrystals,whosemoderadiusesaremorethanseveraltensmicrometersandthose

areperfectlyorientedinhorizontalplane,haveanomalousbackscatteringenhancement

comparedwithasphereatevenhighaltitude.Thismightexplainthephenomenareported

byPlattet.al･(1978)[8]･

Thechapter4istheextensionofchapter3,wherewecalculatewiderangeofsizesof

particles.Weshowthatthereceivedpowerforthehexagonalplatesperfectlyorientedin

horizontalplaneproduces104-109timeslargerslgnalscomparedwiththatforspheres

withsamesizedistributionatthealtitude10km.Andthatforthehexagonalcolumns

perfectlyorientedinhorizontalplaneproduces5×102 - 3×104 timeslargerslgnals

comparedwiththatforspheresatZ-10km.

4

Inchapter5,wereportsynergycloudobservationsbylidar,SPIDERand13.8GHz

precipitationradar,whichiscalledCAMPR(CRLAirborneMultiparameterPrecipitation

Radar)[外 しidarandSPIDERareusedtostudymicro-physicsofcloudparticlesofcirrus･

SPIDERandCAMPRareusedtoobservethecloudwit･hmeltinglayer[10,11].Melting

layershaveverystrongradarechoforCAMPR,thathasbeenknownasbrightband,

while,thoseareweakforSPIDER.Thisshouldbethereflectionofcomplexnatureof

cloudmicroIPhysics,e.9.thedielectricconstantsformixtureoficeandwatersizeof

meltinglayerparticles,etc.Thusthesecombinationseemstobeapowerfultoollbrthe

studyofcloudwithprecipitation.

Inchapter6,wereportcloudobservationsbySPIDERonboardaircraftabovethe

JapanseaonFebruary28th,2000.Themainaimofthisstudyistodesignfuturespace

bornecloudradar,C.9.EarthCareMission.Wederivetheseasurfacereflectance.Our

experimentsshowthatseasurfacecanbeusedasatargettocalibratethespace-borne

cloudradar.

Nextyear,wearegoingtojoinAsianAtmosphericParticulateEnvironmentalChange

Experiment(APEX),andhaveship-borneobservationsbyusing"Miraivessel"･

Forspacebornemissionprojects,PathfinderInstrumentsforCloudandAerosolSpace-

borneObservations(PICASSO,lidar)[12]andCloudSat(95GHzcloudradar)inUnited

Stateshavebeenalreadyapproved.AndEarthCareMission(ECM,1idarand95GHz

cloudradar)inEuropeandJapan,ATMOS-Bl(lidarand95GHzcloudradar)inJapan

areproposed[13],Wehopethestudiesinthisthesiscontributeforthesefutureexperi-ments.

Acknowledgement:

IamextremelygratefultoDr.HajimeOkamotoinCommunicationsResearchLabora-

tory(CRL)forhisusefulsuggestionsandsupportsinmydoctorworks.AndIwouldlike

tothankProf.T,MukaiinRobeUniversity,Dr.H.Kumagai,Mr.H.Kuroiwa,andDr.

T.IguchiofCRLThanksfortheirsupports,Icouldstudyradarandlidarobservations

atCRL ThanksarealsotoDr.M.YasuiinCRLforthelidarstudiesandtoMr.H.

HorieandMr.班.HanadoofCRLforcloudandprecipitationradarstudies.FinallyI

wouldliketoexpressmythankstoDr.H.IshimotoofMRI,Dr.A.KameiandMs.M.

0knzakiinKobeUniversity,Mr.andMrs.NakamurainNASDA,Dr.K.Maruyamaof

FRSGCandcolleaguesinKashimaSpaceResearchCenterwhoalsohelpandencourage

meinmydoctorworks.

5

Bibliography

[1]H.Horie,T･Iguchi,H･Hanado,H･Kuroiwa,H･Okamoto,andH.Kumagai,"De-

velopmentofa951GHzAirborneCloudProfilingRadar(SPIDER)",IEICETrans･

Commun.,2000,inpress.

[2]J･M.Intrieri,G･L Stephens,W･LEberhardandT･Uttal,"AMethodforDeter

miningCirrusCloudParticleSizesUsingLidarandRadarBackscatterTechnique,"

J.Appl.Meteor.,32,1074-1082(1993).

[3]Lammeren,A-C.A･P･,D･Donovan,andH.Bloemink,"SENSORSYNERGYALGO-

RITHM:DEVELOPMENTANDVALIDATION",proceedingsofthe丘rstinterna-

tionalworkshoponspacebornecloudprofilingradar2000,219-226(2000)･

[4]Okamoto,H･,M･Yasui,H･Horie,H･Kuroiwa,H･Kumagai,andSJwasaki,"OB-SERVATIONOFCLOUDSBY95GHzRADARANDLIDARSYSTEMS:RADIUS

VERSUSFALLVELOCITY",SmithandTimofeyev(Eds.)IRS2000:CurrentProb-

lemsinAtmosphericRadiation,DeepakPublishing,2000.,submitted.

[5]Okamoto,H･,S･Iwasaki,M･Yasui,H･Horie,H･Kuroiwa,andH･Kumagai,"95-GHz

cloudradarandlidarsystems:preliminaryresultsofcloudmicro-physics",InWilheit,

Masuko,andWakabayashi(Eds)SPIE2000:RemoteSensingoftheAtmosphere,

Environment,andSpace.,2000.,submitted.

[6]Y･TakanoandK･NILiou,"SolarRadiativeTransferinCirrusClouds.PartI:Single-

ScatteringandOpticalPropertiesofHexagonalIceCrystals,"J.Atmos.S°i.,46,3-19

(1989).

[7]MIBornandE･Wolf,PrinciplesofOptics,(PERGAMONPRESS,Oxford,1975).

[8]Platt,C･M･,"Lidarbackscatterfromhorizontalicecrystalplates,"J.Appl.Meteorol･

17,482-488(1978).

[9JKumagai,H･,K･Nakamura,H･Hanado,K･Okamoto,N･Hosaka,N.Miyano,T.

Kozu,N,Takahashi,T.Iguchi,andH.Miyauchi,"CRLAirborneMultiparameter

6

PrecipitationRadar(CAMPR):System DescriptionandPreliminaryResults",IE-

ICETrams.Commun･,E79-B,770-778(1996).

[1〔I]Stephanes,G･L･,RemoteS e n sing0ftheLowerAlrTWSPhere,(NewYork,O x ford･,

1994).

[11]Russchenberg,H.W･∫ ,andL P.Ligthart了 B̀ackscatteringbyandPropagation

ThroughtheMeltingLayerofPrecipitation:ANewPolarimetricModel",IEEE

trans.,34,3-14(1996).

[12]D.M･Winker,"THEPICASSOICENAMISSION,"inproceedingsofthefirstinter-

nationalworkshoponspacebornecloudprofilingradar2000,2351242(2000).

[13]ATMOS-BITeam/ESTO (Earth Scienceand Technology Organization),3D-

CLARE,ThreeDimensionalCloud-Aerosol-RadiationBudgetExperiment(proI

posalofATMOSIBIMission),(EarthScience&TechnologyOrganization,Japan,

2000).

7

Chapter2

Anomalousbackscattering

enhancementbynon-sphericalice

crystalsforlidarobservation

Abstract

Weexaminethelidarbackscatteringbylargenon-sphericalicecrystalsonthebasis

ofrayopticsanddiffractiontheory.Ournumericalcomputationsshowwhenlargeice

particleshaveflatsurfacesanddistanceZbetweentheparticlesandareceiverislessthan

lkm,ananomalousbackscatteringenhancementcanbeexpectedcomparedwithspherical

case,inthelidarobservations.Wefirstestablishthecriterionforthisenhancement.Then

modificationsforthelidarequationareproposedintermsofdependenceZ.Contraryto

thesphericalparticleswiththeirdependenceofZ12,suchdependencesvarywithparticle's

shapeandorientations;ZOforhexagonalplaterandomlyorientedinhorizontalplane,Z-I

forhexagonalcolumnrandomlyorientedinhorizontalplane.

2.1 Introduction

Inordertoforecastthefutureclimatechange,itiswidelyrecognizedthattheroleof

cloudsandtheirinteractionwithaerosolsareoneofthekeyproblemstobeunderstood.

SuchknowledgeswillbeusedtoassessandtoincreasethepotentialofGeneralCirculation

Models(GCM).Especiallyverticaldistributionofthecloudsshouldbemeasuredwith

certainaccuracyforthesurfaceradiativeforcingbyclouds.Lidar,aswellascloudradar

(95GHz)[1,2],isoneofthepromisingtoolsl3,4]･Forlasttwentyyears,therehave

beenintensivegroundbasedmeasurementsbyuseoflidarandsomeprogresseshavebeen

8

madeintheanalysisIFernaldet.all(1972日5]developedanalyticalmethodforthe

inversionprobleminlidarobservations.Klett(1981)[6]modifiedtheirmethodtoavoid

instabilitiesintheinversionproblems.Plattet,al.(1978)[7,8]pointedoutthatsome

cirruscloudsproduceastrongzenith-enhancedbackscatter(ZEB).Thisphenomenon

havebeendiscussedbymanyauthors(e.9.,Mishchenkoet.al.,1997arereferencesthere

in).Sassen(1991)[9]alsoshowedtheobservationalevidenceoft･healignmentofthe

particleinrelationtothehorizontalplanebyuslngthedualpolarizationlidartechnique.

Mishchenkoet･al.(1997)considereddisksandspheroidswithsizeparameterupto50

asicecrystalsandcalculatedlidarbackscatteringfromtheseparticlesbyusingT-matrix

method.Theyshowed"ZEBpeakcanbeproducedonlybyhorizontallyorienteddisks

butnotbyhorizontallyorientedspheroidsorparticlesinrandomorientation" . Uptonow,

severalspacebornelidarmissionprojects,PICASSO[11]inUnitedStates,ERM[12,13]

inEuropeandATMOS-Bl【14日nJapan･Tbdemonstratethefeasibilityofspaceborne

lidar,NASAhadtheexperimentforthelidarontheSpaceShuttlemission,whichiscalled

LITE[15]･

Inthispaper,toanalyzelidarsignalsbyclouds,thescatteringtheoryisdevelopedto

estimatebackscatteringbylargenon-sphericalicecrystalswithflatsurfaces.Invisible

wavelength,ray-tracingmethod[16,17]iswidelyusedforthescatteringbycloudparticles･

Sinceuptonowthereisnoexactmethodinthisdomainforlidarbackscattering,we

considerray-tracingmethodbasedongeometricaloptics(GO)[16,17]andKirchhoff's

diffractiontheory(KD)[18,19]･NotethatintheusualGO,diffractiontermisnormally

includedonlyintheforwardscatteringbutnotinthesideandbackwarddirections.

Becauseofthisignorance,theapplicabilityofGOislimited.Inthispaper,wedefine

"diffraction"as"thescatteredlightthatcannotbecalculatedbyrayoptics",thatis,

diffractionisdiffusedlightinducedbyitscharacteristicofwaveoptics.Mishchenkoet.al.

(1997)actuallydiscussedaboutpatterndescribedbyKDforthequalitativeunderstanding

ofthecomputedresultsforspheroidsandcirculardisks.Althoughwealsodiscussabout

KD,ourmainaim ofthispaperistotesttheapplicabilityofGO.Thereforewewould

liketodistinguishbetweentheirapproachandours.

Insection2.2,forthebackscatteringbyarectangulartarget,weanalyzethediffraction

patternbyarectangulartargetwhereKDcanbeapplicable.Whenthemainlobeofthe

backscatteredlidarsignalsiswithinasolidangleofthereceiverviewedfromtheparticle

(sop),wenumericallyprovethatthebackscatteredpowerestimatedbyGOisingood

agreementwiththatbyKD･Howeverwhenthe m ainlobeisoutofthesop,GOisnot

applicable.Intheformercase,anomalousbackscatteringenhancementcanoccur.We

proposethecriterionforthisenhancementasafunctionofwavelength,Z,theparticle

size,halfwidthofthereceiverRt,shapeandorientation.Insection2.3,backscatteringby

9

hexagonalicecrystalwithvariousaspectratiosareestimatedbyGO,whenthecriterion

isful丘11ed.Andwederivethemodi丘Cationtotheusuallidarequationinordertotake

intoaccounttheanomalousbackscatteringenhancement.

2.2 Mechanism ofbackscatteringenhancement

ThegeometryofthelidarobservationisdescribedinFig.2.1andthesymbolsused

inthispaperaredefinedinTable2.1.Inthissection,Weestimatethebackscattering

diffractionbythehexagonalcolumnandhexagonalplaterandomlyorientedinhorizontal

plane(hereafter2D-columnand2D-plate)byKirchhoff'sdiffractiontheory(KD)[18,19]･

Thenweestablishthecriterionwherebackscatteringenhancementcanbeexpected.

2.2.1 ComparisonbetweenGOandKD forrectangularsurface

Fbrsimplicitywestartwithrectangularparticlesasthenon-sphericalparticles.And

wealsoassumetheshapeofareceiverisrectangle(seeFig,2.2)･¶)calculatedi駄action

patternsbytherectangularparticles,weuseKD.Thebackscatteringirradiancecanbe

writtenasEq･2･11mFraunhoferapproximation[18]･

･S(x,- - 芸 空碧 (至芸 )2(若 )2

◎x - kl(¢x-2sinせ)/2

- kl(X/Z-2sinせ)/2

◎Y - ka¢Y/2

- kaY/2Z (2.1)

whereSdenotesareaofthescatter,Rf,eisthereflectanceoftherectanglecalculatedby

Fresnelformulal21]･Zoisincidentintensity.Aandkarewavelengthandwavenumber

ofinterest.ianda(i≧a)arethesidelengthsoftherectangle(seeFig.2.2).Theangle

betweenthenormalvectoroftherectangleandtheincidentbeamせandanglesmeaning

of¢xand¢yaredescribedinFig.2.2.Themainlobeisdefinedastheirradiancestood

outaroundOx-0andOy - 0(seeFig･2･3).Thescaleofthemainlobeonthe

receiverisdescribedinFig･2･2byintroducingthecharacteristiclengthsRd,IandRd,a･

Bysubstituting◎x- ◎Y- 7TintoEq･2･1,Rd,landRd,aareObtainedas

(2.2)

10

Whenせ -0,Correspondingthesituationwheretheincidentbeamisperpendiculartothe

surfaceofrectangularparticles,integrationofJβinEq.2.1isthetotalscatteredpower

estimatedbyKDwhichagreeswiththatestimationbyGO.

∫

LIT

･J亡dX/IuudYIs(X,Y,0)-SR freIo･ (2･3)

NumericalintegrationofIsalsoshowsthatthepowerofthemainlobebecomes81%of

thetotal(seeFig.2･4)･

Fig.2.5Showsthediffractionpatternbyarectangulartargetwithorientationalaver-

aglngWheremajoraxisoftherectangleisparalleltotheYaxisandminoraxisisrotated

randomly(0< せ<7T)andtheseminimum irradiancearedeterminedbyRd,I(seeEq･

2.2)･Theshapeofthepatterncanbeunderstoodfromthesuperpositionofthepattern

byrectangular.ThereceivedpowercalculatedbyGOis

ps,GO - ; ; RfreIoS (2･4)

whereRtisahalfwidthofthereceiver(SeeAppendix2･511)･WhenRtisequaltoRd,l,

numericalintegrationofIsdescribedinFig.2.5showsreceivedpowercalculatedbyKD

becomes90%ofPs,GO.

Therefore,wecanproposethecriterionfortheapplicabilityofGOtobe

Rt>Rd,i. (2･5)

AlthoughwederivedaboutthiscriterionfortheparticleswithoutanyrotationsonX-Y

plane,thecriterioncanalsobeappliedfortheparticlebutrandomlyorientedinhorizontal

plane亘 C.themajoraxisoftheparticleisrotatedaroundZaxisandtheminoraxisis

rotatedaroundthemajoraxis.ThisisbecausetheapplicabilityofGO(inEq.2.5)does

notdependontheanglebetweenXaxisandthemajoraxisofthetarget.Pleasenote

thereceivedpowerinEq.2.3andEq.2.4havedifferentZdependence,contrarytothe

usuallidarequationl22,23]dependency,whichhasZ-2(inEq.2.6).

p,(Z)-cz~2(C,bk,a+Jbk,p)e-2('g'Tp) (2.6)

whereC istheconstantofthelidarsystem.Jbk isthebackscatteringcoefEcientand

T istheopticaldepth.ThesufBxesgandpmeangasandparticle.Thisdifference

ofZ-dependencesuggests,whentheconditioninEq.2.5isfulfilled,abackscattering

enhancementinducedbythedifferentZ-dependence(BEZ)ofthereceivedpowercanbe

expectedandquantitativecomparisonbetweensphericalandnon-sphericalparticlesgives

insection2.3.Pleasenotethephenomenonofbackscatteringenhancementdiscussedhere

isdifferentfromthezenith-enhancedbackscattering(ZEB)previouslydiscussedinmany

authors(Mishchenkoet.al.,1997).

iFl

2.2.2 CriterionfわrtheapplicationofGO

Particle'sorientationmightdependonitsshape･Ono(1969)[24]showedtheparticleis

alignedasitslongestaxisisparalleltothehorizontalplane.Forexample,whenhexagonal

columnwithaspectratioasp(il/2a)-3isconsidered,symmetricalaxisisparallelto

thehorizontalplane(2D-column)(seeFig.2.6(a)).Forhexagonalplatewithasp-1/3,

symmetricalaxisisperpendiculartothehorizontalplane(2D-plate)(seeFig･2･6(b))･

Whenthe2D-plateisconsidered,weassumethebackscatteredirradianceIsfor2D-

plateisthesameasthatforthesquarewhichhasthesamegeometricalcrosssectionof

2DIPlate･Thatis,IsforthesquareisobtainedbyusingEq･2･lwithI-a-Rsq,where

Rsqisthesidelengthofthesquare･Similartothediscussionforarectangularparticles,

whenthecriterioninEq.2.7isfulfilled,GOcanbeappliedandtheBEZisexpected.

