HAL Id: halsde-00136133
https://hal.archives-ouvertes.fr/halsde-00136133
Submitted on 12 Mar 2007
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Extinction Coefficients retrieved in Deep Tropical Ice Clouds from Lidar Observations using a CALIPSO-like Algorithm compared to In-Situ Measurements from the
Cloud Integrating Nephelometer during CRYSTAL-FACE
Vincent Noel, David Winker, Tim Garrett, Matthew Mcgill
To cite this version:
Vincent Noel, David Winker, Tim Garrett, Matthew Mcgill. Extinction Coefficients retrieved in
Deep Tropical Ice Clouds from Lidar Observations using a CALIPSO-like Algorithm compared to In-
Situ Measurements from the Cloud Integrating Nephelometer during CRYSTAL-FACE. Atmospheric
Chemistry and Physics, European Geosciences Union, 2007, 7, pp.1-8. �halsde-00136133�
Extinction Coefficients retrieved in Deep Tropical Ice Clouds from Lidar Observations using a CALIPSO-like Algorithm compared to In-Situ Measurements from the Cloud Integrating Nephelometer during CRYSTAL-FACE
!"#"$%'&()*+-,/.%0%1234(!"!5,6378
9:.;%(.<=>%(@?A!5BCDB%EFGAIH.JKGLMNOP..QR.SMT%1.
&UWVYXVZ9:.-F[3H \]Q(.%1_^a`AUD%(6V/bcXV
4b >de[fgb/D.^ba)'b XV
8UYVYX[Vh,6??.%(?cXi.AT>F^P`*Dj%([,@%(j;kD!l9:b XmV
XM;JkD?@=*n6o>p qrtsuvwSx3y/z{uvp xrjo|c}~6uS|rSxGyjr
`*m%D%(QEim?m-F.SM=^%j
N_U
9:.;%(.<=>%(@?A!BSDBm%DmF3A H.J3LMA=OX9
mAO'>HUD^GLM
Sg@OP.3._Q1.CMT%(.
dR353J?gi>HDN_^3LMf%
)'^Q i.ij%{i%(UQ((Q:./mJIi.%( Q1mKf'G3?.% %(.C=gQ:.?adm[kMJK6=C=mKf0fE33(Q =%DmiN.
3lM?[Q( %1C=%EdN?5MQ(F";Q(%Edm.CEmQcf%([J Y >gQ==%0MJK_U(Qj =^-0J zGq uS|grSx3y_r
x7}wE`{O9(.?=^Y7 Q(kM z3q<~ov gw<}ox7~!#" vGsuv$GqpIvUo7vwD` %*i%(;&]=^ [Q==%0MJK(Q
a%( JYMDN? .>%E;mm%E i.CDf=%EJcQ ?M%(F =^ `{\('KX[)'V@9)TV `{ .J i.7F .? m$
JK.Q0M%(JK(Q Mi= *$[Jc`*73?:;gQ1%0d.SE[Q f%([J Y .Q1Q*[f 3 M?eQ*[.SD?cm
=ihmf ?i mUdC=>d QEHgQ0DJcQ .%(J ig.j%(?gAT>%SQ0D/73?.% %(.C=eQ .%( %(C%Ed? f%(J `{O9
;gQ(j%0d.CDgQ:mf .C3DM.SD?a;m.$Q(.CDj%EmMQ(-Fc.@%(C=%=Gdm._e._F%(k=^J f=m%:mi.NLM6M?cQ(GJ3.%'D
lMQ(? =^ %(UE>H 3.CM^? `AV 9 0O:X+ JWQSQ( .? J i.%(? D %(UQ0Mk(Q f%(J =^
%(FM.%]`{O 9 ._F%(k=^Jc)'^Q(3G?.j% %(.C=eQ].%( MQ(U? = %(2=%Ddc=SE [f=fE3GU*i%Ef=G3Q(
I^G^ .%(Y[JIi.%(?D .<M.;Q1%Ed.CD[Q f%([J =^K` 7<Q(kM i%1;m iM3=7-F =^Y_JYi^.Q(0Q
a=^>%{d%0=.ed.j% 3.;Gk=H#"^K;gQR%0dm.CDmgQ:G?N[%(C=%E3d.Qf=%([J ;=^gQ0=%0MJa_U(Q:.%R
dj%1H Q(GJK73.%1W =^Z3Jk(Q [f [N.C=g YfEfD%RUQ .%( Fj%(.7H d.%(3.C=gQ .j%(M? =^
.Cdm%(.F i%([f=3Q1 .? F%1._*=%(?[QKm3.%EF%cQEi.C=./QR.GUQc.%1,a %(i%1[?MN?g)'^ I
gQ0=%0MJY(Q5.F%(-a73YkD^ . .d%1.F ?m3f0fD%R fl3Q<Q =^. /. miU=U. ?[i=^
%(C %Ed.QS\]Q=Mgk(Q*Q=MFFQ==^/` V@9 0O:X+ YNic`*dNCEmK.Fm%E=^J .W;m]=%0MQD?6 ?>d%
%(.Q0D@Q=EJK.CDQ fg=^@G?.j%'%(.C=m.?7F WF? %(<=%Edm._Q f/D7CDma[f=f033(QS
1. Introduction
`At%E%0MQ M?[Q .%( ^F^Y.kDkM?@M?[Q JYgQ0=>HKN[J ieQ1? fU@%EHQ0D.QSX[NA=^HYNmgQ(Q0DjD7H
d% JYm%1 =^.h . fW=^ U.%0=^
Q Q0M%(f=.U # HG3C . j1]=^_t% [fE>MN =^
%(.?.CD ;M?FC/.j ;m dj% [$? <XDi^gQYS/.6j R')'^c%(.?3.C=>d fE>M [f].
