Reduction of Multiple Scattering to Second Order Scattering for Determination of Liquid-Cloud Microphysical Properties

Transcription

1 CAN UNCLASSIFIED Rdution of Multipl Sattring to Sond Ordr Sattring for Dtrmination of Liquid-Cloud Mirophysial Proprtis Xiaoying Cao 1, Gills Roy and Grégoir Trmblay 3 1 Lidar Consultant, Ottawa Dfn Rsarh and Dvlopmnt Canada - Valartir Rsarh Cntr 3 AEREX Avioni, Lvis 8th Intrnational Lasr Radar Confrn 5 30 Jun 017 Polithnia Univrsity of Buharst Dfn Rsarh and Dvlopmnt Canada Extrnal Litratur (N) DRDC-RDDC-018-N006 Fbruary 018 CAN UNCLASSIFIED

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3 REDUCTION OF MULTIPLE SCATTERING TO SECOND ORDER SCATTERING FOR DETERMINATION OF LIQUID-CLOUD MICROPHYSICAL PROPERTIES Xiaoying Cao 1, Gills Roy * and Grégoir Trmblay 3 1 Lidar Consultant, Ottawa, Canada; * RDDC Valartir 459 d la Bravour, Québ, Q, Canada, gills.roy@drd-rdd.g.a 3 AEREX Avioni, Lvis, Canada; ABSTRACT Undr singl sattring onditions, watr droplts louds do not dpolariz th baksattrd light. Howvr, baksattrd light from multipl sattring will b dpolarizd. Th lvl of dpolarization is a funtion of th droplts siz and of th loud xtintion offiint valu and its profil; it has also a strong dpndny on th lidar fild-of-viw (FOV) and azimuth angl [1]- [3]. It has bn dmonstratd in [4] that th multipl sattring ross polarization signal an b rdud to a sond ordr sattring on using th azimuthal dpndny of th ross polarization. In this papr w prsnt how th multipl sattring ross polarization an b rdud to a sond ordr sattring and how this signal is rlatd to th droplt partil siz. Mont Carlo simulations for louds at diffrnt rangs and fftiv radius sizs ar prformd and ompard with th rsults obtaind with an analytial modl. 1. AZIMUTHAL CROSS POLARIZATION PATTERN Baksattrd light from sphrial partils dos not hang th polarization orintation stat of a linarly polarizd inidnt light. This partiularity allows th disrimination of sphrial partils from non-sphrial partils. Howvr, undr multipl sattring onditions, vn sphrial partils do gnrat dpolarizd signals. In fat, th multipl sattring ross polarization shows an azimuthal pattrn. This pattrn is asily obsrvd using a gatd ICCD amra and a polarizd bam splittr as shown in Fig. 1. A linarly polarizd paralll lasr bam is usd. At th rption, aftr ollimation, th ross polarization is imagd on th dttor. An adjustabl dlay is usd to imag th baksattrd light from th loud from a spifi loud dpth. Th gat width of th ICCD is typially 10 to 0 ns. Plas rfr to [1] for rlvant dtails. Figur 1. Lidar st up to aptur th azimuthal ross polarization. Th linarly polarizd sour is mittd on axis (lowr lft). Th rivd signal is ollimatd through a polarizr and th ross polarization is imagd on th amra (right). In ordr to bttr undrstand th mhanism of polarizd multipl sattring, Mont Carlo (MC) simulation has bn prformd. Th Undiqu MC simulator is a multithradd softwar basd on th Bohrn and Huffman Mi sattring algorithm. Th simulator rprodus th haratristis of a Flash Lidar systm. It onsists of an mittr/rivr systm, a targt and a propagation rang inluding arosols of various proprtis. Th partiularity of th Undiqu MC is its apability to imag th sattrd light on a dttor array [5]. Fig. shows th azimuthal pattrn obtaind for th simulation of a pntration of 50 m in a loud of onstant xtintion 0.03 m -1 starting at 1000 m. Th imag at th top ontains all th sattring ordrs, whil th imag at th bottom ontains sond ordr sattring only. Th sond ordr sattring ross polarization follows a Cos ( 4 ) pattrn; it mans thr is no sondordr sattrd nrgy for azimuths qual to 0 o, 90 o, 180 o, 70 o. In multipl sattring onditions (top part of Fig. ) thr larly is a fair amount of nrgy at thos angls. Th subtration of th highr ordr sattring nrgy found at thos spifi angls, whn don at all azimuths, lads to a sond ordr sattring pattrn [4]. So, it appars that multipl sattring ffts ourring in dns watr loud an b simplifid to sond