Rt > Rc

RczAaspl/3

(i7T4)1/12req(2.7)

whereRcisthecriticalradiusglVenbyEq.2.7.Fortheparticleswithvolumeequivalent

radiusreq- 100FLm,Z-loom,asp- 1/6,Rc-0･2m andRt>0･2m,BEZcanbe

expected.InFig.2.7(a),wedescribetheregionwherebackscatteringenhancementcan

beobserved,intermsofZ,volumeequivalentradius reqandaspI

Thebackscatteredirradianceby2D-columnmightbesixtimeslargerthanthatby

therectanglewheregeometricalcrosssectionoftherectangleisthesameasthatofone

ofrectanglesonhexagonalcolumns.ThustheapplicabilityofGOisthesameasthatfor

therectangulartargetrandomlyorientedinhorizontalplaneasdiscussedinsubsection

2.2.1.

Rl > Rc

RcZA

2(品 )1/3asp2/3req (2.8)

Fortheparticleswithreq-100pm,Z-loom,asp-3andRc-0･2m andRt>0･2m,

BEZcanbeexpected(inFig･2.7(b))･

R)r3D-columnand3D-plate,Weassumethecriterionisassameasthatof2D-column.

2.3 Analysisofthelidarbackscatteringbypristine

hexagonalcrystals

lnthissection,werestrictonanalysistothecasewherethecriterionEq.2.7orEq.

2.8isfulfilled.Forthearbitraryshapedparticle,itisnotpossibletosolveKD.SinceGO

12

isingoodagreementwithKD(insection2.2),WerelyonGO.Weassumethatthereis

nomultiplescattering.Inordertoestimatethelidarbackscatteringslgnalsbypristine

hexagonalicecrystals,wefirstneedtoreformulatethelidarequation.Wcstarttothe

generalformulationofthelidarequation(inEq.2.9).

0(0-180)

pr(Z)- Io/vzdv/lZedr警 L:(0-180-∂Op) dOe12(Tg+Tp)

60(180)- 7T602 (2.9)

whereVzdenotesscatteringvolumeilluminatedbylaser.dn(r)/drissizedistribution･0

isascatteringangle.

2.3.1 Caseforsphericalparticle

lntheMiescattering,dCsca(180)/dOisconstant[21].Therefore,Eq.(2･9)becomes

pr- IoVzq(普)2Lizedrdn(r)dCsca(180)dr dO

e-2(Tg'Tp) (2.10)

ThiscorrespondstheusuallidarequationandproportionaltoZ-2･

2.3.2 Casefor2D-column

lnthecaseofhexagonalcolumnrandomlyorientedinhorizontalplane(2D-colum n),

6Csca(180)/60isnotconverged(Fig･2.8).Toovercomethisproblem,werewritethelidar

equationEq.2.9byintroducingdOinsteadofusingdn.

pr - Io/vzdv/iZedr慧 /;;oT60p

e12(Tg'Tp) (2.ll)

InFig.2.9,eachlinecorrespondstotheresultsfordi庁erentrandom seedsusedinthe

computations(opticalconstantl20]is1.31+i2.5419,wavelengthofinterestis0.532FLm)A

Itisfoundthat6Csca(0)/60isconstantforthebackscatteringdirection.Therefore,Eq.

(2･11)becomes

pr - IoVz昔 /tZedr慧 csα

6Csca(180)/60Csca

e-2('g+'p) (2.12)

Inthiscase,thelidarequationbecomesproportionaltoZl1･

Whenweneglecttheabsorptionoficecrystals,6Csca(180)/60/Cscaisindependenton

crystalsizeandCscais2G,whereaisthegeometricalcrosssection.Thisisbecause6Csca

andCscadependonreflectanceRandtransmittanceTandRandTdoesnotdependon

size.Thus,Eq.(2.12)becomes

P, - 2IoVz6Csca(180)/60Rt

Csca Z

13

Lizedr警 G(r)e-2(T9･Tp' (2･13)

SincecylindricalcolumnmightbeapproximatedbyinfinitepolygonalcolumnandZde-

pendencyofcylindricalcolumnl21]isZtl,wecannaturallyunderstandZ~ldependence

ofthe2D-columnappearedinEq.2.12.

2.3.3 Casefor2D-plate

lnGO,backscatteredpowerofthehexagonalplaterandomlyorientedinhorizontal

plane(2D-plate)canbeapproximatedbythatofaslabwithfinitethicknessandinfinite

width.WecallthismethodFiniteSlabApproximation(FSA).Forthisgeometry,itis

notnecessarytouseray-traclngmethodtoestimatebackscattering.

ThereflectanceRfsais

RfsaI6600((oO==1188.0160p)dO些悪 鞘 -180Io

GIo

2Rf,e,i

1+Rf,C,i(2.14)

whereRf,C,⊥isthereflectancefortheverticalincidentlight[21]estimatedbyFtesnelformulas.

Therefore,Eq.(2.9)becomes

pr 竺 IoVzRfsa/ izedr慧 G(r)e-2(T9･Tp' (2･15)

Similartotherectangularparticle,backscatteredpowerfor2D-platedoesnotdependon

Z.

2.3A Casefor3DICOlumnand3D-plate

Hexagonalcolumnandplaterandomlyorientedinspace(3D-columnand3D-plate)

areconsideredinthissubsection･WealsostartfromEq･(2･11).6C sca(180)/60turnsout

tobeconstantbyusingGO(seeFigs･2･10(a)and(b))･Itssize,wavelengthofinterest

andopticalconstantarethesameasthosevaluesusedinsubsection2.3.2.Eachline

correspondstotheresultsforthedifferentrandomseedsinthecomputations.Thelidar

equationbecomes

pr- IoVz鋸 Zedr警 csca

6Csca(180)/60Csca

Forthenon-absorptiontargets,Eq.2.16furtherreduceto

P, - 2IoVz6Csca(180)/60RlI.dn(r)

Csca ZJs7Z｡yy'dr

14

e12(Tg'Tp) (2.16)

L7Z｡dr慧 G(r)e12̀Tg'Tp' (2･17)

2.3.5 Discussion

InFig･2.ll ,wecomputeP,(Z)fordifferentparticleshapesandorientationsbased

onthenewlyderivedlidarequations.Forthesamevolumeoficecrystalinconsidered,

2D-platecanproducethelargestsignalswhenmainlobeiswithin6npandthusGOis

applicable.

Whenthe2D-columnwithreq- 100FLm andasp-3isatZ-loom,GOcanbe

validandP,(Z)isabout50timeslargerthanthatforthespherewithsamevolume(see

Fig.2111(a)).For2D-plat,C,itisabout1000timeslargerthanthatforthesphere(see

Fig･2･11(b)).

2.4 Summary

Weanalyzebackscatteringbynon-sphericalparticleswhichhaveflatsurfaceswith

various ShapeandorientationsbyusingKirchhoff'sdiffractiontheory(KD)andray-

tracingmethodbasedongeometricaloptics(GO)･

First,wecompareKDandGOand丘ndwhenthemainlobeofthebackscattered

signaliswithinthesolidangleofthereceiverviewedfromtheparticle(60p),GOisin

goodagreementwithKD.Forarectangle,Zdependenceofthereceivedbackscattered

powerturnstobedifferenti･e･ZOorzllfromthatforspherical;i･e･Z-2lWeestablish

theapplicabilityofGOasafunctionofユ,Z,req,Rt,shapeandorientation･

Weconsiderthefollowingscatteringtargets,hexagonalcolumnandplaterandomly

orientedinhorizontalplane(2D-columnand2D-plate)andhexagonalcolumnandplate

randomlyorientedinspace(3D-columnand3D-plate).Forthe2D-plate,WeapplyFinite

SlabApproximationandforothersweapplyGO.ItisfoundthatZdependenceofthe

lidarequationsisZOfor2DIPlateandZ-1for2DICOlumn,3DICOlumnand3DIPlate･Note

thedependenceofthewidelyusedlidarequationisZ-2,Correspondingtothecaseofthe

sphere.Thusitisexpectedtoobservethebackscatteringenhancementinducedbythe

differentZ-dependencefromZJ2(BEZ)whenthecriterionfortheapplicabilityofGOis

fulfilled.Thismodificationoflidarequationmightberelevantforairborne-typeaswell

asforground-basedobservationforcoldcloudlocatedinlowaltitude,wherethedistance

betweenthescatterandreceiver<loom.

Whenthemainlobeofthebackscatteringslgnalisoutof60p,diffractiontermisnot

negligibleandGOcannotbeapplied.Thelidarequationfortheabovecaseiscurrently

investigatedbyuslngKDandwillbereportedinfuttirepaper.

ForZ - 1000m,OnlyverylargeparticlecanproduceBEZ,i･C.,req >1mm･How-

ever,theshapesofsizedistributionsisbroad,largerparticlescancontributetothetotal

backscattering.Thus,Zdependencemightalsobedifferentfrom Z~2evenifthemean

15

radiusissmallerthan1mm.Thusinsuchsituationthismodificationbecomesimportant.

R)rtheeffectofsizedistributioll,WeWilldescribeinanextpaper.

TheseresultsarenotonlyImportantforthescatterlngbythepristinehexagonalice

crystals,butalsofortheparticleswithflatsurfacesexceptforthehighlyirregularshaped

particles[25],suchasKochfractals[17].

2.5 Appendix

2.5.1 Received powerforarectangulartargetrandomlyori-

entedinhorizontalplane

Theconfigurationoftheparticle,incidentandscatteredlightissketchedinFig.2.12.

InGO,scatteredirradiancebyarectangulartargetis

Is-Rf,eIo∂0,2や･ (2.18)

whereIoisincidentintensity,Rf,eisreflectanceoftherectangularparticle,60,2中isKro-

necker'sdeltaand申istheanglebetweenthenormalvectoroftherectangleandthe

incidentbeam.Therefore,receivedpowerderivedbyarectangulartargetrandomlyori-

entedinhorizontalplanebecomes

ps,GO-IsS% ; ; RfreIoS･

whereQ'm isRt/2ZwhenQ'm <<1.

16

(2.19)

Table2.1:Thedefinitionofsymbols

Io incidentintensity

Is(X,Y,せ) backscatteringirradianceat(X,Y)

P,(Z) receivedpower

中 rotationanglearoundYaxis

Rd,a,Rd,i thescaleofthemainlobeobtainedbyKD(seeFig･2･2)･

Rf,e reflectanceofFresnelformula

Rfre,i reflectanceofFresnelformulafortheverticalincidentlight

Rt ahalfwidthofthereceiver(telescope)

〟.

.I,

/

叩

I･,i.二3..?

areaofthescatter(α×りaltitudeofthescatter

l/2a(seeFig.2.6)

sidelengthsoftherectangle

solidangle

solidangleofthereceiverviewedfromthescatteredparticle

dn(r)/dr sizedistribution

た

入

旬

bS

T

β

wavenumber

wavelength

volumeequlValentradius

backscatteringcoefEcient

opticaldepth

scatteringangle

Table2･2:Criteriafortheapplicabilityofgeometricaloptics(GO)fortheparticleswith

differentshapes･Rtisahalfwidthofthereceiverandreqisthevolumeequivalentradius･

ZandAarealtitudeofthescatterandwavelengthofinterest.

criterionforapplicabilityofGO

2DICOlumn Rt>2(47T/9/1月)1/3asp2/3,eq

2D-plate Rl, 親3DICOlumn Rt >

3D-plate Rt>

ZA2(47r/9/ヽ乃)1/3asp2/3,eq

ZA

2(47T/9/､β)1/3asp2/3,eq

17

Figu

Figu

_ _ ＼∴-2丁【 -1t 0 T【 27T 3n

◎x[rad]

Figure2.3:Thebackwarddiffractionpatternbytherectangulartargetnormalizedat

maximum.Wedefine"themainlobe"as"thescatteredlightfor-7T<Ox<7T(dashed

curve)",whereOxisgiveninthetext･

20

妻完 il:-:lこ

loglOIntenslty

02

4

∠U000

一

一

l

一l

Figu

Figure215:T九esameasFig･4b

F

1[tu]za

Pn召tV

0

0

0

0

0

0

0

0

1

asp=1/3 -- - /∫asp=1/6 - - 7

′-asp=1/12- ㌢′/;′雪 雲 _,_?_噛 ---:イJ:ン:T/′: :l l

/ ′

: :l l10 100 1000

10000Volumeequivalentradiusreqlpm]

(b)

0

0

0

0

0

1

1【u]zaP

nt!TTV : :

/′@ ,,rJOt.{了や㊨/,:I :

=ヲア~′ 芸;芸≡三二二_HHH.a!p

_〒43_.･.丁.丁 二 _…10 10

0 1000 10000Volumeequivalentr

adiusreqlpm]Figure2.7:Thecriterionthatbackscatteringenhancementisoccurr

ed.Undertheselines,Z12dependenceonthelidarequationisviolatedandbackscatter

ingenhancementoccurs.Rt-0.2m.(a)hexagonalplaterandomlyorientedinhorizontalpl

ane(2D-plate)･(b)hexagonalcolumnrandomlyorientedinhorizontalplane(2D-column).aspdescribe

sa

ugJ(o

)｡3Sug

40+eHH

30+eHH

178.5 179 179.5 180ScattedngAngle[deg]Figure2.8:Therelationbetweend

ifferentialcrosssection6Csca(0)/60for2D-columnandscatteringangle0.Eachlineco

rrespondstothedifferentangularbin60.Whentheangularbinissmaller,∂Cβ｡α(180)/∂nbecomeslarger･

0 0.2 0.4 0.6 0.8

1AngularBin80[deg]Figure2.9:Therelationbetween6Cs

ca(180)/60for2DICOlumn(I-86FLm,a-14FLm)and60calculatedbytheray-tracingmethod.Eachlinecorrespondsthere

0 0.2 0.4 0.6 0.8 1

1e-6 1e-4 1e-2 1e十0 1e+2ReceivedPower[arb.uni

t](b )le-6 1e-4 le-2 l

e+0 1e+2RecievedPower[arb.unit】Figure2.ll:(a)Comparison

betweenthebackscatteredpowerP,(Z)forsphereandthatforthe2D-columnwhenB

Figu

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31

Chapter3

AnalystsOflidarbackscattering●

enhancementforpristinehexagonal

icecrystals

Abstract

Weanalyzelidarbackscatteringenhancementforpristinehexagonalicecrystalsby

usingFraunhoferdiffractionbasedonKirchhoff'sdiffractiontheory(KD).Ournumeri-

calcomputationsshowthatreceivedpowerP,(Z)atthealtitudeZinlidarequationis

proportionaltoZ-α,whereαisafunctionofZ,sizeandshapeofparticles.P,(Z)is

proportionaltoZ1115forhexagonalplateandcolumnrandomlyorientedinhorizontal

planeatZ-200mwhereitsaspectratiosare1/3and3andmoderadiusesarelOOpm.

Ourcalculationssuggesthexagonalicecrystalsthathavemoderadiusesof100pm and

30pmwithperfectlyorientedinhorizontalplanehaveanomalousbackscatteringenhance-

mentcomparedwithasphereatevenhighaltitude.Thismightexplainthephenomena

reportedbyPlattet.al.(1978)[1,2].

3.1 1mtroduction

Lidarisoneofthemosteffectivetoolstoinvestigatethecloudprofilessuchasvertical

structure,shapesandsizesoficecrystals,whicharetheunknownfactorstoestimatethe

radiativepropertiesofcloudswithhigh accuracy.Therefore,forlasttwentyyears,there

havebeenintensiveground-basedmeasurementsbyuseoflidarandsomeprogresseshave

beenmadeintheanalysis.Fernaldet･al.(1972)[3]developedananalyticalmethod

fortheinversionproblem inlidarobservations･Klett(1981)[4]modifiedtheirmethod

32

toavoidinstabilitiesintheinversionproblem.Besides,therearesomeobservationalevi-

dencewhichshowsnon-sphericityplaysakeyrole･Plattet･all(1978)[1,2]showedt･hat

someunusuallidarreturnsfromamiddle-levelcloudwereobserved･Theyalsoshowedice

cloudsinthezenithgaveaveryhighbackscatteringbutaverysmalldepolarization,which

iscalledzenith-enhanc･edbackscatter(ZEB)･Mishchenkoet.al.(1997)considereddisks

andspheroidswithsizeparameterupto50(e･9･r-5pm atA-0.63pm)asicecrys-

talsandcalculatedlidarbackscatteringfromtheseparticlesbyusingT-matrixmethod.

Theyshowed"ZEBpeakcanbeproducedonlybyhorizontallyoriellteddisksbutnotby

horizontallyorientedspheroidsorparticlesinrandom orientation".Despitefrom these

efforts,thereisatheoreticaldi氏cultyininterpretationoflidarslgnals.Thatis,inlidar

signals,itisnotpossibletoderiveanalyticalsolutionsfornon-Sphericalparticleswhen

thesizeofparticlesismuchlargerthanthewavelength.Ray-tracingmethodiswidely

usedinvisibleanalysis,however,ithasalsoafundamentaldi氏cultyinbackscattering.