Fdmc>%E%0MQ M?K?i?gQJYQ0=>H [ =^/?[3.SD];m._3.U ;mCak(Q ._>;?c.j?F%(^MQ1
f0fDC(Q1g.?gmK.@. Q1.3gYk(QJY3%(i^HgQ(3U..?i=.[i%1mi%==QSU!gQ0'=.;Hm=^
LM.UEk=Hamf Q0MGF[^U%(f=GNCD?6;HK.@%E%0MQ M? E.?I=^UMQ k(Q .>;?f=fDC GQ ?7%1CDHIEN?ID k(Q
i=. =^3$QSQ
τ
?f=7N? .Qτ
α
=^ dj%0=3.lDF%1.C= f k(QZD7CDm
f=fE3_3
α ( )
;SYj =^ M? ;M?.%(Q .? ) ^ ._>;m? fK. _M?"GQ=^MQ?>%(CD>Hh?i? m"k(Qcd%0=. i%(f03G[f $-=CD N[f=f033_UR V F?Z$I?F[f
-ESE f0f=3GU(Q( .? =^MQi=N._ ?i=^ >%D%0MQM?eQ aM? 3.? D . ;C3D%
Q==7JK.CDYfe=^7%'Fj%(..;N?f=fENCR
/M =^ ^F^ ._EkM? f@>%E%0MQIM?[Q(?>%(NC@x>~lr2xolJYU.Q=M%(JU@fA=^>% J3%1mi^HQ(GN.
i%(iC%=Q/Q .c?fEfE3CMk*D.QE$ =^.C].*;iM%<Q=MN? . QEHQ0DJK.CE ;m.Q(Q2e!5m%(Ndm%('7 =^
=%DmiUQ 3YM?[Q .%(Y[fGD .CD?c=i mf:?i mUdSE>dQEHQ0DJcQ( Q(UYFg,/.%E%(<G <:.
( I^3^ JK.gQ ^F^E.kDkM? ;Q(%Ed.SE[QZ.%( . UUQSQ(k0H&].CMQ( [f =^% 3.%EF
^%(UD.:._? dm%0D.*DQ([gQ1 =^Q1 QEHQ0DJcQ/^.d . 3.%EF (Q(.3 %1.?m3.CD>d JYi.C]m =^
i.C Q=M%(f=. .? .SEJYgQEi^%( Y.j%0=JK._ C .=ljEc.j? =^_t% %(N.CEm =^%(MF^ f=.Q0
dmS=mK3.?gQ QDi7fDG/JW3%1mi^HQ(G/.?Kmi=U.i%(mij%=UQ!T.%(LM^.j%.?aHJ Q(fDG3?