4 ordr sattring. In th following, w will xamin what ar th mhanisms lading to dpolarization of th lidar signal from sond ordr sattring. Using Mi thory, it an b shown that: ( P os P os P ) 3 1 ( ), () lin (3 P os P os 3 P ) 3 whr in P 1, P and P 3 ar th Mi sattring phas matrix lmnts dfind by Dirmndjian. Fig. 3 shows th phas funtion and th dpolarization ratio at a wavlngth of 0.53 µm for linar inidnt wavs on watr-droplts of fftiv radius of 6 µm. Th watr droplts siz distribution is a gamma distribution with = 7 and = 1.5. For dpolarization, th major obsrvations ar: 1) Th light is not dpolarizd in th forward sattring dirtion for angls smallr than 0 o ; ) th dpolarization is qual to 0 at 180 o ; 3) th dpolarization inrass vry sharply around Figur. Mont Carlo simulation of ross polarization azimuthal pattrn. Th top imag ontains all ordrs sattring. Th imag at th bottom is for sond ordr sattring only.. BACKSCATTERING AND DEPOLARIZATION Lidars with polarization apabilitis usually work at a spifi FOV and dtt th paralll and ross polarization omponnts of th lidar rturn. Th lidar signals will ontain all sattring ordrs. In this papr, w want to rdu multipl sattring ffts to sond ordr sattring. To do so, it is nssary to hav a look at th Mi sattring phas funtion and how th sattrd light is dpolarizd. Th linar dpolarization ratio (δ lin ) at a sattring angl β is dfind as th ratio of th powr intgratd ovr th azimuthal angls φ in th plan of polarization orthogonal ( I ) and paralll ( I // ) to th linarly polarizd sour: ( ) I I I 0 y (, )d I (, )d lin. (1) // 0 x Figur 3. Phas funtions and linar dpolarization ratio for a watr droplts gamma distribution with fftiv radius of 6 µm. So, for a lidar, dpolarization is mainly ausd by a baksattring ourring aftr on or many forward sattrings as illustratd in Fig. 4. A lidar with a givn FOV ( i ) will masur th baksattrd light without any distintion rgarding th forward sattring vnt position in spa. Th ross polarizd sond ordr sattring signal dttd will b th sum of all thos signals and it will b givn by: P D (z, ) i P ( z ) z i 0 0 F ( z, ) sin d d z

5 Our analysis has lad us rathr to us th dpolarization paramtr ( D p p p ) /( ) // rathr than p r, ). Fig. 5 shows th dfinition ( b of various paramtrs usd to xprss th dpolarization paramtr as a funtion of sattring angls ranging from 170 o to 180 o. Th omplt drivation of th paramtrization for r ranging from to 1µm will b publishd in Appl. Opt in 017. Th mathmatial rprsntation is as follows: Figur 4. Doubl sattring prosss and highr sattring prosss lading to baksattring dpolarization. 4 whr P(z ) P xp[ ( z ) dz ] 0 F(z, s s b z 0 ) [ ( z ) p ( r, )][ ( z ) p ( r, )], z A, and whr,, and A ar rsptivly th spd of light, th puls width, and th ollting optis ara; is th sattring xtintion offiint; s p( r, z, ) is th valu of th phas funtion for th forward sattring ( ), and p ( r, z, ) th b valu of th prpndiular omponnts of th phas funtion at bakward sattring angls ( b ) for a partil of radius r; z is a whr th loud starts; z is th distan whr th sattrd radiation is masurd; th quantity [ s ( z ) p( r, z, )] rprsnts th forward sattring offiint whil ( z ) p ( r, z, )] rprsnts th ross [ s b polarization baksattring offiint. Th FOV is asily rlatd to th sattring angl via: tan ( z tan ) /( z z ). Max ( r ) ln( r ) If, Max r ) D ( 4 (, r ) A ( r )[1 xp (( ) /( ( r ) w ( r )) ] d w ( r ) r If, Max r ) ( D (, r ) B ( r ) xp( B (0.944 ( )) B 3 o ( r ) 1 In short, D, r ) starts from a valu of zro at ( 180 o and inrass quikly following a supr- Gaussian. It nds to b notd hr that th width of th supr-gaussian is dirtly rlatd to th width of th forward sattring pak. Past th maximum valu, in th dirtion of drasing angls, D, r ) drass xponntially. ( d Th forward sattring phas funtion is modlld as a summation of Gaussians [6] p ( r, ) 1 1 d xp( / d ) A g 1 g xp( /.585 ( / r ) ; ; A ; d 0 r : fftiv radius, : wavlngth. g Thr is no xisting modl for p r, ), th g ( b prpndiular omponnts of th phas funtion. g ) Figur 5. Paramtrization of baksattring dpolarization paramtr. A watr droplt loud of fftiv radius of 6 µm is rprsntd. 3. RESULTS Fig. 6 shows th alulatd and normalizd dttd nrgy in rings dlimitd by FOV i