Theapplicabilit′yofthismethodistestedanditturnsoutthatgeometricaloptics(GO)

canbeapplicablewhenthealtitudeisveryclosetotheground(e･91100m)[6]･Ourfinal

goalofthisstudyistoexplainthemechanismofunusuallidarreturnsshowedbyPlatt

et･al.(1978)[1,2]･

Atfirst,westartwithFraunhoferdiffractionbasedonKirchhoff'sdiffractiont,heory(KD)

[7,8]･Insection3･2,thetheoreticalproducesaregiven･Thenweanalyzethebackscat-

teringpatternbyarectangulartarget.Ⅰnsection3.3,Wecalculatethescatteringby

hexagonalcolumnsandplatesrandomlyorientedinhorizontalplaneanddiscussthedif-

ferencesofbackscatteringbetweenspheresandhexagonalcrystals.

3.2 Scatteringbyrectangularparticles

lnthissection,Wecalculatethebackscatteringpropertiesbytherectangularparticleswith

丘Xedorientationandrandomlyorientedinhorizontalplane(hereafter2D-rectangle)･

3.2.1 Definitionofsymbolsanddiffractionpattern

ThegeometryofthelidarobservationisdescribedinFig.3.1.Weassumetheshapeofa

receiverisrectangle.

Tocalculatediffractionpatternbytherectangularparticles,weuseKirchhoff'sdiffraction

theory(KD)[7,8].ThebackscatteringirradiancecanbewrittenasEq･3･1inFraunhofer

33

reC(tele

incidentbeam -右I VⅠo SCa tte r

-, ZdlPraction

:.::: /■ ■ 院 ･:.'es̀.■::I:: _Y

elVer 室≡蔓

scope' / RtFigure3.1:Thegeometryofthelidarobservation.Zoistheincidentlight.A

particleislocatedatthealtitudeZ.LengthofthetargetisspecifiedbyaalongX axisandlal

ongYaxis(I≧a),respectively.e7ande-sdenotetheincidentandsc

attereddirections.approximation[5,7]which

isderivedfrom KD･･S(I,y,Z

,o)- 芸 讐 (若 )2(若 )2e-2T◎x - kl(I/Z-2sinせ )/2

◎Y - kay/2Z (3･1)whereG denotesgeometricalcrosssectionofthescatter,Rslisthe

reflectanceoftheslabwithsomethicknessanditiscalculatedbygeometricalopti

cs(GO)[12]･Io isincidentintensity.Tistheopticaldepth.Aandkarewavelength

andwavenumberofinterest.ianda(l≧a)arethesidelengthoftherectangle(seeFig.3

.1).Qrdenotestheanglebetweenthenormalvectoroftherectangleandtheincidentb

eam.Thehorizontaldistributionofbackscatteredirradiancebyascatteriscalculate

dinFig.3.2(a).3.2.2 Scatteringbytherectangularparticleswithfixed

orienta-tionForarectangularparticlewithfiⅩedorientationwithせ-0,backs

catteredpowerintothereceiv

erisformulatedbypr(Z)-C′/_RRttdx/_RRttdyIs(I- ,0), (3･2)whereRlisthehalfwidthofthereceiverandC′istheconstantofth

elidarinstrument,whichisalsoappearedinusuallidarequation(Eq.3.5).

Casefurverylow cloud

Whenthealtitudeofcloudislessthan80m,thesizeofrectangleis200lLm X200FLm,

andthereceiverismuchlargerthan0.3m,mostofthebackscattere,dpowerisreceived

bythereceiver(seeFig･3･2(b))andisestimatedbysubstitutionofEq･3･1intoEq･3･2,

P,(Z)-C'RsII.GeL2T (3.3)

ItturnsoutthatP,(Z)doesnotdependonZ,contrarytothesphericalparticleswhere

P,(Z)isproportionaltoZ-2.

CasefTorhighcloud

Whenaltitudeislargerthan2km andotherconditionssuchassizesofrectangleand

receiverarethesameasthoseinprevioussubsection.Eq.3.2becomes

p,(Z)- C,S % RZe12T (3A)

Z-dependenceinEq.3AisZ12,whichisthesameastheusuallidarequation(Eq.3.5).

pr(Z)-C芸 e-2T (3･5)

whereCistheconstantofthelidarinstrument[3,11]･Ubkisthebackscatteringcoefncient.

Z-dependenceofthiscaseisthesameasthatofsphere,however,sizedependenceG2is

differentfromthatofsphere(Gl).

CasefTorintermediatestate

Thissubsectionisthecasewhenaltitudeis80m<Z<2kmandrestisthesameasin

subsection3･2･2･Inthiscase,itiseasilyexpectedthatZ-dependenceofP,(Z)hasthe

valuebetween-2and0,wherethedependencemightbechangedasthealtitudechanges.

WeestimatetherelationbetweenZ-dependenceofP,(Z)andZforagiVensizeofparticle

andreceiverarethesameasthoseinsubsection3･2･2lFig･3･3(a)showsZ-dependence

oftheexponentofthereceivedpower,dloglOP,(Z)/dlo910Z.WhenZisabout200m,

receivedpowerbecomesproportionaltoZ-1･5･whenaltitudeislessthan50m,oscillation

occurs,becauseofthesingleparticlescattering･Fig･3･3(b)showsZ-dependenceofthe

receivedpowerscatteredbytherectangleandthatbyaspherecalculatedbyEq･3･6[12]

whereweneglecttheinternallyreflectionofthesphere.Therectangleandthesphere

havethesamegeometricalcrosssectionsforthefaircomparison.

pap(Z)- 慧 GIo; e-2,

35

(3.6)

whereStisthegeometricalcrosssectionofthereceiver.Atthealtitudeof1000m,

receivedpowerproducesabout2×106timeslargerslgnalscomparedwiththatofspherical

scattering.

3.2.3 Scatteringbytherectangularparticlesrandomlyoriented

inhorizontalplane

ForarectangulartargetwithorientationalaveraglngWheremajoraxisoftherectangle

is丘Xedalongyaxisandistakentobeparalleltothehorizontalplaneandminoraxisis

takentobealongZaxisandrotatedaroundYaxisrandomly(2D-rectangle),scattered

irradiancecanbewrittenasEq.3.7byuslngEq.3.1.

Is(I,y,Z) - 1ノ汀/:Is(x ,y ,Z,0)dO

& % (% )2e 12T(3.7)

Fig.3.4Showsthehorizontaldistributionofbackscatteringfromthetarget.Theshape

ofthebackscatteringpatterncanbeunderstood丘･om thesuperpositionofthatbythe

rectangularwitha丘Ⅹedorientation.

Receivedpowerbecomes

pr(Z)-C′/_RRttdx/_RRttdyIs(I,y,Z)(3.8)

CasefTorlow cloud

Whenthealtitudeofcloudislessthan80m,andthesizeofrectangleis200pmx100FLm,

Eq.3.8becomes

pr(Z)-C,;% RsIIoGe12T (3･9)

ThisZ-1dependencecanbeunderstoodbytheZ-dependenceofcylindricalcolumnl12]

tobeZ-1.

Caseforhighcloud

Whenaltitudeislargerthan2km andsizesofrectangleandreceiverarethesameas

thoseinprevioussubsection,Eq.3.7becomes

pr(Z)- C,& % Rie12T

36

(3.10)

Z-dependenceisthesameasthatintheusuallidarequation(Eq.3.5).Contraryto

thesize-dependenceinusuallidarequation(cx:G),thatdependenceinthiscasebecomes

C 2/α.

Caseforintermediatestate

Similartothecaseforthefixedorientation,Z-dependenceofreceivedpowershould

bechangedbyitsdistancelike丘Ⅹedorientationalcase･Figs.3･5(a)and(b)arethe

sameasFigs･3･3(a)and(b)butfor2D-rectanglewhosegeometricalcrosssectionis

200Fl机 X100FLm.Fig.3.5(a)showsreceivedpowerisproportionaltoZ-1L5whenZis

about200m.Whenaltitudeislessthan50m,oscillationalsooccurs.Fig.3.5(b)shows

receivedpowerproducesabout103timeslargerslgnalscomparewiththatofspherical

scatteringatthealtitude1000m.

3.3 Scatteringbyhexagonalcrystals

Particle'sorientationmightdependonitsshape･Ono(1969)showedtheparticleis

alignedasitslongestaxisisparalleltothehorizontalplane.Forexample,whenhexagonal

columnwithaspectratioasp(=I/2a)-3isconsidered,symmetricalaxisisparallelto

thehorizontalplane(2D-column).Forhexagonalplatewithasp-1/3,symmetricalaxis

isperpendiculartothehorizontalplane(2D-plate).

Whenthe2DIPlateisconsidered,weassumethebackscatteredirradianceIsfor2DIPlate

isthesameasthatforarectanglewithfixedorientationwhichhasthesamegeometrical

crosssectionfor2D-plate.Thatis,IsisobtainedbyusingEql3･1withI- a- Rsq,

whereRsqisthesidelengthofthesquare･Thebackscatteredirradianceby2D-column

mightbe3timeslargerthanthatby2D-rectanglewhosegeometricalcrosssectionisthe

sameasthatofarectangleonthehexagonalcolumn.

Figs.3.7(a)and(b)arethesameasFigs.3.3(a)and(b)butfor2D-plateand2D-

column.Weassumetheaspectratiosare3and1/3,Io-1W/m2,Opticalconstant[9]is

1.31+i2.54xlOJ9,andicewatercontent(IWC)is1g/m3.Andlog-normaldistribution

(Eq･3･11)isassumed,wheremoderadiusrm islOOpm andstandarddeviationJis1.5.

Weneglecttheattenuationforthesignals(71-0).For2D-plateand2DICOlumn,P,(Z)

isproportionaltoZll5whenZisabout500m･Inaddition,receivedpowerfor2D-plate

producesabout107timeslargersignalscomparedwiththatforaspherewithsamesize

distributionatthealtitude1000m･Andthatfor2D-columnproducesabout5x103

timeslargersignalscomparedwiththatforasphereatZ-1000m.

37

Figs･3･8(a)and(b)arethesameasFigs.3.7(a)and(b)butrm -30FLm.For2D-plate

and2D-column,P,(Z)isproportionaltoZll･5whenZisabout150m.Inaddition,

receivedpowerfor2D-plateproducesabout8×105timeslargerslgnalscomparedwith

thatforasphereatZ-1000m･Andthatfor2DICOlumnproducesabout103times

largerslgnalscomparedwiththatforasphereatZ-1000m.

些坦 _･.｣

dr 挿 rlnJeこrP-(

1nr-1nrm(3.ll)

3.4 Summary

Weanalyzelidarbackscatteringenhancementforpristinehexagonalicecrystalsbyusing

FraunhoferdiffractionbasedonKirchhoff'sdiffractiontheory(KD).

Firstwestartwiththebackscatteringbyarectangulartarget.Thenwecomputethe

scatteringbyhexagonalicecrystalsbyuslngtheanalogyoftherectangularcalculations.

Wecalculatethescatteringbyhexagonalcolumnandplaterandomlyorientedinhorizontal

plane.Weassumethattheaspectratiostobe3and1/3andsizedistributionislog-normal

distribution,wheremoderadiusrm is100pm andstandarddeviationcTis1.5.For2D-

plateand2D-column,P,(Z)isproportionaltoZll･5whenZisabout500m.Inaddition,

receivedpowerfor2D-plateproducesabout107timeslargersignalscomparedwiththat

forsphereatthealtitude1000m･Andthatfor2DICOlumnproducesabout5x103times

largersignalscomparedwiththatforsphereatZ-1000m.

For2D-plateand2D-columnwhoserm-30pm,P,(Z)isproportionaltoZll･5whenZ

isabout150m･h addition,receivedpowerfor2D-plateproducesabout8×105times

largersignalscomparedwiththatforsphereatZ-1000m.Andthatfor2D-column

producesabout103timeslargersignalscomparedwiththatforsphereatZ-1000m･

Theseresultsarenotonlyimportantforthescatteringbythepristinehexagonalice

crystals,butalsoapplicablefortheparticleswithflatsurfacesexceptforthehighly

irregularshapedparticles,suchasKochfractalsl14].

Inthispaper,weconsiderthescatteringbythehexagonalcrystalsperfectlyorientedin

horizontalplane.However,Sinceitmightberarethatthecloudparticlesstayinsuchori-

entationduetoturbulenceandmighthavetumbling.Thismightleadtodrasticallyreduce

38

thebackscatteringenhancement.TheeffectofsuchtumblinglSCurrentlyinvestigatedby

uS.

39

∴log10Irradiance

N.

e

V

X

Z

u)u!S

∠ U

4

2

0

0

0

-1 -0.50

Ⅹ[m] 0.5 1Figure3.2:(a)Thehorizontaldistributionsofbackscatteringpatternby

therectangulartargetnormalizedatmaximumwhen中is0,入is0.532Fm ,Iandaare200

pm andZis100m.(b)Sliceofthebackscatteringprof

00(X)10ら.0 -

1.5 -1.0 -0.5 0.ExponentorReceivedPower sヽph.er＼.ヽ

＼reCtangIe

＼ヽヽ ＼～ヽ

＼ヽ ヽヽヽヽヽ ヽle-18 1e-15 1e-1

2 1e-09ReceivedPower【W]Figure3.3:(a)Z-dependenceoftheexponentofthereceiv

edpower,dloglOP,(Z)/dlo910Z･Weassumethatshapeofarectangleis200pmx200pmandRt

isO･2m･(b)Z-dependenceofthereceivedpowerscatteredbytherectangleandasphere.B

othofthem havesamegeometricalcrosssection.Weneglecttheinternallyreflectionofthesph

(a)

ヽヽヽ､ヽ-

ち■I一Il-1.5 -1.0

-0.5 0.0ExponentofReceivedPower ヽヽ～●●～

sph叫 .ヽ (b)ヽヽrectangle＼

ヽ＼＼､､､ ､. ､

ヽヽ ヽヽ＼ヽ～ ＼ヽ･､∴le-18 le-15 1e-1

2 1e-09Received Power[W]Figure3.5:(a)and(b)arethesameasFigs.3.3(a)and(b)butfor2D-rectanglewhosesiz

eis200pm x100FLm･嘩 Ⅰ2a l'IbbFigure3.6:Alignmentofahexagonalcrystal.(a)Sym metricala

xisisparalleltothehorizontalplane(2D-colum n)and(b)Sym metricalaxisisperpendiculartothehorizontalplane(2D-plate).

∈Olてココ･=守 1

0(XK)

1(XX)10

01

01 (a)

2D-plateヽヽ

2ヽD-Clumn-2 -1.5 -1 -0.5

0ExponentofReceivedPower BO｢コ:⊃･=守 100001

0(X)10010

1 (b)

●ヽ●ls

here ヽヽ 2D-plate●●

2D-Cヽ…olumn

ヽヽヽヽヽ1e-12 1e-09 1e-06 1e-03Power[arb.】Figure3.7:(a)and(

b)arethesameasFigs.3.3(a)and(b)butfor2DIPlateand2DICOlumn･Weassumetheaspectratiosare3and1/3andsizedistributionislog-normald

≡

O｢ココ

･≡

岳

10(X)0

1000

100

10

1

te

-----ヽ2-jc.otumn

IIlー2 -I.5 -

1 -0.5 0ExponentofReceivedPower ＼ヽsp

h , ヽe r e ､ 2D-plate

-I

... 2Dcolumnヽヽヽ

ヽ1e-12

1e-09 1e-06 le-03Power【arb.]Figure3･8:(a)and(b)arethesameasFigs

Bibliography

[1]C.M.Platt,"Lidarbackscatterfromhorizontalicecrystalplates,"J.Appl.Meteorol.

17,482-488(1978).

[2]C.M.Pla叫 N.LAbshire,andG.T.McNice,"Somemicrophysicalpropertiesofan

icecloudfromlidarobservationofhorizontallyorientedcrystals,"I.Appl.Meteorol.

17,1220-1224(1978)･

[3]F･G･Fernald,B･M･Herman,andJ･A･Reagan,"DeterminationofAerosolHeight

DistributionsbyLidar,"J･Appl･Meteor･,ll,482-489(1972).

[4]I.D.Klett,"Stableanalyticalinversionsolutionforprocessinglidarreturns,"Appl.

Opt.20,21 1-220(1981).

[5]M.Ⅰ.Mishchenko,D.J.Wielaard,andB.E.Calson,"T一matrixcomputationsof

zenith-enhancedlidarbackscatterfrom horizontallyorientediceplates,"Geophys.

Res.Lett.,24,771-774,(1997).

[6]SIIwasaki,andH･Okamoto,"Anomalousbackscatteringenhancementbynon-

sphericalicecrystalsforlidarobservation,"Appl.Opt.,insubmission.

[7]M･BornandE･Wolf,PrinciplesofOptics,(PERGAMONPRESS,Oxford,1975).

[8]Jackson,J.D.,ClassicalElectrvdynamics,(Wiley,NewYork.,1983).

lg]S.G.Warren,"Opticalconstantsoficefromtheultraviolettothemicrowave,"Appl.

Opt.23,1206-1225(1984).

[10]F.G.Fernald,"Analysisofatmosphericlidarobservations:somecomments,"Appl.

Opt.23,652-653(1984).

[11]G･L･Stephanes,RemoteSensing0ftheLowerAtmosphere,(NewYork,Oxford･,

1994),pp.427-438.

[12]C･F･BohrenandD･R･Huffman,AbsorptionandScatteringofLightbySmallPar-

ticles,(Wiley,NewYork.,1983)

44

[13]A･Ono,"TheShapeandRimingPropertiesofIceCrystalsinNaturalClouds,"J.

Atmos.Sci･,26,138-147(1969).