jYHJcQ(fE3G? .? !T.%1LMg^.%(@j SebIf=%0M.CDjHm a^ ?MCDFQ(.CDGkD Q=M?mQ
MQ(F i.UQSQ(dY%(JYD Q(j[Q(F k*Q@fGD ?mfEfDGSMgk:= Q1i.%(.CDK. i=U.7H =^7 GNM? 3.Hj%
f%([J .WM?j% HF mdmCD>dQEHgQ=D_Ja JKU._F ^F[^YMgj%0D.DQ*=^ %(C=%ENdm.Q(D`A^>%(3.U
C:.m2[)'^Q@Q0=%(UQ<Q(UQ{=^YN? f=%*.CD>d6%1_J DWQ(j[Q(FQ0Me_^ .Q 73?.%( I^gQ(WQR[Q(E>dkEH
O3.CGD@j* /.? N._ F[>d dm._>M.;3 gQ(F[^U(Q6UD 3 _M? J3%(i^HgQ(3Q GK[ C].2
9:?[.j%'%(C%Dd._Q fD7CDma[f=f033(Q .%1@._a_f=f(S=dmADmf=%Q0M?HF =^@i=.?i=^a[f
3YM?gQ M:f{%(N.^ mf Q(M ;gQR%=d.CDgQ(.j? .%1a*Q=M;RC = i.QRQ(>d %(JYD Q1[Q(F
G3JkD.S=mgQ1[.UQ=^ d.%(3.;G3k0Ha[fDCDY_f=f=G(Q Q ;gQ(j%1dm?Y.Q . fMCDYmfiS=%(.C=[
gQ(3?5=^ M? .H%S !5m%(Ndm%( =^--0J Q(i.NN;mm%D G?.j% "=^ f%(.JK Y%E$ mf=^
`V 9 =OX+ JKQRQ([ 0#"$%C .Y Q CM%E%(U=H i%(?MF %(C=%ENdm.Q [f DCD[
f=fE3_3(Q].? =^UMQ@i=. ?i=^gQ] .YF[;.AQRN._'d f=m%*=%Ei. GNM?eQ]mcDi f
i=.37H/=^Gj$NmdmCDdm6QEHgQ=D_JcQ2
E6=^ i%1Q( Q=M?H.CGDUM.CD?6;.U$gQ1.CD%'i%Df03GQ ;gQ1%Ed?K?iY=%EiU.g3/_M?[QMQ(F
=^ z 3qluS|rSxGyr x}w,E`{O9Ym +(MgH gK.?5K?M%(7-F5=^ z xw<w mr v x3q~}oS| q
wSqEs*x3y} n]~Nx7rc}~ZzxGw<w r
}S|vwSr GqwSx} n wjv}Zzx7wSw/r0s*vwSxp vj~o E`{\ 'KX){V 9)0TV/`:
+SQ( S .g@.%1aMQ(N? = %(<=%Ed33?.% %(.S=eQ1 MQ(F =^`AV@9 0O:X+YNi `*mdmUC=
%(C %Ed.._F%(k=^J D#Z7$j%( S\]Q=Mgk(Q .j%(YJYi.%(?= %12%Ed. QMQ(Fc=^ %(FM.% `{O9
.>F% =^JYA=^ YkD^ .SM._@2Q(Mh;Q(%Edm.CEmQcf%([J =^l.%E;%E 7g.CD?i%E; z 3q
<~ov gw<}ox7~! "/vGsuv 3qp v_o7vw D` @,/.%E%(SGK<K. S*)'^l`{\('KX[) V 9)DTV/`{ .JYi._F 0Q
i%(Q1DN?5 XSR *.F Yk=^ =^ gQ0=%0MJa_U(Q6MQ1? ;Hl=^ i%(Q1_UYQ0M?H ) ^ `V 9 =OX+
ai `*dCD %1C=%Ed. .Fm%(k=^J Q i%1Q(DN? .? k(Q %(Q0Mk(Q][J i.j%(? YE^ %(Q=Mgk(Q]f%(gJ
=^ `:O9 .Fm%Dk=^J XCR/g 9?.% %(.C= %(S=%ECdm._Q .%15=^ MQRN? = %(2=%Dd DCD[
f=fE3_3]i%Ef=G3Q XCR ^_^ .%1 J ig.j%(? l Q(kM ` ;gQ1%Ed.CD[Q2 YQ(CMQ<Q(e
.?WNm_>MQ(Y.%( F>dY7 X[NCR
2. Volume extinction coefficient retrievals during CRYSTAL-FACE
)'^/`:\('KX){V 9)0TV/`{ .JYi.F[ a.Q^_3?+(MgHc dm% T%E?./._?a=^6, Mgf f!3
.? .JK? D i%Dd? =^"[J i%1^[Q(>d JU.QEM%1_Ja_U(Q N?? D ;mCDS% M?%RQ0D.? =^
J3%1mi^HQ(GN._ .? %(.N?m3.CD>d i%(i% =3Q .? f=%(JY.C=ci%([NQ<Q1Q f3M?[Q mDi mf'=^3$
dmS=d M?ZQEHQ0DJQ2 T>d J3?6=^>F[^E.kDM? .t%(%(.fGa.%E%E3? MJK%(MQYx7~rSxo .?