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7 DOCUMENT CONTROL DATA (Surity markings for th titl, abstrat and indxing annotation must b ntrd whn th doumnt is Classifid or Dsignatd) 1. ORIGINATOR (Th nam and addrss of th organization prparing th doumnt. Organizations for whom th doumnt was prpard,.g., Cntr sponsoring a ontrator's rport, or tasking agny, ar ntrd in Stion 8.) a. SECURITY MARKING (Ovrall surity marking of th doumnt inluding spial supplmntal markings if appliabl.) DRDC Valartir Rsarh Cntr Dfn Rsarh and Dvlopmnt Canada 459 rout d la Bravour Qub (Qub) G3J 1X5 Canada CAN UNCLASSIFIED b. CONTROLLED GOODS NON-CONTROLLED GOODS DMC A 3. TITLE (Th omplt doumnt titl as indiatd on th titl pag. Its lassifiation should b indiatd by th appropriat abbrviation (S, C or U) in parnthss aftr th titl.) Rdution of Multipl Sattring to Sond Ordr Sattring for Dtrmination of Liquid-Cloud Mirophysial Proprtis 4. AUTHORS (last nam, followd by initials ranks, titls, t., not to b usd) Cao, X.; Roy, G.; Trmblay, G. 5. DATE OF PUBLICATION (Month and yar of publiation of doumnt.) Jun 017 6a. NO. OF PAGES (Total ontaining information, inluding Annxs, Appndis, t.) 4 6b. NO. OF REFS (Total itd in doumnt.) 6 7. DESCRIPTIVE NOTES (Th atgory of th doumnt,.g., thnial rport, thnial not or mmorandum. If appropriat, ntr th typ of rport,.g., intrim, progrss, summary, annual or final. Giv th inlusiv dats whn a spifi rporting priod is ovrd.) Extrnal Litratur (N) 8. SPONSORING ACTIVITY (Th nam of th dpartmnt projt offi or laboratory sponsoring th rsarh and dvlopmnt inlud addrss.) DRDC Valartir Rsarh Cntr Dfn Rsarh and Dvlopmnt Canada 459 rout d la Bravour Qub (Qub) G3J 1X5 Canada 9a. PROJECT OR GRANT NO. (If appropriat, th appliabl rsarh and dvlopmnt projt or grant numbr undr whih th doumnt was writtn. Plas spify whthr projt or grant.) 9b. CONTRACT NO. (If appropriat, th appliabl numbr undr whih th doumnt was writtn.) 03bb- Air Intgratd - EO/IR SEN 10a. ORIGINATOR S DOCUMENT NUMBER (Th offiial doumnt numbr by whih th doumnt is idntifid by th originating ativity. This numbr must b uniqu to this doumnt.) 10b. OTHER DOCUMENT NO(s). (Any othr numbrs whih may b assignd this doumnt ithr by th originator or by th sponsor.) DRDC-RDDC-018-N006 11a. FUTURE DISTRIBUTION (Any limitations on furthr dissmination of th doumnt, othr than thos imposd by surity lassifiation.) Publi rlas 11b. FUTURE DISTRIBUTION OUTSIDE CANADA (Any limitations on furthr dissmination of th doumnt, othr than thos imposd by surity lassifiation.)

8 1. ABSTRACT (A brif and fatual summary of th doumnt. It may also appar lswhr in th body of th doumnt itslf. It is highly dsirabl that th abstrat of lassifid doumnts b unlassifid. Eah paragraph of th abstrat shall bgin with an indiation of th surity lassifiation of th information in th paragraph (unlss th doumnt itslf is unlassifid) rprsntd as (S), (C), (R), or (U). It is not nssary to inlud hr abstrats in both offiial languags unlss th txt is bilingual.) Undr singl sattring onditions, watr droplts louds do not dpolariz th baksattrd light. Howvr, baksattrd light from multipl sattring will b dpolarizd. Th lvl of dpolarization is a funtion of th droplts siz and of th loud xtintion offiint valu and its profil; it has also a strong dpndny on th lidar fild-of-viw (FOV) and azimuth angl [1]- [3]. It has bn dmonstratd in [4] that th multipl sattring ross polarization signal an b rdud to a sond ordr sattring on using th azimuthal dpndny of th ross polarization. In this papr w prsnt how th multipl sattring ross polarization an b rdud to a sond ordr sattring and how this signal is rlatd to th droplt partil siz. Mont Carlo simulations for louds at diffrnt rangs and fftiv radius sizs ar prformd and ompard with th rsults obtaind with an analytial modl. 13. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Thnially maningful trms or short phrass that haratriz a doumnt and ould b hlpful in ataloguing th doumnt. Thy should b sltd so that no surity lassifiation is rquird. Idntifirs, suh as quipmnt modl dsignation, trad nam, military projt od nam, gographi loation may also b inludd. If possibl kywords should b sltd from a publishd thsaurus,.g., Thsaurus of Enginring and Sintifi Trms (TEST) and that thsaurus idntifid. If it is not possibl to slt indxing trms whih ar Unlassifid, th lassifiation of ah should b indiatd as with th titl.) Lidar, polarization, Multipl sattring