[14]A･Macke,J･Mueller,andE.Raschke, "SingleScatteringPropertiesofAtmospheric

lceCrystals,"J･Atmos･Sci･,53,2813-2825(1996).

45

Chapter4

AnalystsOflidarreturnsfrom●

rectanglesandhexagonalicecrystals

Abstract

Thereisatheoreticalproblem toapplygeometricalopticsforthebackscattering

calculationsoficecloudparticles.hordertoknowthebackscatteringbypristinehexago-

nalicecrystals,wecalculatethescatteringforarectangularparticlebyusingFraunhofer

diffractionbasedonKirchhoff'sdiffractiontheory(KD).Thenwecomputethebackscat-

teringbyhexagonalplatesandcolumnsperfectlyorientedinhorizontalplane(2D-plate

and2D-column).Weshowthatthereceivedpowerforthe2D-platesproduces104-109

timeslargersignalscomparedwiththatforsphereswithsamesizedistributionatthe

altitude10000m･Andthatfor2D-columnsproduces5×102 - 3×104 timeslarger

slgnalscomparedwiththatforspheresatZ-10000m.Thismightexplaintheunusual

largelidarreturnsreportedbyPlattet.al･(1978)ll]･

4.1 Introduction

LidarisoneofthepromlSlngtoolstoinvestigatethecloudprofilessuchasvertical

structure,shapesandsizesoficecrystals,whicharetheunknownfactorstocorrectly

estimatetheradiativepropertiesofclouds.Inordertoretrieveaboveinformationofsize

from thelidarobservationl2],weneedtoknowthebackscatteringcrosssectionofthe

cloudparticles･Itiswellknownthatgeometricaloptics(GO)isoneofthemosteffective

methodtocalculatethescatteringpropertiesbytheicecrystalsforthelidarwavelength.

However,thereisatheoreticalproblemtoapplyGOforthebackscatteringcalculationsof

icecloudparticles.WetestedGOanditturnedoutthatGOisonlyapplicableforthecase

46

thealtitudeisveryclosetotheground(C.9･100m)andshowedtheneedofmodifications

tothelidarequation･Ontheotherhands,Mishchenkoet･all(1997)[3]considered

disksandspheroidswithsizeparametersupto50asicecrystalsandcalculatedlidar

backscatteringfrom theseparticlesbyusingT-matrixmethod.SinceT一matrixmethod

cannotapplytothelargersizeparameters,wedevelopthemethodthatusesFraunhofer

diffractionbasedonKirchhoff'sdiffractiontheory(KD).

Insection2.1and2.2,wecalculatethescatteringbyarectangularparticleforsimplic-

ity.Ⅰnsection2.3wecomputethescatteringbyhexagonalcolumnsandplatesrandomly

orientedinhorizontalplanebyuslngtheanalogyoftherectangularcalculations.

4.2 Scatteringmodel

reC(tele

incide n t b eam 一石I V

lo SCatter∫ 早 ...㌔.;;i;aてrion Z

r

-eiver :二.二:.1.:.二-::::(x,y):::::scope)

∠一一一㌧ .R,一一一~/ ーFigure4.1:Thegeometryofthelidarobservation.Aparticleislocatedat

thealtitudeZ.Lengthoftherectangleisspecifiedbylanda(I≧a),respectively.e7ande-Sdenotetheincidentandscatt

ereddirections.Forsimplicity,Westartwitharectangularparticleasthenon-Sp

hericalparticleandweassumetheshapeofareceiverisalsorectangle.Tbcalculate

abackscatteredpattern,weuseFraunhoferdiffractionbasedonKirchhoff'sdiffraction

theory(KD).ThebackscatteringirradianceforarectangleiswrittenbyEq.4.1wherei

tsmajoraxisisparalleltotheYaxisandminoraxisisfixedinsom

edirectionl4].･S(x ,Y,Z,せ)

-芸誓 (若 )2(若 )2e12 T◎x - kl(x/Z-2sin中)/2

Oy -

whereGdenotesgeometricalcrosssectionoftherectangle,Rslisthereflectanceofthe

slabwithsomethicknessanditiscalculatedbygeometricaloptics(GO)(e･9･Bornand

Wolf1975).Ioisincidentintensity.Aandkarewavelengthandwavenumberofinterest.

せdenotestheanglebetweenthenormalvectoroftherectangleandtheincidentbeam

andTistheopticaldepth.Ianda(l≧a)arethesidelengthsoftllerectangle(see

Fig.4.号

4.2.1 ScatteringbyarectangularparticlewithaGXedorienta-

tion

Forarectangularparticlewithafixedorientationatせ -0,backscatteredpowerinto

仙ereceiverisformulatedby

pr(Z)-C,/_RRttdx/_RRttdyIs(I,y ,Zlg), (4･2)

whereRlisthehalfwidthofreceiverandC'istheconstantforthelidarinst.ruments.

10000

]000

Eq)

3 100≡

召

10

1

､ヽ●ヽヽ ヽ lrectanglew

ithfixedorienta

tion■●.sphereヽヽヽ

､ヽ､ヽヽ

'､､. _ヽ1e-18 1e-15 1e-12 1e-

09ReceivedPower[W】Figure4.2:Z-dependenceofthereceivedpowerscatteredbyther

ectangleandasphere.Weneglecttheinternallyreflectionofthesphere.Therectanglean

dthespherehavesamegeome

tricalcrosssections.Fig.4.2showsZ-dependenceofP,(Z)forarectanglewithafiXe

dorientationandthatforaspherewhereweneglecttheinternallyreflect,ionofthesphere.

Therectangleandthespherehavethesamegeometricalcrosssectionsforthefaircomp

arison.Weassumethattheshapeofarectangleis100FLm X100pm,Rt-0.2m,A-

0.532pm,Io-1W/m2,C′-1andopticalconstantis1.31+i2.54×10-9.Andwenegle

cttheattenuationforthesignals(T-0).Atthealtitudeof1000m,receivedpower

producesabout5×105timeslargersignalscomparedwiththatforthesphere.

10000

1000

≡4)'9 100

毒

10

1

highcloudCase

一ow

C一oudCaSe-2.0 -1.5 -I.0

-0.5 0.0Exponent

ofRecelVedPowerFigure4.3:Z-dependenceoftheexponentofthereceivedpower,dl

o910P,(Z)/dloglOZ.Fig･4･3showsZ-dependenceoftheexponentofthereceivedpower,d

loglOP(Z)/dloglOZ･WhenZissmall,mostbackscatteredpowerisreceived(seeFig.

4.4).ItsreceivedpowerisderivedbysubstitutionofEq.

4.1intoEq.4.2,P,(Z)-C'RsIIo

G･ (4.3)ItturnsoutthatP,(Z)doesnotdependonZ,contrarytothedep

endenceZ~2intheusuallidare

quation(Eq.4.4). pr(Z)-

C芸 e-2T, (4･4)whereCistheconstantofthelidarsystem l2]･Jbkisthebackscat

teringcoefBcient･WhenZislarge,receivedp

owerisderivedbypr(Z)- C′芸 芸

RsII.e-2T, (415)whereStistheareaofthereceiver,(2Rl)2. ItturnsoutthatZ-dep

endenceisassameasthatintheusuallidarequation,however,sizedependenceG2appe

aredinEq･4･5isdifferentfromGintheusuallidarequation.Theexponentdrastically

changesfrom0atZ= 50

mto-2atZ= 500m.4.2.2 Scatteringbyarectanglerandomlyorientedinh

orizontalplaneForarectangulartargetrandomlyorientedinhorizontalplane(

2D-rectangle),thebackscatteredirradiance

becomes･S(xM )-三

∈≡≡ヨreceiver(2)diffractionpatte

rn(3)∈≡≡∃r｡｡｡i,｡r(3)Figure4.4:Thesketchoftherelationbetweenbackscatteringlrradiance,

receiverandaltitude. & % (i )2e12T (4.6)Fora2D-re

ctangle,receivedpowerisformulatedbypr(Z

)-C′/_RRtfdx/_RRttdyIs(I- )･ (4･7)Here2D-rectanglewithgeometricalcrosssec

tionof100ILm X100FLm isconsidered.Fig.4.5isthesameasFig.4.2butfor2D-

rectangle.Fig.4.5showsreceivedpowerproducesabout2×102timeslargerslgnalscomparewiththatofsphe

ricalscatteringatthealtitude1000m.Similartothecaseforthefixedorientatio

n,Z-dependenceofreceivedpowershouldbechangedbyitsdistance.P,(Z)ispro

portionaltoZ-1･5whenZisabout80m.WhenZissmall,receivedpowerisderivedbysubstitutionofEq.4.6intoEq.

4.7,pr(Z)-C,;%RsIIoG･ (4･8)ThiscanbeunderstoodthatPr(Z)ispropor

tionaltoZJl,contrarytothesphericalparticles.Intheseregion,GOisapplicableandthedependenceisZ-1as

10000

1000

≡l〉

? )00≡

守

10

1

l ーヽ ー

ヽヽ 2ヽ D -columnI.J ヽ .､ヽ 'ヽ

lt. ･ヽsphere､ヽ:ヽヽヽ

､ヽ､ ＼ヽ

ヽ ､､､ ヽヽヽ.ヽle-18 1e-15 1e-12

1e-09RecelVedPower【W】Figure4.5:ThesameasFig.4.2butfor2D-rectanglewhosegeometricalcrosssec

tionis100FLmX100FLm.WhenZislarge,Z-dependenceforthiscasebecomesZ12

,whichisthesamedepen-denceforthesphere.Thiscanbeunderstoodbythefollowing

explanation.Thedistancebetweentheparticleandthereceiverislargeenoughsothatt

hehorizontaldistributionofthebackscatteredpowerishomogeneousoverthereceiver,

whichisthesameasthatforthescatt

eringwavebythesphere.4.2.3 Distancedependenceofthereceivedpowe

rbyhexagonalcrystalsWhenthehexagonalplatewithanaspectratioof1/3rando

mlyorientedinhorizontalplane(2DIPlate)isconsidered,weassumeitsbackscatteredir

radianceIsisthesameasthatforthesquarewithafiXedorientationwhichhasthesamegeometrical

crosssectionof2D-plate.Whenthehexagonalcolumnwithanaspectratioof3rando

mlyorientedinhorizontalplane(2D-column)isconsidered,weassumeitsbackscattered

irradianceJβisgivenbythesuperpositionofthebackscatteredwavefromeverysurfac

ewherethebackscatterlngsignalsfromasurfaceofhexagonalcolumnisestimatedbythesimilarprocedure

describedinsection2.2.Weassumethaticewatercontent(IWC)is1g/m3,andsize

distributionislog-normaldistributionwheremoderadiusesrm are10,100,1000lJm andsta

ndarddeviationo-is1.5.Fig.4.7(a)showsthatreceivedpowerfor2D-plateprodu

ces104- 109timeslargerslgnalscomparedwiththatforsphereswithsamesizedistributio

natthealtitude10000m.Andthatfor2D-columnproduces5×102-3×104timeslargerslgnalscomparedwith

10000

]0(X)≡

1ノ3 100言

】O

l

highcloudCase

lowcloudCase-20 -1.5 -1.0

-0.5 0.0Exponento

fReceivedPowerFigure4.6:ThesameasFig.4.3butfor2D-rectanglewhosegeometricalcrosssection

islOO〃m xlOO〃m･thatforspheresatZ-10000m.Fig.4.7(b)isthesameasFig･4･3butfor2DIPla

teand2D-co

lumn.4.3 SummaryWeanalyzelidarbackscatteringenhancementforpristinehexagona

licecrystalsbyusingFhunhoferdiffractionbasedonKirchhoff'sdiffrac

tiontheory(KD).Atfirst,wecalculatethescatteringbyarectangularparticleforsi

mplicity.Thenwecomputethescatteringbyhexagonalcolumnsandplatesrandomlyorien

tedinhorizontalplane(2D-plateand2D-column)byusingtheanalogyoftherectangu

larcalculations.Itturnsoutthatthereceivedpowerfor2D-plateproduces104 -

109 timeslargersignalscomparedwiththatforsphereswithsamesizedistributionatthe

altitude10000m.Andthatfor2D-columnproduces5×102-3×104timeslargersign

alscomparedwiththatforaspher

eatZ-10000m.Ourtheoreticalcalculationsshowtheexistenceofthehexagonalp

articlesrandomlyorientedinhorizontalplanemightbeexplainedfortheunusuallargelidar

returnsreportedbyPlat

tet.al.(1978).Inthispaper,weconsiderthescatteringbythehexagonalcrystalsp

erfectlyorientedinhorizontalplane.However,sinceitmightberarethatthecloud

particlesstaylnsuchorientationduetoturbulenceandmighthavetumbling.Thismi

ghtleadtodras-ticallyreducethebackscatteringenhancement.Theeffectofsuchtumb

lingiscurrentlyinves

◆◆●●◆l●l●●I.●..1()pml◆ ●l●●◆● ヽ (XX)pm

◆◆ ●●● ●●◆●●●●..1(叫mIヽ. ヽヽ◆◆ lOtX小m 1()um ~~~

11tnpm◆1(XX)um..◆...◆...ヽ◆...◆...●､.I◆●●ヽlヽ&叫mヽ2D-plate-

◆●●◆●● ヽ

llm.寸...ヽ◆､1●le-12 1e-09 1e-06 1e-03

PowerlW】

(b)10000

1000

≡'ノ召 100毒

1

01

rm=1tXX)HmI

rm=1(npm

ヽ .rm二1(小

m ヽ .2D-plate- IZD-columln- - J l

-2 -1.5

-1 -0.5 0ExponentofReceivedPowerF igure 4.7:(a)and(b)arethesameasFig.4.2a

Bibliography

[1]Platt,C･M･,N.L.Abshire,andG･TIMcNice,1978:Somemicrophysicalproperties

ofanicecloudfrom lidarobservationofhorizontallyorientedcrystals,I.Appl.

Meteorol.17,1220-1224.

[2]Fernald,F･G･,1984:Analysisofatmosphericlidarobservations:somecomments,

Appl.Opt.,23,6521653,

[3]Mishchenko,M･I･,DJ･Wielaard,andBIE･Calson,1997:T-matrixcomputations

ofzenith-enhancedlidarbackscatterfromhorizontallyorientediceplates,Geophys.

Res.Lett.,24,771-774.

[4]Born ,M･andE･Wolf,1975‥PrinciplesofOptics,PERGAMONPRESS,0Xford･

54

Chapter5

Cloudobservationbylidar,95GHz

cloudprofilingradarand13.8GHz

precipitationradar

Abstract

Wereportsynergycloudobservationsbylidar,95GHzcloudradarand13.8GHzpre-

cipitationradarin2000.Ourexperimentsshowthesesynergyobservationshaveagreat

potentialtoretrievemicro-physicalpropertiesofcloud.臥)rexample,lidarand95GHz

cloudradarobservations,Okamotoet.al.(2000)succeededinretrievingeffectiveradiiof

cloudparticlesandicewatercontent(IWC).TheradarTe月.ectionofcloudswithprecipita-

tionby95GHzcloudradarturnstobedifferentfromthatby13.8GHzprecipitationradar.

Thisdifferencesattributetothedifferentscatteringsignaturesinbothwavelengths,that

is,backscatteringofparticleslargerthanlOOFLm isbeyondRayleigh scatteringregion,

while,thatfor13.8GHzisstillwithinRayleigh region.Weconcludethatthesetworadar

isidealtoolfわrlargeparticlesizlng.

5.1 Introduction

Receivedpowerbyradarandlidardependsontheseveralmicro-physicalpropertiesof

scatters,i,C .,size,numberconcentration,Shapeandalignmentofcloudparticles,How-

ever,therehavebeenonlyfewsynergyexperimentsbyusingtheseinstruments.Inorder

toretrievethesemicrDphysics,synergyobservationsareeffective.Forexample,Okamoto

et.al.(2000)[1,2]succeededindevelopmentofthemethodtoretrieveeffectiveradiiof

55

Table5.1:Specificationsoflidar,SPIDERandCAMPR.Thevalueswithindex*denote

parametersandaretypicalvaluesforusualobservations.lidar SPIDER CAMPR

Wavelength(frequency)

PulseReputationFrequency

Transmittedpower

Verticalresolution

Pulse width

Dopp lercapabilityPolarizationfunction

532nln(564THz) 3･154mm(95.04GHz) 2.17cm(13･8GH

1064nm(281･8THz)

20Hz* 700Hz*

8W lkW

15m*(oscilloscope) 82.5m*

96m*(photoncounter)6-7ns

X

dual

1･1〃β*

Odual

2kHz*

3kW

150m*

2FLS'

Odual

function.Fig･5･l(b)isthe95GHzcloudradarcalledSPIDER(SpecialPolarimetricIce

DetectionandExplicationRadar).SPIDERsystemhasdualpolarizationfunctionand

Dopplercapability.Fig.5.1(C)isthe13.8GHzprecipitationradarforground-basedobser一

vationcalledCAMPR-G(CRLAirborneMultiparameterPrecipitationRadar).CAMPR

systemalsohasdualpolarizationfunctionandDopplercapability.SPIDERandlidarare

cO-locatedandCAMPRissetabout500mfarfromthesetwosystems.Table5.1isthe

speciBcationsofourlidar,SPIDERandCAMPRsystems.

Eqs.5.1arethedefinitionofbackscatteringcoefBcientβandequivalentradarreflec-

tivityfactorZe.Thosevaluesareoftenusedfortheresultsoflidarandradarobservation

respectively.