%(JYDWQ(j[Q(F gQ==%0MgJa_U(Q( Yk=^ Q(3J MgkD.MQ:F%(M?;m.Q(? ;gQ(j%1dm.CDmQSV6JYFc=^Q1[=^
YVYX[V z 3q uS|r2xGyr
x7}w `{O9:. =^-%( a.CdF=^ D JY - J .? j J
;.N$ Q1.CD%:73?.% !,/GGPC:.g( Y.Q*[$F ?I a.%(?cf%([J =^@VYX[V \ 0 .>%R%(.fG
IF ._?c. *.?i%1d?? Q1Ndm%(.?.HgQ*f ;Q(%0dm.CDmgQ*f%1[J .Q*^F^c.Q:$[JY Y=^ .
dj%0E.'%(Q(kMEm [f* J .? . ^m%D_mUD._%(Q1m>MDm f J .C=^ H-i[3U.{\ 0 f=7HF
QEiN? f J >QE)'^K`{O 9 D_3Q1if033? mfd QKj
µ
%1.?m._gQ1{Q( =^f=[=i-%E . M?[N.CD?QSQ'=^._ jY$[J ./K.H =^ Hi3U._e?m=Q0D.6?M%(Fc`{\('KX[) V 9)DTV/`{) aM?W;m3Q<Q =^._ JYCDj% Y?{k- %(MF^>H j DJUQWQ(JK.G3% =^. `AV 9 0O:X+
QS) ^Q/Nmf=FM%(.CDm
.a? Mg3LM6JYkDm%D7-Fc[f'/M?[Q.CD?K DmiYf =%DiGN._emdmCD>d QEHgQ0DJcQ( ^3^
aM? ; GJYigQ<Q(>;g3 f%([J =^lF%(M?Z;m.CMQ(mf =^5 a% 3.Hj%<Q [f =^3$ Y.SD% M?[Q
;$7F =^cG3?.% iC=%(.C=ggT%(J =^Y%(. ;.$gQ(.CDS%(? .Q1%@GF^ JY.Q0M%1? ;H =^c`:O9
DQ1miNei%Di% =Q mf:M?c._? .N%(gQ( 3.Hj%<Q .%(6%(C %E3Cd?7M?F=^ .kDkM? [f M?
;.Q1 .?hM? =i6(Q miU=U. ?i=^
τ
.?"i%Ef=G3Q [fc?jim.j% U.SE"%(.C= .j?Zdm[kMJK -ESEcN[f=fE3_3R)'^ JKC=^?WMQ(N? f=%*..7HQ(Q ._?%(C=%E3d.[f=^Idm[kMJKW-ESEc0Qi[3.? !5,6G3C:.0 (.? 3Q;.QR?cW=^WQ0D.j?.%(?3?.%*d%<Q(WD^3LM DF
Xi[^>%( C].@j[- I3C=@j[/Sg# ^ igQ<Q(>;3 1 >f=%/i=.37H =^ M?[Q 1P=^ 3G?.j%
=^-%EMF^ . %(.j[Q(JQSQ(EgQSQYD^3LMS{#"^5=^QcQcYieQRQE>;3 E*f=m%Ki=U.7H=^3$
M?[QQ0M^ .QYdUC=>dm QEHQ0DJcQ ( GQIi%(dG?U? ;m_ jS` ;H. LM.N?%(.CD fGMgCEm [f
DJ ij%(.CM%( ak=^ } U* E =k[-$ .?Zy U-
Y.Nd$. i%(>d.CDlJYJ Mg3U.C= ! .CW. a.NdmG-F=^"mf -"J E. ?fEfEj%(KLM.?%1.C=3
fMgCEm Q6MQ1? .C j J 2PT m%@DJ i%1.CM%(Q Y.%(JYj%6=^. j<`*{=^ dm._>M @ *g> Q
MQ(N?gV dm%EH Q(3J3G.j%WD^3LMlQYMQR?Y^_ ..HU7FZ;QR%0d.C=gQcf%(J =^ QEi.U;%E
vqrSyx3v~yv }rSvwn ox7pIvUo7vjw S|grjovp Y.7HKS'.S
)'^/` i%(;m a.Q*JYMgUD? =^ # & *.%(%(.fGD I^3^%a.Q:.;3]Df=7HY=^-%(MF^ =^ DmiKf
D.dNCE>dmWQEHgQ=D_JcQ'=^.-$gQ D(Q{^F^KGF DMiY=lI$J S)'^/` JK.UQ0M%(Q:D7CDm
f=fE3_3(Q f%1[J =^ Q1.CD%E-F [f M? i.%0=_Q f . J 3.QRj% F^ 7UD Q1gQ(%<Q1
[Q(Q0DF f %(CM3.%/7F^ E?f0fMQ(F ?mQE$Q/.? i^=J6MkEti[3Gj%<Q E,/%E;%/S@.' <)'^Q1
Q(Q(%<Q JK.Q=M%(=^ f=m% Y.%1? Q(.SGD%(N?l.? ;.$QR.C3D%(? 7F^ ;Ca"jK.? * <f%(J
I^G^=^Idm[kMJKW-ESEci.%(.JYSD%* Q fEj%E%(? ;m.Q(N? . Q0=JK.CDYmf'=^Y7F^:f=%Y.j%(?