β -/iZedr禁 慧

ze(-- 6/-3) - 蕊 /lZe dr慧 Jcl

K m?ef-1mr2ef+2 (5.1)

wherecTcldenotesbackscatteringcrosssectionofascatter.risthesizeofscatterand

dn(r)/drdenotessizedistribution･m refisthecomplexreflectiveindexofscatterandK

isOl83forliquidwaterl6]andOA2forwatericel7]･Zeisoftenexpressedindecibelunits

dBZwheredBZ= 10log10Z(mm6/m3).

57

wa･tcl･si7J(10fmeltinglayerparticles.,etc_Thusthecombina･tionoftheseradarss(､(!I11StO

beaI)OWerfultoolfort･hestudyofcloudwithprccIPltat.ion.

【tzZ]q電dPTY

抑

州

側

2W

O15:5

3抑州側刑【旦

qpqpTY

蓋 蚕 室 義 盛

Tilneコ= 二

._二コ-40-30-20-10 0 10 20

JBZeFigtlre5･4:Resultsofthesynergyground-basedobservationofcloudsandrainf

allbySPIDER′(95GHz)andCAMPER(13･8GHz)Ⅰ･espectivelyfrom 15:53to17:08(J

ST)atKashimacityonNovember2nd,2000.Horizontalaxisdenotesobservationti

meandverticalaxisdenotesalt

itude.5.5 S

ummaryWehadintensivesynergyground-basedobservationsbylidar,95GHzcloudrad

arand13.8GHzprecipitationradarinFebruary,October,NovemberandDcccmber,2()0().Our

experimentsshowthesesynergyobservationshaveagreatpotentialtoretrievemicro-

pllySicalpropertiesofcloudparticles.Currentlyweareintensivelyanalyzingt･hoseobser-

vation,andwewillreportretrievedresultsinthenearfuture.

61

Bibliography

ll]Okamoto,H･,MIYasui,H.Horie,H･Kuroiwa,H.Kumagai,andS.Iwasaki,"OB-

SERVATIONOFCLOUDSBY95GHzRADARANDLIDARSYSTEMS:RADIUS

VERSUSFALLVELOCITY",SmithandTimofeyev(Eds.)IRS2000:CurrentProb-

lemsinAtmosphericRadiatlion,DeepakPublishing,2000.,submitted.

[2]Okamoto,H･,S･Iwasaki,M.Yasui,H.Horie,H･Kuroiwa,andH.Kumagai,"95-GHz

cloudradarandlidarsystems:preliminaryresultsofcloudmicro-physics",InWilheit,

Masuko,andWakabayashi(Eds)SPIE2000:RemoteSensirlgOftheAtmosphere,

Environment,andSpace"2000.,submitted.

[31H･Horie,T･Iguchi,H･Hanado,H･Kuroiwa,H･Okamoto,andH･Kumagai,"De-

velopmentofa95-GHzAirborneCloudProfilingRadar(SPIDER)",IEICETrans.

Commun.,2000,inpress.

[4]Wu,T.,R.Cotton,andW Y.YICheng,"RadiativeeffectsontheDiffus ionalGrowth

ofIceParticlesinCirrusClouds",J･Atmos.S°i.,57,2892-2904(2000)･

[5]Kumagai,H･,K･Nakamura,H･Hanado,K.Okamoto,N.Hosaka,N･Miyano,T,

Kozu,N.Takahashi,T.Iguchi,andH.Miyauchi,"CRLAirborneMultiparameter

PrecipitationRadar(CAMPR):System DescriptionandPreliminaryResults",IE-ICETrans.Commun.,E791B,7701778(1996).

[6]Ulaby,F･T･,R･K･Moore,andA.KIFung,MICROWAVEIWMOTESENSING

ACTIVEANDPASSIVE,VolurneIII,From TheorytoApplications,(Artechhouse,

Inc.,1986).

[7]S･GIWarren, "Opticalconstantsoficefromtheultraviolettothemicrowave,"Appl.

Opt.23,1206-1225(1984).

[8]Stephanes,G･L.,RemoteSensing0ftheLowerAtmosphere,(NewYork,Oxford.,

1994)･

62

[9]Russchenberg,H.W.∫,andL.P.Ligthart,"BackscatteringbyandPropagation

ThroughtheMeltingLayerofPrecipitation:A New PolarimetricModel",IEEE

trans･,34,3-14(1996)･

63

Chapter6

Air-borneobservationby95GHz

cloudradar

Abstract

Weanalyzetheresultsofair-borneobservationsofcloudsandseasurfacesby95GHz

cloudradar.Weshowthatthebackscatteringcrosssectionperunitareaofseasurface

isalmostconstantfor95GHzanditisabout-0.5dB.Therefore,ourexperimentsshow

thatseasurfacecanbeusedasatargettocalibratethespace-bornecloudradar.Next

weanalyzetheresultsofair-borneobservationsofDopplervelocityofcloudparticles.

Oneofthedi臨cultiesinthevelocitymeasurementsisthecontaminationofhorizontal

componentsofvelocity.Inordertoovercomethisproblem,Weintroducethecorrection

wheretruevelocityisobtainedbysubtractionofthevelocityofseasurface.Theretrieved

terminalvelocityofsnowparticlesislargerthanthatofcloudparticles.Thiscannaturally

beunderstoodthatthesnowparticlesarelargerthancloudparticles.

6.1 Introduction

Theconventionalcentimeterwavelengthsradars(radiodetectingandranging)donot

havesensitivitytodetectcloudparticles.Becausethosewavelengthsaremuchlonger

thancloudparticles,generallylessthan100FLm,theradarechofromtheseparticlesare

lessthanthedetectionlimit.Thisisthemainreasonwhyweneedmillimeterwavelengths

radars.Fromthetechnicalpointofview,sincetheirfrequencyisveryhigh,i.e.,95GHz,

W-band,itisverydifBculttodevelop95GHzcloudradars.Thereforeonlyfewcountries,

suchasU.S.,U.K.,GermanyandJapanhave95GHzcloudradars.InJapan,onlyCom一

municationsResearchLaboratory(CRL)succeededindevelopmentofthe95GHzcloud

64

Figllr

C6.1:(a)SPIDERinstalledi一lanairera町 GulfstreamII.(b)magnificat･ionofrd(hrin(a

)･rcfle,ctivityfa(･tor.FortheRayleigh scattering,Zebecomesze -/7ZedD誓 D6 (6.2)

whereDisthediameterofascatteranddn(D)/dDisasizedistributionanditisindcIpendentonthewavelengthofinterest.Therefore,whenthesizesoftargetsare

largeroranumberdensityishigher,Zebecomeslargervalue.P,andZeareoftenexprcsscdindc(li-

belunitsdBmanddBZwheredBm =10lo910P,(mW)anddBZI10lo

gmZ(mm,6/m･3),resI)eCtively.Inor(iertocalculatethereflectionbytheseasurface,weuseEq.6.3asther

adareqtlat･ion(sccAp

pendix)･ pr(-,W)- C憲pt(m

w) (6･3)wherecToisthecrosssectionperunitareaandC2isacalibrationconstant,arldgivenby

E

(I.6.4. C2- 10 18cl22ln2̂ 4c

DopplervelocityofcloudparticlesarederivedbyEq･6･6[3].

V=i

C60/47r6Tf (air-borneobservation)

-C60/47T6Tf (ground-basedobservation)(6.6)

wherecisthelightspeed,6TisthepulsereputationtimeandsettobellO〃S,Iis

thefrequencyand60isDopplerphaseshiftrecordedbyradar.Wedefinetheupward

directiontobe"plus".

6.3 Results

Figs.6.2(a)and(b)aretheresultsoftheair-borneobservationsofcloudsandsea

surfacesabovetheJapanseaon28February2000.Fig.6･2(a)isthereceivedpower

thatSPIDERobservecloudsinnadirdirection.Theplaneflewfrom lefttorightwith

aconstantheightof6kmanditsvelocityisabout200m/S･Thestrongestechoisabout

-44dBmandcorrespondstotheseasurface.Thesignalsunder0m areinducedbythe

timedelayduetothemultiplescatteringbetweentheseasurfaceandclouds.Fig.6.2

(b)isthesameasFig.6.2(a)butforZe.Strongechoofabout0dBZcorrespondsto

snowfall.

Figl6.3ShowsthatthecrosssectionperunitareaofseasurfaceinFig.6.2(a).Itis

almostconstantanditisabout-0.5dR Therefore,ourexperimentsshowthatseasurface

canbeusedasatargettocalibratethespace-bornecloudradar.

Fig.6･4(a)isthesameasFig.6･2(a)buttheobservationofDopplervelocityV

calculatedbyEq.6･6･Fig.6.4(a)showsthatthevelocityoftheseasurfaceisnot

0m/S.Thisisbecausetheobservationdirectionandseasurfacearenotperpendicular

undertheconditionofconstantflightaltitude.Forexample,whenthevelocityofthe

air-planeis200m/sandtheanglebetweenflightandobservationdirectionis89°egin

凸ightdirection,pseudovelocityofscatterisinducedand3.5m/S.Thisiscomparableto

thatofcloudparticles.Thusthecorrectiontoeliminatepseudovelocityisnecessaryto

derivetheterminalvelocityofcloudparticlesinthecaseofair-borneexperiments.Fig.

6.4(b)showstheDopplervelocitysubtractedfromthatofseasurface.Thevelocityof

snowparticlesisabout-4m/S,andthatofcloudparticlesisabout-1m/S.

6.4 Summary

Weanalyzetheresultsofair-borneobservationsbySPIDER.Weshowthatthecross

sectionperunitareaofseasurfaceisalmostconstantandtobe-0.5dB.Thusweshow

67

[u[]apnt!)tV

O

0

O

0

O

0

/LU

4

0002

0102030405060 70

Horizontaldistance[km]

Figure6.3:Resultofthereflectionbyseasurfacefor95GHz.Observedareaisthe

sameasthatofFig.6.2.Leftsideofverticalaxisdenotescrosssectionperunitareaof

theseasurface(Solidcurve).Horizontalaxisdenoteshorizontaldistance.Rightsideof

verticalaxisdenotesaltitudeoftheairplane(dash edcurve)and isa

Bibliography

[1]H.Horie,T.Iguchi,H.Hanado,H.Kuroiwa,H.Okamoto,andH･Kumagai,

"Developmentofa95-GHzAirborneCloudProfilingRadar(SPIDER)",IEICE

Trans.Commun.,2000,inpress.

[2]MasukoH･,K･Okamoto,M.Shimada,andS･Niwa,"Measurem entofMicrowave

BackscatteringSignaturesoftheOceanSurfaceUsingX BandandKaBand

AirborneScatterometers,"∫.Geophys.Res.,15,13065-13083(1986).

[3]DoviakR･J･,andD.S･Zrnuc,DOPPLERRADARANDWEATHER

OBSERtlATIONS,(AcademicPress,Inc.,1993)･

[4]Stephanes,G･L･,RemoteSensing0ftheLowerAtmosphere,(NewYork,Oxford･,

1994).

[5]Ulaby,F.T.,R,K･Moore,andA.K.Fung,MICROWAVEREMOTESENSING

ACTIVEANDPASSIVE,volumeIll,From TheorytoApplications,(Artechhouse,

Inc･,1986).

[6]S.G.Warren,"Opticalconstantsoficefromtheultraviolettothemicrowave,"

Appl.Opt.23,1206-1225(1984).

72

Chapter7

ListofPublications

●*S.IwasakiandT.Mukai,"ANALYSISOFTHELIGHTSCATTERINGBY

ROUGHSURFACES",inpreprintsofConferenceonLightScatteringby

NonsphericalParticles:Theory,Measurements,andApplications,GISS,New

York,pp.229-232,1998.

●S.IwasakiandT.Mukai,SimulationforLightScatteringbyRoughSurfaceBased

onKirchhoff'sDiffractionTheory.,Adv,Space.Res.,23,1213-1217,1999.

.岩崎杉紀､岡本 創,水雲の LIDAR観測 :LIDAR方程式の再考,第 7回リモートセ

ンシングフォーラム,カタログ番号 ooPGOOO3,23-26,2000.

.S.Iwasaki,andH.Okamoto,Analysisoflidarreturnsfromrectanglesand

hexagonalicecrystals.,InSmithandTimofeyev(Eds.)IRS2000:Current

ProblemsinAtmosphericRadiation,DeepakPublishing,2000.,inpress.

●*H.Okamoto,S.Iwasaki,M.Yasui,H,Horie,H.Kuroiwa,andH.Kumagai,

"95-GHzcloudradarandlidarsystems:preliminaryresultsofcloud

micro-physics",ⅠnWilheit,Masuko,andWakabayashi(Eds)SPIE2000:Remote

SensingoftheAtmosphere,Environment,andSpace.,2000.,inpress.

.*H.Okamoto,M.Yasui,H.Horie,H.Kuroiwa,H.Kumagai,andS.Iwasaki,

"OBSERVATIONOFCLOUDSBY95GHzRADARANDLIDAR

SYSTEMS･.RADIUSVERSUSFALLVELOCITY",SmithandTimofeyev(Eds.)

IRS2000:CurrentProblemsinAtmosphericRadiation,DeepakPublishing,2000.,

inpress.

.S.Iwasaki,andH.Okamoto,Analysisoflidarbackscatteringenhancementfor

pristinehexagonalicecrystals･,InSingh,Itabe,Sugimoto(Eds)SPIE2000:

RemoteSensingoftheAtmosphere,Environment,andSpace.,2000.,inpress.

*reprintsarenotincludedhere.

73

SIMUIJATION FOR LIGHT SCATTERING BY ROUGH SURFACEBASEDONKIRCHHOFfl,SDIFFRACTIONTHEORY

S.IwasakiandT.Mukai

TheGraduilteSchoolofScL'.andTL.(･h.,̂'obcUniy.,NzJ(ね657-8501̂ 'obc,JLJPan

ABSTRACT

Wcexaminethelightscatteringbyrough surfaccbasedontheKirchhofftheoryofdiffractioncquatioll･Theelcctricfieldonthearbitrarysmoothsurfacesurroundingtherough surfaccofinterestisdcrivcdbytherayopticssimulationfortheseattcringbysuchrough surface.Afterth(lt,theintensityofthescatteredlightfarfromthesmoothsurfaceisdcduccdfromanusualanalyticalway,Itisfoundfromacomparisonofourresultswiththoseobtainedbyothermethods.suchasT-matrixmethod.thatourmethodisapplicable.atleast,forspheroids.Wcalsotestourmethodtoapplytothescattcl･irlgbyatwodimensionalcomT-1laPCdsurface,whichisaspecialcaseoftherough analogucforthercgolithlayeronthesurfaceoftheairlCSSSlllallbodvinthesolarsystem.

INTRODUCTION

Itiswellknownthatthefollowlngmethodsarcavailabletoolstocalculatethelightscatteringbyirregularlyshapeddustparticles,i･e･thediscrete-dipolcapproximation(DDA)(Draine,1988),thcfinite-diffCrerICetimedomainmethod(FDTD)(YangandLiou,1996),andthegcomctricalopticsmethod(Jackson,1975;Mackc,1993)･However,thesemethodshaveanapplicablelimitatioILforthesizeparameterE,whereIisdeGncdas°-2打a/A(入isawavelengthandaisaparticlc'sradius).Whenwetreatthes(･attcrillgbyanirregularlyshapedparticle.Weusuallychooseaasitsmeanradius.InthecaseofDDA.IshouldbclessthanaboutlO･ForFDTD,20≦x≦40.InI≧50,thegeometricalopticsisavailable.Although DDAandFDTDhavegreataccuracy,itishardtopredictthescatteringpropertiesoftheparticleswithI≧50.Thercgolithlayerexistingonthesurfaceofthcairlcssbodiesinthesolarsysttlm containssuchlargerparticleswith2>_50.Therefore.intheanalysisofthescattcrcdlightfromsucharegolithlayerobtainedbyinsiiumcasuremcnts,wehavetodevelopanotherconvcnicntmethod.IntcgralequationmethodbasedontheKirchhofftheoryofdiffractionequation(Jackson,1975;Muinoncn1989;YangandLiou,1996)isapowerfulschcmctocalculatetllClightscatteringbysuchlargeraggregates,anditslimitofapplicabilitydcpcndsonthewaytosolvethescatteringcquation･Although theKirchhofftheoryofdiffractionisusedillforthescatteringbyaslnglcparticlcLitisalsoapplicableforthescatteringbythegrating.Inthispaper,wcapplythismethodforarough surfaccundertheassumptiollthattherough surfaccisapartofthesul･faccofahugeSlngleparticle.

SCATTERINGMODEL

IftheparticlehasIlotrueChargesa-1d'･urrclltS!theequationoftheKirchhofftheoryofdiffraL･tiollglV｡Sthesolutionofthelightsc･attcrillgPrObl｡InattheobservationpointwhenthedistallぐC I･bLttWeenth(Iparti'･leandtheobscrvcrisfarenough.Namely,

EJr)-芸 芸 再 dS,a-7'k･r′(Ix(A,×cBe)一点′×ES), '1'

whcrci=√巧,k=2n/A.TileilltCgrationshouldbcdoIICOveran arbitrarysurface,whiL･llCOIltai-1SthLLparticleofilltCrCStitself.iisaullitpOSitiollVeCtOr之IttileiI血lityobsLLrVCt･,r'alltl血'之u･e,r(t叩CCtively,il

S Z

｢ 二⊃ ^

x｣＼JC ＼

J ＼ノ Uroughs

urfaceFigurぐ1･ TllegCOllletryOfcoordillatealldtlleSalllPlelavtT･ St･之ItteI･irlgplalleWitllroughlleSSisdeもnedollZ-ⅩplallCLalldtilear-bitraryClosedsurfaceS-CdeIIOtCSthe(･losedsurfaceforintegrationofEq.(1). 0.