Q(N.CDC%1?a;HK?GfDf%(.UC=*Lg*K,/%E;%:C .j[ SgX/?Gf=f0%(.NCEmK Q:UQSQ1.%(7H m6^.Gf
f QRN.CGD%1?Y%DFmHm=^@[JYkD? f%(.CDY Q:gQ0=%1.?K._?WQ:Q0DJK.CD?6= ;@g * gk-)'^
Yj% =^-%(Q(^?lf=m%I -ESElJK.Q=M%(JY ;H =^ ` a.Q g J jc.? =^ Q0DJ.SD?
MN%0D.=H 7c=^YJK.UQ0M%(JK(Q ?M%(F `{\('X)'V 9)TV/`{ a.QY !. f=%d._MQ fDCD[
F%(.SD%{=^.j .N;mM g6JUg)'^Q %E%(% Q0=JK.CD ^.Q@Q(W;N_cd.3G?.SD? MQ(F F%(M? ._?
.>%E;%E6=%(.j[Q(JQRQ([JKCD%*i%D;mQ(E,/%0;m%( * ,/.%E%(C3=* E ^3^ .%(YGUQSQ@Q(gQ(kDd6=^._
=^@` ;MP.S%(@=t%(7HYfEt%CQ=i%Ei[3Q2
3. The CALIPSO Deep Convection Algorithm
1. Lidar ratio retrieval
T%/.Q0D;.j$gQR.CDS%@73?.%RQ(d[kMJKcD7CDm f=fE3GU i%Df03GUQ
α
.%(%(<=%Edm? f%(J;gQ(j%0d.CDgQ:[f'.CDjM.CD? ;.j$gQ(U.CGDj%{i%Dmf=G3Q
β
-Ec%(?% c? Q(. %(.SE[Q(^i;mCYN_=^A;m.$Q(.SD% .?Y -ECEmYN[f=f033_U(Q JaMQ=;/.Q<Q=MgJK?g +6fGDY?f0?Y.Q
= α β
=^ 3?.%
%(.C=[=^-QP%(.CDmYQ .QRQ0MJK?6 Q=D.CHamQ0D.U Yk=^Y.@M?W.Hj%S
)'^ JK.F[M? [f=^ 3G?.j%%(.C= ?i?[Q mY=^YJ3%(i^HgQ(3.i%(i%0=Q [f=^I_M?g;M:7
JK.H.Q1Q U. ;m %(C=%Dd? f%([J .CDUM.CD? ;m.$gQ(.SDC%I;Q(%=d.CDgQ .( =^ %(M-=
.._HgQRQf `AV 9 =OX+ ;gQ1%Ed.CD[Q(?mfEfD%( .>F%EkD^JcQ.j%(]MQ1??jig?F m =^/i.k0HW[f
=^K.C=JYgQEi^%(c3.H%S[T m%/Q(JY =%(.[QDi.%(A_M?[Q1'.a=%(.Q(JYkD.UK._F%Ek=^J Q MQ(?;.UQR?
a=^6?f0fD%(/7c3?.%{%1CM%EcQ(>F.f%([J _3U.% %(FgQ.;mdm6.?W;m =^ M?G.Hm%SE
=^ .Q( mf f MGH .C3DM.SEF .Hj%CQ1Q0M^ .Q ?Ui =%Ei. =^$ NmdSE>d"QEHgQ0DJcQ(6=^
=%(.Q(JYkD.NW.F% =^J N._ ;Y.ii3?.Q=^ G.Q1% .:iC=%1.2D =^ fGMg33.H% .?