Z1

C Xrough

surtae aFigure2. TILegCOIllCtryOfCOOrdillatCandtileSalllplelayer

. S｡atteringplalleWitllcolllb-sllaPedroughnessisdefiTledollZ-Xplalle,TlleShapeofc

olnlJisdcGncdbytllreCscales

showllaboveasa.b,C.positiollandaullitIIOrlll之IIvectorsotlthesurfaceoftheintegralcontour.Subindiccssand- ofEalldBindicatetheclcctro-1nagIICticfieldolltheilltCgralsurfaceandtheobscrvcdpoint,respectiv

ely(C.g.Jackson,1975).TosolveEq･1,wcllluStknoWtheclcLCtrO-lllagneticficld.EsalldB"ontheintegralsurfacc･However,itishardtodecidetllぐ111ぐXaCtly,SinceMaxwellequationshavenocxaL.tSOlutiollinthecaseofanirr

egularlyshapedparticle.Kok(1993)showedtllCSCatteredlightusillgFourierscricscXpaIISionfortheeleCtricficldin thccaseofatwodiIIlenSionallnCtallicsurface.However.beL･auSCtheyusedapcrfeCtlycollducting

surfacc･itset.Illshardtoimprovethissolutionforthescatteringbythearbitrary.material･Maradudinetal･(1990)calL'ulatcdthelightscatteringbyatwodimensionalrough sul･faccbyuslngHankclfunctionofthefirstkindforintegralequationmethod.HoweveritisalsodifEculttoapplythismethodforthesurfaced

efinedbythemany-valuedfunctionasthesuI･faccshowninFig.I.0ntheotherhand.toapplyforthescatteringbythearbitrarytwodimensionalshapedsurface,i,'lcndoza-SuarezandMclldez(1996)dcvclopedtheirtheory.TheycalrulatcdthescatteringbythetriadicI(Ochcurveandtheyhaveshownthattheirmethodisval

idcvellifawavelcrlgthisshorterthantheRayleigh smoothncsscriterion.ItisknowTl.however,thatitisvalidonlyforthecaseofatwodimensionalsurfaceanditalsoseeIllShardtoextendittocalculatethe

scatteringpropcrtiesforthethrccdimensionalproblems･YangalldLiou(1996)Calculatedthelightsc.attcl.ingpropcrticsofanirregularlyshapedparticlebasedontheIくirt.hhofftheoryofdiffractioncquatioIluSIIlgthegeornctricalopticsapproximation･Itispossibleforthegeometricalopticsapproximationtoappl

yforthearbitrarythreedimcnsiollalease,Thus,wcuseth

ismethodtosolveEq.1.First,wcdivideallinL.identlightintothinlightbundlesthathavethesamephaseineachbundleray.Tobcsamephaseontheareaclllightcnbythebulldlc･wcsetawidthofthediffusedlig

htbundlelessthanaboutA/10evcrywhcrc(YallgandLiou,1996).WcassumethateachlightburldlerayisdcscribcdbyFrcsne

lformula(Jackson1975)･SincethelightbulldleisllOtaparallellightafteriIICidcncc,wcassumethattheclectriC鮎ld

charlgCSitsmagllitu

dcas EP'1-EPcxp(葦 l) (2)whCrCEralld(Esp arctheeleL･tl.illfieldaTldthecrosssectionofthelightbundleattheIJ-threncctionalldtransmissiorlPOillt,alldγrんisanopticalcoIIStallt,iisthelttllgthbctwceIIP+1-thandp-thrcflcctiorLalldtransmi ssiorlpOirltS･Thisrel之ItioIIL･OmLISfromtheulCrgy(∝IE(

r')l2)conservationlaw,IntheIくirL･hllO#'theoryofditfr之lL･tioll,WernuStChoostttheilltCgratCdcontour之ISthe.surfacethat｡ov｡rsupallthepartiL,kOfilltel･e丸 ThisirllplicsthatwccanolJt之1irlthesamercsultofEq.1afte

l･theiIltegrationovttranarlJitr之Iryt･OntOul･(･ollt之IilledtileIJartiL･lcasthatov(.rth"･cal別lrfilCCOfthepartiL･le･WhenWetakttthecolltOurtlぐartllCk･,attぐr(･dsilIllple,thttrt.iHlOIlCedtom之lkeIIluChlightlJulldleir上SiI

IlulatiotlStOCarlltilenumbertlぐnSityofthcl･aytoillぐ1･e之lSethestatistit･alsiglliもぐallCLt.ⅠIlthecaseofrough surface,wctaketht:Ihtt.gralとlreaOfthf,IsurfautS-CitsSllOWnillFig.1.Tll之Itis.weconsidL.ra｡orltOllrSpl之ll

lL.,WhiL･hisaSIrlOOthplallCalJovetilt-urfilH･1之Iyぐl･.hlilddition,aL･ontourC,whiL･hmakesa(･losetlsurfi

lf+08

1くW>0

書.-

喜.｡00表 .-

10

zo 〇̀ °ooT【d増】120

…

.

〇

心

0

0

音竜一で蔓

宣

誓慧首長

20̀○○Oorld昭】.20

水雲の LIDAR観測 :LIDAR方程式の再考

神戸大学大学院 自然科学研究科 ○岩崎 杉紀通信総合研究所 岡本 創

LidarObservationfわrtheRemoteSensingoftheIceClouds:ReconsiderationoftheIJidarEquation

OsuginoriIWASAKI,GraduateSchoolofScienceandTechnology,KobeUniversityHajimeOKAMOTO,CommunicationsResearchLaboratory

Abstract

本研究では､水雲粒子のような非球形粒子に適応できる一般的な lidar方程式を導出した｡この結果､球形粒子に村して

通常用いられる1idar方程式が距離の二乗に反比例することのに対し､非球形粒子に対しては 1idar方程式の距#依存性が粒子形状やオリエンテーションにより変化することが示された｡すなわち､水平ランダムオリエンテーションをしている針状

六角柱では距離の一乗に反比例し､板状六角柱では距掛 こ依存しないことが示された.また､三次元ランダムオリエンテー

ションをしている針状と板状六角柱の場合は､共に距書の一乗に反比例することが示された｡

1 導入

lidar観測では､地球の放射収支の大きな不確定性要因である雲の雲底や雲頂､雲粒子の粒径や形状といった情報を得られ

ることが期待されているo近年､lidarによる雲の観測は地上のみならずスペースシャトルを用いた観測も行われているLl)0

この削 り結果の定量的な解釈のために､Iida,方程式 [2日3JTt4】を用いた解析法 [511(61が用いられているolidar観測の結果

の解釈には､lidar方程式中に含まれる後方散乱断面積を理論的に求めなければならないが､従来からの ray-tracing法を用い

た研究では､後方散乱断面積の計算は困難であることが示されている[7)･I87｡本研究では､第2章で実際に氷粒子の後方散乱

断面棟が発散することを数値的に示した｡第3章では､そのような場合にも適用できる一般的な lidar方程式を ray-tracing法を用いて後方散乱における散乱断面積の展開係数を導いた後､それを利用して lidar方程式の一般形を導出した｡第4章で

は水平ランダムオリエンテーションやランダムオリエンテーションをしている六角柱の氷粒子の 1idar方程式を導いた｡

2 従来のlidar方程式とその問題

1idar方程式は､

p,(Z)-ECZ-2fcbk,m.i+Cbk.ae,o)T3LOITa2m (1)

で与えられる(2)･E3l･L4】oここで､E,Cは lidarの機器の定数､Cbた,mo,,Cbh,aeroは大気分子とエアロゾルや雲粒子の後方散乱断面積､Zは高度､T,,10L,Tae,Oは大気分子とエアロゾルや雲粒子の透過係数である.したがって､式 1を取 り扱うために

は､後方散乱断面積を知らねばならない｡しかし､以下で見るよう仁Cは,ae,Oは発散してしまい､lidar方程式を使うことができない｡

まず､eC… は散乱角とその角度刻の関数であるべきなので､6CaCa(e)を68で展開すると､

6C- (e)-C-cdffo(0)6ccJ fl(0)de.妄f2(e)de2+･･･) (2)

6cc.はクロネッカーのデルタで 0,は鏡面反射する時の散乱角ある｡第-項は､平らな鏡面に垂直入射したときに効 く項である｡細に依らないのは､鏡面散乱の場合は入射光が平行であれば反射光は角度分散を起こさないからである｡第二項は､第4.2節で示すように無限に長い円柱のように散乱する場合【10】に効く項である｡第三項はMie散乱【10Iのように球面波で散乱する場合に効く項である｡また.立体角は

6n-LIBeL2JsinCd- 〈f600,2 ‡S=崇;去8dOe冨;9' (3,

で定義されている｡ここで､Cbk,ae,Oが 4打dC.ca/6口と定義されているので､式 2と式 3によりJ.か /1が値を持った場合Cbk,ac,.は発散するoMie散乱の場合は/OとJlは0である.

図 1は､針状六角柱の軸を水平面に平行にさせながらランダムオリエンテーションをさせた時の 位相関数 Pll(0)と散乱

角の関係である｡Pll(e)は､旦お /cBCaで定義される散乱確率を現す関数である｡図より角度刻が小さくなればなるほどPll(180)が大きくなる｡これより60を無限小にするとpll(0)が発散することが解る.Cbk.脚 ｡は､4汀Pll(180)C.caとも書けるのでCbk.am も発散することが解る｡したがって､この場合は従来のIidar方程式を用いることができない｡このような発散は球形粒子では起こらない｡したがって､この発散は散乱体が非球形であるために起こる｡氷事は裏粒子が不規則形状

をしているので､Iidar枚洲の結果を解析するためには式 1を見直さなければならない｡

(o

)Lid

Q

lAngularBin-1deg - ;AnglularBin=1:/4deg -I :AngUlarBin=川 6de91} Il

IIll f: ロ:

′′lldn I-.-.I....-llIl一t178 178.5 179 1

79.5 180Scatterhg

Angl○【deg】Figure1:散乱角Oとpll(e)｡角度刻60が小さくなればなるほどpll(180)が大きくなる｡したがって､60を無限小にするとP

ll(e)が発放すること～が解る｡枚方散乱断面棟qbkは 47rPll(180)CaCaなので､q

bkも同様に発散する｡3

一般的なlidar方程式まず最初に､単純化した lidarシステムとIidar観測の幾何と記号を図 2のように定義する｡

また､雲粒子は表面がレーザー光の波長に比べ十分滑らかで､針状六角柱か板状六角柱が水平ランダムオリエンテーションをして

いると仮定し8.が 180とした｡また､レーザー入射光は十分平行になっているため望遠鏡の視野角に常に入っているもの

とする｡怖単のため､散乱体は入射レーザー光の幅に比べ十分高い高度にあるので雲中の体積 Vから望遠鏡を見る立体

角6nは一定とした｡inciden

tlaserbeam Z'

散乱体の存在する高度8Z 高度分解能V 高度分解能と入射レーザー光の断面がなす体棟10 短時間単位面積当たりのレーザ

ー光のエネルギーpr 書中の体積Vからの散乱を望遠鉄が受信する電力dn(r)/dr散乱体のサイズ分布

G(r

) 散乱体の幾何断面積so 望遠鏡の

半径a 入射レーザー光の半径Tmol 分子の透過率Tcloud 雲粒子の透過率telescopeFigure2:lidarシステムとIidar検潮の幾何と記号の定義

｡このとき､望遠鏡の受信電力 P,は

､p, -Io/∂∩(〟-180)∩(0-180-8C,/vdvL edr響 些 碧 塑 dOTLoLTc2L

oud･ (4)と書ける｡式 4に式 2を代入し整理すると,pr - IoV/.ledr等C-a(r,･fo(180,･fl(180,署.響 (箸)2+-･,TLo･Tc

2

となるCこれは従来の lidar方程式に一致する0

4.2 水平ランダムオリキンテーションをした針状六角柱の場合

図3は､長軸を水平面に平行にしながらランダムオリエンテーションをしている針状六角柱の場合の80と誓㌻/C.C.の

関係を示したものであるOこの計算はray-tracing法を用いて計算をした｡また､後方散乱では回折が無いので 19)I(101､回折を含めない計井をした｡それぞれの曲線は､10個の異なる種を元にして乱数を振って計井した結果である｡また､ここでの

光学定牧の美都は 1.31､虚部は2･54x10-9で波長0.53ILmL8).六角柱の長軸の長さを86FLm､六角形に外接する円の半径を

14lLm(軸比 3)とした｡この図と式 2よりJl(180)が支配的な散乱であることが解る｡このときの et=誓㌢ は 2･5×10~2

0 0.2 0.4

0.6 0.8 1AngubarBin80

ldeg】3:水平ランダムオリエンテーションれ た針状六角柱の場合

の角度刻み∂βと誓計 の関係｡乱数は10個の異なる種を元にし計井した｡このより/1(18

0)の項が支配的な散乱であることが解る｡Siigu;:となった｡可視で氷を見た場合､吸収がほとんどな

いため C…は2G(r)にほほ等しく､Jl(180)は吸収と回折がないため氷粒子のサイズに依らない関数と考えら

れる｡したがって､Iidar方程式はpr 空 2IoVf"180,普/izedr警 G(亜 o･TfL-d･

(7,となり､雲粒子と望遠鏡の間の距離 Zの一乗に反比例するOこのことは､次のような類推から考えると解りや

すい｡今､水平ランダムオリエンテーションをしている金属製の六角柱の散乱を考える｡このとき､光散乱は六角柱の側

面の長方形で一回だけ散乱する｡水平ランダムオリエンテーションは六角柱を長軸の周 りに無限に回転させ､その各々の散乱

を計算し､散乱角ごとに散乱エネルギーの総和を求める｡すなわち､全ての散乱事象をまとめて考えると､いろいろな方向

に側面を向けた無数の六角柱の散乱角ごとの散乱エネルギーの捻和を計算していることと同じになる｡

ここで､円柱は側面の数が無限にある正多角柱であるため､これら無限の回転をしている六角柱の散乱は円柱一つの散乱と同じ性質を示すと考えられる｡以上のことは､ここでの理論計算では六角柱が

氷ではなく金属であり､有限回転数ではなく無限に回転させるという違いがあるが､その類推から針状六角柱の光散乱が円柱

の光散乱と同じ距離依存性を示すことが分かる｡4.3 水平ランダ

ムオリエンテーションをした板状六角柱の場合六角形を水平面に平行にしながらランダムオリエンテーションをしている板状

六角柱の光散乱は､ray-tracing法を使わなくとも簸何光学近似で解ける｡これは､後方散乱には回折がないため､無限の幅､有限の

厚さを持った氷の板に光が垂直入射した場合の散乱と同等のものになるからである｡この板の反射係数は

Rp- e･9eOtbk-些 芸 警 - 12.Rd買 ,taeie/.'::,nee:e,

(8)と書ける｡ここで､RpLate.I,C.neLは垂直入射したときの Fresnelの反射係数である.これより､この場合の散乱は式 2のJi,(i≠0)が 0の

o･｡2

…

…

.0-4.0120･｡.朋朋

0

0

00000のt月)tjUめー

一 一l l II-■

▲■-I

午inCidenltight

0.2 0.4 0.6 0.8 1AngularBin80ldeg] f l l L

l l ■

l l l l

I l l'ncidentIⅠihl

0.2 0.4 0.6 0.8 1AngulaTBinSeldeg]Figure4:針状六角柱(a)と板状六角柱(b)の三次元ランダムオ･)エンテ-ション%Lた針状六角柱の場合の角度刻み60と誓㌢ の関係｡針状六角柱は第 4.2節と同じものを使用した｡板状六角柱はこの針状六角柱と同体棟で軸比が 1/3のものを使用した｡この図よりどちら

の鴇合でもfl(180)の項が支配的な散乱であることが解る｡4.4 三次元ランダムオリエンテーションの場合

この節では針状と板状六角柱の三次元ランダムオリエンテーションの計井を行った｡図 4は､三次元ランダムオリエン完.Ii

-i/言>flflt.1)=SI{笠孟宗慧諾 至宝禁 nt慧監 禁 慧忘蛋zt義 認 賢三戸,LL:書写三,誓 二三票 差ご詣 孟宗歪柱の場合と同じであるoつまりこの場合の lidar方

程式は式 7となるoこのときの 己と誓㌢ は､針状の場合が 1･7×10~2,板状の場合が 1.6×10~2である｡本章より､水雲の lidar観測を解析す

るための 1idar方程式は､今までのlidar方程式に変更を加えなければならないことが解る｡5 まとめ本研究では､水雲粒子のような非球形粒子に適応できる一般的な lidar方程式を導出した｡この結果､lidar方程式の拒

蕉依存性が粒子形状やオリエンテーションにより変化することが示されたOすなわち､従来のlidar方程式では距従の二乗に

反比例すると仮定しているが､水平ランダムオリエンテーションをしている針状六角柱では距鮭の一乗に反比例し､板状六

角柱のでは距軌 こ依存しないことが示された｡また､三次元ランダムオリエンテーションをしている針状と板状六角柱の場

合は､それぞれ距牡の一乗に反比例することが解った｡この方程式は､六角柱

の氷粒子の光散乱に限ったことではない｡後方散乱断面棟が発散するものであればどんな形状の粒子に対しても成 り立つC通信

稔合研究所では95GHzのレーダと1idarの同時観測が計画されている｡このときここで示したIidar方程式を実際の解析に用いる予定である.また､距#依存性が違うため､bi-staticlidarを用いればこの方程

式の検証ができると考えられる.この観測結果および検証は今後御報告する予定である｡ReferenceslllMillerSID･,GILISt

ephens,andA･C･Beljaars･,Geophys.Res.Le臥,26,1417,1999.[2】Fernald･F･G･,B･M.Herman,andJ･A･RBagan･,J･Appl.Meteor.,ll,

482,1972.[3]Fernald.F.G.,Appl･Opt･,23,652,1984.[4】Stephanes･GIL･,RemoteSensing0/theLowerAtmosphere,NewYork,

Oxford.,1994.[5]KlettJ･D･,Appl･Opt･.20,211,1981.[6]SassenK･,H･Zhao,andG･CIDodd･,AppL･Opt･,31,2914,1992

.[7】Takano･YandK･N･Liou･,J･Atmos･Sci･,46,3,1989･[8】Macke･A

･,J･Mueller,andE.RがChke.,J.Atmos･Sci.,53,2813,1996.(9】HapkeB･,Theoryo/ReJ7cctan

ceandEmiuanceSpectroscopy,CambridgeUniv.Press.1993.(101Bohren･C.F.andD.a.Huffman.,AbsorptionandScatte

4 Analysisoflidarreturnsfrom rectanglesandhexagonalicecrystals

4.1 Introduction...‥ .

4.2 Scatteringmodel.

4.2.1 Scatteringbyarectangularparticlewithafixedorientation ...

4.2.2 Scatteringbyarectanglerandomlyorientedinhorizontalplane ‥

4,2.3 Distancedependenceofthereceivedpowerbyhexagonalcrystals‥

4.3 Summary - - - - .- - .- -

5 Cloudobservationbylidar,95GH2;Cloudpronlingradarand13.8GH2;

precipitationradar

5.1 Introduction‥ ‥ ‥ ‥ ‥ .‥ ..‥ ‥ ‥ .‥ ‥ ...

5.2 Descriptionofourlidar,95GHzcloudradarand13.8GHzprecipitation

radarsystem.‥

5.3 Cirruscloudsobservedbylidarand95GHzcloudradar‥ ..

5.4 Cloudsandprecipitationobservedby95GHzand13.8GHzradars .

5.5 Summary - .

6 Air-borneobservationby95GHzcloudradar

6.1 Introduction.

6･2 Theoryforcloudsobservedby95GHzcloudradaronboardaircraft.