Q(>F.6Q .Ndm.G3.;Gl;H[?5=^ _M? 3.H%S*V/"LM.C= . ;ml?%(>d?a^G^ %1_.CDQY=^
M?1UDF%(.<D? .<GDUM.CD?5;m.$gQR.C3D% QD>F._
γ
=5=^lM? =%1.[Q(JYkD.U O3.CG j*O'.C<'.j'j j
γ
−
η
/
I^%(
η
3Q./JaMkDi[3 QR.CDS%EFcNm%E%1C=fD.CD%SUE =^/.Q16f'.Kmi.LM/M?.H%(=
Q( =^.C
γ
η
/)'^ 3?[.j% %(.C= ."=^MQ ; %(C=%ENdm? f%([J G3?.% i%1mf=GQ mf .CDjM.CD?
;.N$ Q1.CD% .? . Q0DJK.CDf
η
g)'^Q@QA=^QRQ(f{=^.>F%Ek=^J MQ(N? ;H `AV 9 =OX+ =%(C %Ed DCD =^ DigQ fK?ihdUC=>dM?[Q D#Z7$j%( 2 )'^GQ .7F%Ek=^J
^JYmFjMQ JY3%(i^HgQRGN._N[J igQ(kEm =^%(MF^M=^ M? .Hm% Q( =^ G3?.%
iC=%(.C=YQ{3JkD?YYmi=.G7H/=^3$KdCD>d QEHgQ=D_JKQ=^Q{Q . %1.Q(.;[email protected]
2. Lidar ratio retrieval on July 29 th
+@ + M7H 1c. `{\ 'KX){V 9)0TV/`: JYQSQ([ f=NMQ1? . Q(JK._3 QR.3 dUC=>d QEHQ0DUJ
!5,6GC ._ =^.C /D?[?^m%(_mUD._Hcd%/jW$J .? MiDa=^ =%Dmimi.CMQ1 =^7F^j%
=^.j $J ( JY.F5=^ ^F^Q0KQ(Cdm%(. $G[JcCDj%<Q Yj%( mJIieQ1? f 3 %EHgQ=D. Q2`{O9
;gQ(j%0d.CDgQK[fI.CDM.SD? ;m.$Q(.SD% ;Ca N .? j .%(5Q(^I7TF/ .Q .
fMgCEm mf=JKc.? .kDkM?' .mF.%(kD^JY3cmm%/Q(U.G-[6M%(F =^Q =JKf0%1._JK =^a \ 0
.%D%1HF =^ `{O9 f03 d%@=^ dmCDdm QEHQ0DJ . Q0=%1._tF[^U@.?l`{O9 ;Q(%Ed.S=mgQ
QE^ =^W mi mf=^ QEHgQ0DJ %(Q(Q/f%(J S $J .C](Q ?FQ*= Jam%( =^. $J 7 k(Q/U=%(.
.%(N.[jeQ1AD =^@NmUdCD>d@UD%S-) ^@`:O9 a.Q .C;3AD iS=%(.2D=^@M? G.Hm% .C.Q0 m
$7[JKCD% ;f=%( =^ 3.Q(% Q(>F._ a.Q [J i3NDjH .C3DM.SD? T>F /15;M 3?_U
;gQ(j%0d.CDgQ f%1[J =^ E Q=^ Ie9: C . (.GQ( JYMD? =^
\ =eQD^ =^-Q M?QEHQ0DJ Dj??Y?I6=@=^6Q0M%DfE.N
)'^ 33?.%Y%(.CDeQY%1C=%Ed??M%(7F =^ Q(.JK DJf=%(.JYl.j%(lQ(^ TF{MQ(F =^ `:O9
.>F% =^J E;3.U$*.?W=^ `AV@9 0O:X+ ai `*mdmCDm .>F%(k=^J ?Q(%(>;? .;d Ec%(? 2
&].CMQR f6=^ Q(JK._@fE33? fad3 [f =^l`{O9 gQ0=%0MJYa.?5=^ .%(QRQK[f@=^lM?
J MgEiG Q1.CD%D7-F Q gQ(7FGfDGN._UD6.j? =^ G?.j% %(.S= LM.S=m *LgY/ .; Q(GJYiGfE3U?
=
γ
QE^M? ;YD?W=^.C:kYGPm>H ;aigQ<Q(>;36D -=%(.i.CDYkMQ([Q f%1[J =^CM%E%1 Q0M?HcD `V 9 0O:X+ %(S=%E3Ndm. Q].Q@fD.% .Q].Wd.73? J MkD7i3 Q1.CD%E-F %E%(<= f=.UC=%*Q
.Cdm._33.N;3 a^WMQ(F=^ fGMg3[ Lg /?M%D7-F=^ `*V69 0O:X+ .j.7HQ( Q2){^ I Q(S(Qfd.kMeQ*.%1
dj%1H Q(GJ33.%(6JYgQ0K =^l %(.FN Y=^ Q1mJK M=Gj%cim(QKMiZ -AE=^ i.LM
i%=[Q f'=^M?e=^Y.F%(JY GQAdj%1H F[?g.%=^YM? N?FQ(=:mi.LM (edm._MQ
i%(.<=m.g?AMQ(UQ . JY%(@.ii%(i%E.CDA%(.j[Q(JD.U ;m.Q(? %(C=%Dd.=
)'^ Q(.JK [J i.j% Q1m a.Q:?MSD?K._3M?G.Hm%<Q:?[SDCD?YW+(MgHK g.j?c Q(3J3G.j%
;gQ(j%0d.CDgQ Ja.?[Yc+ M>H g
) ^W.dm%(.FY?7fDfE%(Y.? k(Q@Q=D.?.j%(? ?d3.CD .%(QE^Y
c. F.%(k=^JYGQ1.G cTF.Q*. fGMCDc[f^ JGJ MJ NmQ(G?j%(?ci=.?i=^
τ
#"^_ gQ(?%(7-F .GP_M? 3.H%<Q
τ
(g=^.Sd%(.jFc?7fDfE%1_WFQ].Q ^7F^ .Qj f=%+ M>H g( Q(^a7-F =^ ai `AdNCEm .Fm%=kD^J 3.N?[Q5D M-%(.Q0D3 %1Q0Mk(Q Q0M^
?kDmQ('.Q]$iCD?ga YCdm%('.Q
τ
7j%(.Q1Q1 ^?Gf=fE%1_NLMGj$[H ?j%(.Q(Q ;m_jWf=%
τ
0+ M>HK .?τ
0+(MgHYg 1[? /DW 0+ M>HK .? (0+(MgHg f=m%τ
) ^ Q0D.?.%(? ?d3.CDm Q(3J6MkD.MQ(>H F[Q/=^%(MF^ =^ Q(.JK ?U%(N.Q(*?%(ii>F f%([J d.>MQ F%(N.CD%=^.j j =UQSQ =^. )'^/?[j%(.Q16QUQEiG.37HKGJYi%0D.f=%{+(Mg>HYg 2TF{ QD^ Q/=^.C =^ `V@9 0O:X+ ai`*dCD .Fm%Dk=^J Q aG@Q0MkD? D =^ Q=M?H f
i=.37H/=^Gj$M?W3.Hj%<QS
3. Extinction retrieval
bKQ(7-F =^ `{O9 .CDUM.CD? ;m.$gQ1.CD%];Q(%Ed.SE[Q<XSR'g I.? =^c%(C%Dd?lG?.j%6%(.S=eQ
<XC1'g ( k/GQ/ieQRQ(>;g3Dl%(2=%Dd=^ .SM._ i.%0=CM3.CD;.$Q(N.CD%
β ( )
.C*=^ .kDkM?f%([J =^ Y0$ Yf=% Y.j%(?Q(kM=6D =^@3?.% LM.C= OP.CS.'j* j
β ( )
! "β
#$!( )
%
−
&η
'β
(
#)!*#
( )
+ !*#0
Yk=^
β
,$-( )
=^Y;Q1%0d? .CDUM.CD?;.$Q(N.CD%D.?.0/=^Y.kEM?Wf*G3?.%*iC=%1.C= c=^3.H%)E=^/M?aDif=%.@.?%Em$Fc33?.%G3$]=^6`{O9SV Q'=^@F[.f =^Q Q0M?HQ ._
i%(.<=m.6d.73?.C=h[fW=^ `V@9 0O:X + ai `*mUdCDh._F%Ek=^J RX[NCR@[/D . QEJYi[
.iiGN.CEmYfg=^Q .7F%Ek=^J Y3Gi%(d3?@. F[? f=G%<Q='.jii%DJK.CDmYf=% J i.%(Q( iM%EigQ(Q2
+@;.U$gQ1.CD%@i-%Ef033Q
β ( )
.%(%12=%ENdm? DCD _f=f=G3(Qα ( )
β ( )
⋅
( )
N._ ;.Q(37H ;D.? f=m% .H Fd 3.Hj% <XCR G/S ) ^Q"D^3LM a.Q .ii[33? D `{O 9