6.3 Results.‥ ‥ ‥ ‥ ‥ ‥ .‥ ..

6.4 Summary .

7 ListofPublications

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73

AnalysISOflidarbackscatteringenhancementforpristine●

hexagonalicecrystals

suginoriIwasakiaandHajimeOkamotob

aTheGraduateSchoolofScienceandTechnology,KobeUniversity.

1-1Rokko-dai,Nada,Kobe657-8501,Japan.

bcommunicationsResearchLaboratory･,893-1Hirai.Ka5hima,Ibaraki314-0012,Japan.

ABSTRACT

WeanalyzelidarbackscatteringenhancementforpristinehexagonalicecrystalsbyusingFhunhoferdiffractionbasedonKirchhoff'sdiffractiontheory(KD).OurnumericalcomputationsshowthatreceivedpowerP,(Z)atthealtitudeZinlidarequationisproportionaltoZ-cL,whereαisafunctionofZ,sizeandshapeofparticles.P,(Z)isproportionaltoZ1115forhexagonalplateandcolumnrandomlyorientedinhorizontalplaneatZ-200mwhereitsaspectratiosare1/3and3andmoderadiusesarel00〃m･Ourcalculationssuggesthexagonalicecrystalsthathavemoderadiusesof100ILmand30pmwithperfectlyorientedinhorizontalplanehaveanomalousbackscatteringenhancementcomparedwithasphereate､･enhighaltitude･ThismightexplainthephenomenareportedbyPlattet.al.(1978).1･2

Keywords:lidar,backscatteringenhancement,diffraction

l.INTRODUCTION

Lidarisoneofthemosteffectivetoolstoinvestigatethecloudprofilessuchasverticalstructure,shapesandsizesoficecrystals,whicharetheunknownfactorstoestimatetheradiativepropertiesofcloudswithhighaccuracy･Therefore,forlasttwentyyears,therehavebeenintensiveground-basedmeasurementsbyuseoflidarandsomeprogresseshavebeenmadeintheanalysis.Fernaldet.aL.(1972)3developedananalyticalmethodfortheinversionprobleminlidarobservations.Klett(1981)4modifiedtheirmethodtoavoidinstabilitiesintheinversionproblem.Besides,therearesomeobservationalevidencewhichshowsnon-sphericityplaysakeyrole.Plattet.al.(1978)1･2showedthatsomeunusuallidarreturnsfromamiddle-levelcloudwereobserved.Theyalsoshowedicecloudsinthe2:enithgaveaveryhigh backscatteringbutaverysmalldepolarization,whichiscalledzenith-enhancedbackscatter(ZEB)･Mishchenkoet･al･(1997)considereddisksandspheroidswithsizeparameterupto50(e.9.r-5JlmatA-0.63lJm)asicecrystalsandcalculatedlidarbackscatteringfromtheseparticlesbyusingT-matrixmethod.Theyshowed"ZEBpeakcanbeproducedonlybyhorizontallyorienteddisksbutnotbyhorizontallyorientedspheroidsorparticlesinrandomorientation".DespitefromtheseeHorts,thereisatheoreticaldifBcultyininterpretationoflidarsignalS･Thatis,inlidarsignals,itisnotpossibletoderiveanalyticalsolutionsfornon-spheriCalparticleswhenthesizeofparticlesismuchlargerthanthewavelength.Ray-tracingmethodiswidelyusedinvisibleanalysis,however,ithasalsoafundamentaldifRcultyinbackscattering.Theapplicabilityofthismethodistestedanditturnsoutthatgeometricaloptics(GO)canbeapplicablewhenthealtitudeisveryclosetotheground(e.9.100m).6 ourfinalgoalofthisstudyistoexplainthemechanismofunusuallidarreturnsshowedbyPlattef.αJ.(1978).1,2

Atfirst,westartwithFhunhoferdiffractionbasedonKirchhoff'sdiffractiontheory(KD).8,9 Insection2,thetheoreticalproducesareglVen.Thenweanalyzethebackscatteringpatternbyarectangulartarget.Insection3,wecalculatethescatteringbyhexagonalcolumnsandplatesrandomlyorientedinhorizontalplaneanddiscussthedifferencesofbackscatteringbetweenspheresandhexagonalcrystals.

2.SCATTERING BY RECTANGUI.AR PARTICLES

Inthissection,wecalculatethebackscatteringpropertiesbytherectangularparticleswithfixedorientationandrandomlyorientedinhorizontalplane(hereafter2D-rectangle).

S.Iwasaki.:E-mai):iwasaki◎komadorLp)anet･sci･kobe-u.ac.jp

2.1.DeRnitionofsymbolsanddiffractionpattern

ThegeometryofthelidarobservatiollisdescribedillFig.1.WeassulnethesllapeOfareceiverisrectangle･

F

gxe >

1｡gl｡Ⅰ汀a｡ia｡｡｡ IⅠ｡Isl

N

.

(慧

JX

Z

u)u!S

8

エリ

4

2

0

0

0

0

-1 -0.50

X【m】 0.5 1Figure2･(a)Thehorizontaldistributionsofbackscatteringpatternbytherectangulartargetnormali2;edatmaxim umwhenQ'is0,入isO･532FLm,landaare200pmandZis100m.(b)Sliceofthebackscatteringp

roBleof(a)aty-0･2.2

.2.CaseforhighcloudWhenaltitudeiSlargerthan2kmandotherconditionssuchassizesofrectangleandreceiverarethesameasthoseinpreviousSubsection.Eq･2becomes

Z-depel一dellCeil一Eq.4isZ-'2,whicllisthesameastlleusuallidarequation(Eq.5).

pr(Z)-C芸 e-2'

whereCistheconstantoft1-elidarinstrument.3,12 gbkisthebackscatteringcoe瓜cient･

(5)

Z-dependenceofthiscaseisthesameasthatofsphere,however,sizedependenceG2isdifferentfromthatofsphere(C l).

2.2.3.Caseforintermediatestate

Thissubsectionisthecasewhenaltitudeis80m<Z<2km andrest.isthesameasinsubsection2.2.1.Int,his

case,itiseasilyexpectedthatZ-dependenceofP,(Z)hasthevaluebetween-2and0,wherethedependencemightbechangeda5thealtitudechanges.

∫

･.0 -1

.5 -1.0 -0.5 0.ExponentofReceivedPower '＼ ＼

sphir rec

tang.Ie＼＼

､＼ ＼ヽ ､＼

＼＼leIs le

15 le-12 1elT.ReceivedPower【W]Figure3･(a)Z-dependenceoftheexponentofthereceivedpower,dloの oP,(Z)/dlo910Z･Weassumethatshapeofarectangleis200FLmX200pmandRtisO･2m.(b)Z-dependenceofthereceivedpo

werscatteredbytherectangleandasphere･Bothofthemhavesamegeometricalcrosssection.Weneglectthein

ternal1yreflectionofthesphere･WeestimatetherelationbetweenZ-dependenceofP,(Z)andZforagivensizeofparticleandreceiverarethesameasthoseinsubsection2･2.1.Fig･3(a)showsZ-dependenceoftheexponentofthe

receivedpower,dlo910P,(Z)/dlog10Z.WhenZisabout200m,receivedpowerbecomesproportionaltoZll･5･whenaltitudeislessthan50m,oscillationoccurs,becauseofthesingleparticlescattering.Fig･3(b)showsZ-dependenc

eofthereceivedpowerscatteredbytherectangleandthatbyaspherecalculatedbyEql613whereweneglecttheinternallyrenectionofthesphere･Therectangleandthespherehavethesamegeometricalcrosssectionsforthefaircomparison.

psp(Z) - 慧 GIo; e-2, (6)whereStisthegeometricalcrosssectionofthereceiver.Atthealtitudeof1000m,receivedpowerproducesabout2×106timeslargersignalscompare

dwiththatofsphericalscattering･2･3.Scatteringbytherectangularparticles

randomlyorientedinhorizontal planeForarectangulartargetwithorientationalaveragingswheremajoraxisoftherectangleisfixedalOngYaxisandistakentobeparalleltothehorizontalplaneandminoraxisistakentobeal

ongZaxisandrotatedaroundYaxisrandomly(2D-rectangle),scatteredirradiancecanbewrittenasEq.7byu

singEq.1.･S(I- )

Fig,4Showsthehorizontaldistributio1-0fbackscatteringfromtlletarget.Theshapeoftllebackscattcrillgpatterncanbeunderstoodfromthesuperpositionofthatbytherectangularwithafixedorientatio11･

loglOhadiance

xB

IⅠ∴ sI

Figure4.ThesameasFig.2(a)butfortherectangulartargetwithorientationalaveragingwhere

majoraxisoftherectangleisparalleltotheYaxisandminoraxisisrotatedrandomly.Receivedpowerb

ecomes pr(Z,-C,/RRL.dx/_RRt▲

dyIs(x･y,Z,2.3.1.CaseforlowcloudWhenthealtitudeofcloudislessthan80m,andthesizeofrectangleis200F

LmX100FLm,Eq.8becomespr(Z)-C,;;RsLIoGe-2T (8)(9)ThisZ-IdependencecanbeunderstoodbytheZ-dependenceof

cylindricalcolumn13tobeZ-1･2.3.

2.Casefb∫high(:loudWhenaltitudeislargerthan2kmandsizesofrectangleandreceiverarethesameasthose

inprevioussubsection,Eq.7becomes p,(Z) - C,& % Rie-2

2.3.3.Casef♭rintermediatestate

SimilartothecasefortheBxedorielltatioll,Z-dependenceofreceivedpowershouldbechangedbyitsdistallCelike丘xedorieI一tationalcase.Figs,5(a)al一d(b)arethesa111eaSFigs･3(a)alld(b)butfor2D-rectallglewl10Segeometricalcrosssectionis200FLmX100ILm.Fig.5(a)showsreceivedpowerisproportionaltoZ-ll5whe.IZisabout200 m,Whellaltitudeislesstllal150m,oscillationalsooccurs.Fig.5(b)showsr∝eivedpowerproducesabout103timeslargersignalscomparewiththatofsphericalscatterillgattllealtitude1000m･

o (aー

Iヽ ヽヽヽ

一一IIIlI-.0 -I.5

-1.O -0.5 0.ExponentofR∝eivedPower rbー'＼ヽヽsphteTC＼

ヽ ヽヽrectalgle

ヽ＼ ヽヽ

＼ヽ＼ ヽヽヽ

ヽ＼ ､､＼ tle18

le15 lelZ lelT.ReceivedPower【W】Figure5･(a)and(b)arethesameasFigs･3(a)and(b)butfor2D-rectanglewhosesizeis200FLmX100jim.

3.SCATTERINGBYHEXAGONALCRYSTAIJSParticle'sorientationmightdependonitsshape.Ono(1969)showedtheparticleisalignedasitslongestaxisisparalleltothehorizontalplane.Forexample,whenhexagonalcolu

mnwithaspectratioasp(=I/2a)-3isconsidered,syでmetricalaxisisparalleltothehorizontalplane(2DICOlumn)･Forhexagonalplatewithasp-1/3,symmetriCalaxISisperpendiculartothe

horizontalplane(2D-plate)i嘩 Ⅰ2a l'IbbFigure6･Alignmentofahexagonalcrystal.(a)Sym metricalaxisisparalleltothehorizontalplane(2D-∽lumn)and(b)symmetricalaxisisperpendicu)a

rtothehorizontalplane(2D-plate).Wh enthe2D-plateisconsidered,WeassumethebackscatteredirradianceIBfor2D-plateisthesameasthatforarectanglewithaxedorientationwhichhasthesam egeometricalcrosssectionf

or2D-plate.Thatis,ISisobtainedbyusingEq･lwithI-a-Rsq,whereRsqisthesidelengthofthesquaredThebackscatteredirradianceby2D-columnmightbe3timeslargerthanthatby2D-rectanglewhosegeometricalcrosss∝tionisthesameasthato

farectangleonthehexagonalcolumn.Figs･7(a)and(b)arethesameasFigs.3(a)and(b)butfor2D-plateand2DICOlumn.Weassumetheaspectratiosare3and1/3,Io-1W/m2,opticalconstantlOis1,31+i2.54x10-9,and

log-normaldist･ribution(Eq･ll)isassumed,wheremoderadiusr･mislOOILmandstandarddeviatiollqisl･5･We

neglecttheattelmationforthe'signals(T-0).For2D-platealld2D-column,P,(Z)isproportionaltoZ-" wheIIzisabout5007n･Il"ddition,receivedpowerfor2D-plateproducesabout107timeslargersignalscomparedwiththatforaspherewithsamesizedistributionatthealtitude1000m .Andthatfor2D-columnproducesabout5×103

timeslargersignalscomparedwiththatforasphereatZ-1000m.

Figs.8(a)and(b)arethesameasFigs･7(a)and(b)butrn-30FLm･For2D-plateand2D-Column,P,(Z)isproportionaltoZ-1･5whenZisabout150m･Inaddition,receivedpowerfor2D-plateproducesabout8×105times

largersignalscomparedwiththatforasphereatZ-1000m･Andthatfor2D-columnproducesabout103timeslargersignalscomparedwiththatforasphereatZ-1000m.

dn(r) 1

dr v雪蒜rlnq

(aー

2 -pla

teヽ ヽ

ヽ2

D-Clumn-2 -

1.5 -1 -0.5 0ExponentofReceivedPower

lnr-

1nrm≡t)｢ココ･≡守 1

∝〉∝)

I0α)

1(X

)101 (b)ヽl●■I-.i

shereヽヽ I2D-plate●●▼●■■2D

-Cヽlumnヽヽ

ヽヽIIe-1

2 1e-09 1e-061e-03Power【arb.】 (ll)Figure7･(a)and(b)arethesameasFigs.3(a)and(b)butfor2D-plateand2D-column.Weassumetheaspectratiosare3and1/3andsizedistributionislog-normaldistributionwheremoderadiusislOOpmandstandarddeviationis1.5.

----2D-Ilumn te-一一一.一一一一一ヽヽ2D-

-2 -1.5 -1 -0.5 0

ExponentorReceiyedPower ≡

一)｢ココ･=守 1(XI∝)

low100IOl ●＼.

ヽヽsphヽere ヽ7L 2 D - p l a t

●●､.. 2 D●●●●●

c o l u m nヽ ヽ㌔ ... ､●● 一1e-12 le-09 1e-06 1e-03Power【a

rb.】Figure8.(a)and(b)arethe

sameasFigs.7(a)and(b)butrm-30FLm.4.SUMMARYWeanalyzelidarbackscatteringenhancementforpristinehexagonalicecryst

Firstwestartwiththebackscatteringbyarectangulartarget･TllellWeCOlnputethescatteringbrhexagollalicecrystalsbyuslllgtheanalogyolfthercctallgularcalculatio11S･

Wecalcuhtethescatteringbyhexagollalcolumnandplaterandomlyorientedinhorizontalplane･Weassumethattheaspectratiostobe3and1/3andsizedistributionislog-normaldistribution,wheren10deradiusrm is100pmandstandarddeviationqis1.5.For2D-plateand2D-column,P,(Z)isproportionaltoZ-1･5 wllenZisabout500m･Inaddition,receivedpowerfor2D-plateproducesabout107timeslargerslgnalScomparedwiththatforsphereatthealtitude1000m･Andthatfor2D-columnproducesabout5×103timeslargersignalscomparedwiththatforsphereatZ-1000m.

For2D-plateand2DICOlumnwhoserm -30ILm,P,(Z)isproportionaltoZ-1･SwhenZisabout150m.Inaddition,receivedpowerfor2D-plateproducesabout8×105timeslargersignalscomparedwiththatforsphereatZ-1000m･

Andthatfor2D-columnproducesabout103timeslargersignalscomparedwiththatforsphereatZ-1000m･

Theseresultsarenotonlyimportantf♭rthescatteringbythepristinehexagonalicecrystals,butalsoapplicablef♭rtheparticleswithnatsurfacesexceptforthehighlyirregularshapedparticles,suchasKochfractalS.15

Inthispaper,weconsiderthescatteringbythehexagonalCrystalsperfectlyorientedinhorizontalplane.However,sinceitmightberarethatthecloudparticlesstayinsuchorientationduetoturbulenceandmighthavetumbling･Thismightleadtodrasticallyreducethebackscatteringenhancement.TheeffectofsuchtumblinglSCurrentlyinvestigatedbyus.

REFERENCES

l･C･M･Platt,"Lidarbackscatterfromhorizontalicecrystalplates,"I.Appl.Meteorol.17,4821488(1978)1

2.C.M.Platt,N.L.Abshire,andG.T.McNice,"Somemicrophysicalpropertiesofanicecloud&om lidarobseⅣationofhorizontallyorientedcrystals,"∫.Appl.Meteorol.17,1220-1224(1978).

3.F.G.Fernald,B.M.Herman,andJ.A.Reagan,"DeterminationofAerosolHeightDistributionsbyLidar,"I.Appl.Meteor.,ll,482-489(1972).

4･JID･Klett,"Stableanalyticalinversionsolutionforprocessinglidarreturns,"Appl.Opt.20,211-220(1981).5.M.I.Mishchenko,D.J.Wielaard,andB.E.Calson,"T-matrixcomputationsofzenith-enhancedlidarbackscat-

terfromhorizontallyorientediceplates,"Geophys･Res.Lett.,24,771-774,(1997).

6･S･Iwa5aki,andH･Okamoto,"Anomalousbackscatteringenhancementbynon-sphericalicecrystalsf♭rlidarobseⅣation,''Appl.Opt.,insubmission.

7.K.Sassen,Thepolarizationlidartechniqueforcloudresearch:Areviewandcurrentassessment.Bun.Am.Meteorol.Soc.72,1848-1866(1991).

8lM･BornandE･Wolf,PrinciplesofOptics,(PERGAMONPRESS,oxford,1975).

9･Jackson,J･D･,ClassicalElectrodynamics,(Wiley,NewYork.,1983).

10･S･G･Warren,"Opticalconstantsofice丘･omtheultraviolettothemicrowave,"Appl.Opt.23,120か1225(1984).

11･F･G･Fernald,"Analysisofatmosphericlidarobservations:somecomments,"Appl.Opt.23,6521653(1984).

12･G･L･Stephanes,RemoteSensing0ftheLowerAtmosphe7℃,(NewYork,Oxford.,1994),pp.427-438.

13･C･F･BohrenandD.R.Huffman,AbsorptionandScatteTin90fLightbySmallParticles,(Wiley,NewYork.,1983)

14.A.Oho,"TheShapeandRimingPropertiesofIceCrystalsinNaturalClouds,"I.Atmos.Sci.,26,138-147(1969).

15･A.Macke,J.Mueller,andE.RBSChke,"SingleScatteringPropertiesofAtmosphericIceCrystals,"∫.Atmos.Sci.,53,2813-2825(1996).

AnalysisOflidar-returnsfrom rectanglesandhexagonalicecrystals

S.Iwasaki

TheGraduateSchoolofScienceandTechnology,KobeUniversity

l-1Rokko-dai,Nada,Robe,Hyogo657-8501,Japan

H.Okamoto

CommullicationsResearchLaboratory

893-1Hirai,Kashima,Ibaraki314-0012,Japan

ABSTRACT

Thereisatheoreticalproblem toapplygeomet-ricalopticsf♭rthebackscatteringcalculationsoficecloudparticles.InordertoknowthebackSCatteringbypristinehexagonalicecrystals,WecalculatethescatteringforarectangularparticlebyusingFfaun-hoferdiffractionbasedonKirchhoff'sdiffractionthel

ory(KD).Thenwecomputethebackscatteringbyhexagonalplatesandcolumnsperfectlyorientedinhorizontalplane(2D-plateand2D-column).Weshowthatthereceivedpowerfわrthe2D-platesproduces104 - 109timeslargersignalscomparedwiththatforsphereswithsamesizedistributionatthealti-tude10000m.Andthatfor2D-columnsproduces5×102-3×104timeslargerslgnalscomparedwiththatforspheresatZ-10000m.ThismightexplaintheunusuallargelidarreturnsreportedbyPlattet.αJ.(1978).

1.1NTRODUCTION

Lidarisoneofthepromisingtoolstoinvestigatethecloudpro丘leSSuchasverticalstructure,shapes

andsizesoficecrystals,whicharetheunknownfac-torstocorrectlyestimatetheradiativepropertiesofclouds.Inordertoretrieveaboveinformationofsize

from thelidarobservation(el9･Fernald.1984),weneedtoknowthebackscatteringcrosssectionofthecloudparticlesIItiswellknownthatgeometricalof>tics(GO)isoneofthemosteffectivemethodtocalcu-latethescatteringpropertiesbytheicecrystalsforthelidarWaVelength･However,thereisatheoreticalprob-lemtoapplyGOf♭rthebackscatteringcalculationsoficecloudparticles.WetestedGOanditturnedoutthatGO isonlyapplicableforthecasethealtitude

isveryclosetotheground(e.9.100m)andshowedtheneedofmodificationstothelidarequation.On

theotherhands,Mishchenkoet.al.(1997)Considereddisksandspheroidswithsizeparametersupto50aLSicecrystalsandcalculatedlidarbackscatteringfromtheseparticlesbyusingT-matrixmethod.SinceT-matrixmethodcannotapplytothelargersizeparameters,WedevelopthemethodthatusesFraunhoferdiqrac-tionbasedonKirchho庁'sdiffractiontheory(KD).Imsection2.1and2.2,Wecalculatethescatteringbyarectangularparticlefb∫simplicity.Insection2.3wecomputethescatteringbyhexagonalcolumnsandplatesrandomlyorientedinhorizontalplanebyusingtheanalogyoftherectangularcalculations.

2.SCATTERING MODEI一

F

Kirchhoff'sdiffractiolltheory(KD).Thebackscatter-lngirradiallCeforarectangleiswrittenbyEq.1whereitsmajoraxisisparalleltotheY.axisal-dlllil10raxisis触edinsomedirection(e.glBornandWolf1975).

･･(x,Y･Z,中)-筈 等 ( 筈 )2 ( 筈 )2el2,

4'x - kL(I/Z- 2sinQ')/2

4'Y - kay/2Z, (1)

whereadenotesgeometricalcrosssectionoftherect-angle,RBListherenectanceoftheslabwithsomethick-nessanditiscalculatedbygeometricaloptics(GO)(e･9.BornandWolf1975).Zoisincidentintensity.AandAarewavelengthandwavenumberofinterest.QrdenotestheanglebetweenthenormalvectoroftherectangleandtheincidentbeamandTistheopticaldepth.Ianda(I≧a)arethesidelengthsoftherectangle(seeFig.1).

2.I.SCATTERINGBYARECTANGULARPARTICLEWITH AFIXED ORIENTATION

Fbrarectangularparticlewitha丘Ⅹedorientationatや - 0,backscatteredpowerintothereceiverisformulatedby

P,(Z)-C'/_RRI,dx/

R1

刀dyIs(I ,y,Z,0). (2)

whereRtisthehalfwidthofreceiverandC'istheconstantfb∫thelidarinstruments.

100(X)

ltXのE

4)3 100･≡i

10

J

I､､; ヽ lrectanglewitJ1†､ fixedorienl

ationspheletヽ

＼

､､. .ヽle-18 le-I5 1e-12 )e-09

ReceiyedPowerlW)Figure2:Z-dependenceofthereceivedpowerscat-teredbytherectangleandasphere.WeneglecttheinternallyreAectionofthesphere.Therectangleandthespherehavesamegeome

tricalcrosssections.Fig･2showsZ-dependenceofP,(Z)forarectanglewitha丘xedorientationandthatforaspherewhere Weneglecttheillternallyreaect

iollOfthesphere･Therectangleandthespherehavethesamegeometricalcrosssectionsforthefaircom

parison.Weassumethattheshapeofarectangleis100ILm X100FLm,Rt-0.2m,A-0.532FLm,

Io- 1W/1n2,C'- landopticalconstantisl･31+i2･54×10-9･Andweneglecttheattenuationforthesignals(T-0)･Atthealtitudeof1000m,receivedpowerproducesabout5×105timeslargerslgnalscomparedwiththatforthesphere.

10(KX)

lOW

E一IE l00=

< 10 hi

ghcloudlCase

lowcloudCas°

-2.0 -1.5 -1,0 -0.5

0.0ExponentofReceivedPowerFigure3:Z-dependenceoftheexponentofth

ere-ceivedpower,dlo910P,(Z)/dlog10Z･Fig.3showsZ-dependenceoftheexponentofthere･ceivedpower,dlog10P(Z)/dlo910Z

.scat

teLe>{==コ･b

ackscatteringhighcloudll唱ご芸'euuu 〔≡ヨFigure4:Thesketchoftherelationbetweenbackscat-t

eringirradiance,receiverandaltitude.WhenZiss

mall,mostbackscatteredpowerisreceived(seeFig.4).Itsreceivedpowerisderivedbysubstitu-tionofEq.1i

ntoEq.2,P,(Z)-C'R.LIoG. (3)Itturns

outthatP,(Z)doesnotdependonZ,con-trarytot

tion(Eq･4)･

pr(Z)-C茅er2'- (4)

whereaistheconstantofthelidarsystem(Fernald.1984).qbkisthebackscatteringcoe爪cient.WhenZislarge,receivedpowerisderivedby

p,(Z) - C′芸 芸 RsII.e-2,, (5)

whereSIistheareaofthereceiver,(2RI)2.ItturnsoutthatZ-dependenceisassameasthatintheusuallidarequation,however,sizedependenceG2appearedinEq.5isdiGerentfromGintheusuallidarequation.Theexponentdmsticallychangesfrom0atZ-50mto-2atZ=500m.

2.2.SCATTERING BY ARECTANGLERANDOMI.Y ORIENTED IN HORIZONTAI.

PLANE

R)rarectangulartargetrandomlyorientedinhor-izontalplane(2D-rectangle),thebackscatteredirradi-ancebecomes

･S(x･y,Z) - 汀 Is(I,y,Z･V )d中

- & % ( % )2e12,･ (6)

Fora2D-rectangle,receivedpowerisformulatedby

pr(Z,-'C,IRRt̀dx/_RRItdyIs(I,y,Z,I (7)

10000

)∝氾冒rL:3 100萱<

10

1

l ヽ l

I､､J ､､2p-co一umn

ヽ_ヽ ヽsphere ヽヽヽヽ ヽ

ヽヽ＼ ヽヽヽ

ヽヽ ヽ､ヽ!l＼∴lc-1S le-15 1C-12 Ic-09

ReccivedPowerlW]Figure5:ThesameasFig.2butfor2D-rectanglewhosegeometricalcrossSectionis100FLmX100FLm. Hcrc2D-rectanglewithgeo

metricalcrosssectioll0f100/Lm X100FLm isconsidered.Fig15istheSallleasFig.2butfor2D-rectangle.Fig･5showsreceivedpowerproducesabout2×102

timeslargersigllalscom-parewitht･hatorsphericalscatterillgatthealtitude100

0m. highctoud

Case

lowcloud

Case-I.5 -I.0

-0.5 0.0ExFX)RentOfReceivedPowerFigure6:ThesameasFig.3butfor2D-rectanglewhosegeome

tricalcrosssectionis100ILmX100FLm.Simil

artothecasefort,heGXedorientation,Z-dependenceofreceivedpowershouldbechangedbyitsdistance.P,(Z)i

sproportionaltoZ-1･SwhenZisabout80m.WhenZissmall,receivedpowerisderivedbysubsti-tutiono

fEq.6intoEq.7,pr(Z)-C,;; RsLIoG. (8)Thiscan

beunderstoodthatP,(Z)isproportionaltoZ-1,contrarytothespheriCalparticles･Inthesere-gion,GOisa

pplicableandthedependenceisZ-1asEq.8.WhenZ

islarge,Z-dependenceforthiscasebecomesZ12,whichisthesam edependenceforthesphere･Thiscan

beunderstoodbythefollowingeXPlanation･Thedista

ncebetweentheparticleandthereceiverislargeenough sothatthehorizontaldistributionofthebackscatteredpowerishomogeneousoverthereceiver,whichisthesameast

hatforthescatteringwavebyth

esphere.2.3.DISTANCBDEPENDENCEOFTHERECEIV

EDPOWERBY HEXAGONAI.CRYSTALSWhen

thehexagonalplatewithanaspectratioof1/3randomlyorientedinhorizontalplane(2D-plate)isconsid

IeisIhcsallleaSthatforthesquarewithaRxcdori-entationwLlichhastheSalllCgCOmCtJricalcrosssectionof2D-plate.

WhellthelleXagOllalcolumllWithanaspectratioor3

randomlyorientedinhorizontalplane(2D-column)isconsidered,weassumeitsbackscatteredirradiancelsISgivenbythesuperpositionofthebackscatteredwavefromeverysurfacewherethebackscatteringsignalsfromasurfaceofhexagonalcolumnisestimatedbythesimilarproceduredescribedinsection2.2.

Weassumethaticewatercontent(IWC)is1g/m3,andsizedistributionislog-normaldistributionwheremoderadiusesrm are10,100,1000Ilmandstandarddeviationqis1.5.

Fig･7(a)showsthatreceivedp?werfわr2D-platepro-

duces104- 109timeslargerslgnalscomparedwiththatforsphereswithsamesizedistributionattheal-titude10000m･Andthatfor2DICOlumnproduces5×102-3×104timeslargersignalscomparedwiththatfbrspheresatZ-10000m.Fig.7(b)isthesameasFig.3butfor2DIPlateand2D-Column.

●◆l◆lI.'..1(hm:冗 - O(叫 m●●●一一●~11f叫m--一一一㌧ ● ●● ●●●●●l●●●l●､●､.◆lI..1叫1m●1叫 m 10pm100thm'.ー■●●ヽ●●..ヽ●..●◆..●...I●●●ヽ ヽI丸mヽ2D-plate

- ●●111+ 1ヽ∩2D-column-- ●●●....●､◆:.(I...ヽ:●..ヽヽ1e-I2 le109 1e106 le-03

Power【W】

(b)l(伽0

100

0∈

4)3 100童<

10

1 TIP)(

叫rrlIー‥‥~HHT

rm=)ー叫m

.ヽrTn=1叫TT1

ヽ .2D-plate- I2D-colLJm

ln~ ~ 一 l-2 -I.5 _1

-0.5 0ExponentofReceivedPowerFigure7:(a)and(b)arethesameasFig.2andFig.3butfb∫2D-plateand2D-column. 4.SUMMARY

WeanalyzelidarbackscatteringenhallCemelltforpristinehexagonalicecrystalsbyusingFraunhoferdiffract

ionbasedonKirchhoLf'sdiffractiontlleOry(KD)tAtf

irst,wecalculatethescatteringbyarectangularparticlefわrsimplicity.ThenwecomputethescatteringbyhexagonalcolumnsandplaLteSrandomlyorientedin

horizontalplane(2D-plateand2D-column)by

usingtheanalogyoftherectangularcalculations･Itturnsoutthatthereceivedpowerfor2D-platepro-

duces104-109timeslargersignalscomparedwiththatforsphereswithsamesizedistributionatthea

l-titude10000m.Andthatfor2D-columnproduces5×102-3×104timeslargersigna

lscomparedwiththatforasphereatZ-10000m.Ourtheoreticalcalculationsshowtheexistenceoftheh

exagonalparticlesrandomlyorientedinhorizontalplanemightbeexplainedfortheunusuallar

gelidarreturnsreportedbyPlattet.aL.(1978).Inthispaper,weconsiderthescatteringbythehexag-on

alcrystalsperfectlyorientedinhorizontal plane.However,sinceitmightberarethatthecloudpar-ticlesstayinsuchorientationduetoturbulenceandmighthavetumbling.Thismightleadtodrasticallyreducethebackscatteringenhancement.Theeffecto

fsuchtumblingiscurren

tlyinvestigatedbyus.ACKNOWLEDGMENTS

WewouldliketothankforDr.YasuiandDr.

Sug-imotoforfruitfuldiscussion.ReferencesPlatt,C.M.,N.LAbshire,andG.T.McNice,1978:Somemicrophysicalproperties0fanicecloud

fromlidarobservationofhorizontallyorien

tedcrystals,∫.Appl.Meteorol.17,1220-1224.Fernald,F.G.,1984:Analysisofatmosphericlidarobserva

tions:somecomments,Appl.Opt.,23,652-653.

IwaSaki,S.,andH.Okamoto,submitted:Anomalousbackscatteringenhancementbynon-spherica

licecrystalsf♭rlidarobservation,Appl.Opt.Mishchenko,M.Ⅰ.,D.J.Wielaard,andB.E.C

a1-80m,1997:T一matrixcomputationsofzenith-enhancedlidarbackscatterfrom horizontallyoriented

iceplates,Geophys.Res.Lett.,24,771-774.

Born,M.andE.Wolf,1975