;gQ(j%0d.CDgQ f.SDM.CDN?I;m.$Q(.SD%'>Y3@M?gQ{f%1[J + M7HYg .? <XCR-[S\]Q0Mk(Q
f =^Q(c%(C=%Dd.Q a73{;i%(Q1D? .? [JIi.%(U? = Q(kM i%(;c;gQ(j%1dm.CDmQ =^c
Q(NCEm
4. Coincident observations of extinction in cirrus clouds
/M% -F`{\('KX[) V 9)DTV/`{ [>%E%=MQ M?[Q Y%1@;Q(%0dN?WJK.HY^M%<Q;H =^@`{O 9 E6=^A{\ 0
.? =^` Emc=^W# & * ( ;M JYgQ0 f{=^aD7JK =^;gQR%0dm.CDmgQ a%(c@QEJ MgD._MQS
)'^Q i.%0Kf =^ Q0M?H YGIf=[CMQ m =^li%(?[Q mf =JK Y^ =^ I [Q==%0MJY(Qa%(
fMgCEmF Q(GJ MkD.MQ(7HK.?a=^>%'a.>%1%(.fG a%(@f0HF E^aQ1._JK/.%(.NeQ1a=^.S =^AI
gQ0=%0MJY(Q a%( Ja[kD%EF =^ Q(.JK _M?g') lSd.>M.CD=^d.j% 3.;G3k=H f/ -ESE Yk(^
.kDkM?g.?a=^ %E%(.SE;SYjW%1Q=Mg(Qf=%([J ;m=^K7gQ==%0MJY(Q1gH .QRQ Y^ =^@# &
* a.Q k=^j% G3J ;gF % ?Q(j?7F =^ _M? .Hm%a%( [Q(3?%(N?gWOP%([?[Q f
;gQ(j%0d.CD fEk=F =^QI?Q(%(iDm f=%@+ M>H g .? .%(c?QR%(>;N? ){.;3lUeT m%/.N_^
`{O9i%(mf=G3%(?.CDQ [f=^Q=Miim%0=tFc{\ 0 .%(%(.fG a%( N[J i.%(N? =^eQ1 mf=^6# &
* =^l=7JKf%(.JK fc3?[N =^JY.GJWMJ ?_3.H";Ca ;m=^h.t%(%(.fG;m7F j
JMDQ2
VYQQ(N_ "XCR '=^ +(Mg>H g .?l .Q1Qa.%( H-i3. f =^ Q(JK.<Q1.G mdmCD>d
QEHgQ=DJQ@=^.C ?Cdi?lf%RLM=>H =^=%EiU.*.%(. JYmDm%(N?l?M%EF `{\ 'KX){V 9)0TV/`:]
ImkMJK $-ECEm f0fDG3(Q"%(S=%Ed? f%(J `{O9 ;.j$ Q1.CD%";gQ1%0d.C=mgQ MQ(F =^
`V 9 =OX+ YNi `*mdmCDm .7F%Ek=^J <XSR[@.?cgk .%(WQD^ cTF #=+ MH g ._?
TF #0+ M>H (Y=^ =^W# & * .kDkM?.CAm_3? im(Q i3D? dm%@ %(N? QEHJ ;m[QS
+@+ M7H g [=^6G?.j%iC=%(.<=c?i=^cQdm%EHd.%(.;3 W=JKWQ(.3Q*f{3QSQ =^. . JWMD
i%(f03QcQ(^ ?Ni% iS=%(.C= .?l%1.U_^hjl$[J E-F .%1M?l * S )'^QcQ1JcQK?M D
%(.i? Q(JK.G2Q1.3Wd.%(3.CDmQ@ =^cQEi.CD. ?Q==%(;-M=[ mf _M? a.CD%]DU()'^/D7CDm
f=fE3_3 Q F%1._37H c=^ j
j
J %(.F 0F%( mc=^K[%6Q1.S)'^cQ0M?U?
=JK_f%1._JK/mY+(MgHY0TF !Q(^KQ . Q0D.C;363G?.%'iC=%(.C=mY?i=^ *$J K.Ndm%(.FNm;MP Q
3Q<Q ^[JamFMQ( Yk=^ Y3?%'d.j% 3.C=mgQ Y%(C=%Ed?Y -ECEm d.>MQEf%([J
×
j D j JS EUDF%(.<=7-F =^Q( =C= i%(mf=G3Q/F[>dmQI.c^GF^H d.j% .N;3EJK Q(%(3QImf]mi=.?i=^gQ
0*QD^ ( Yk=^d.>MQ{=H-i[3.GHc%(.-F[Fc;CalI.? [V Q=^ i=.?[i=^ .ii%(.^Q
=^UQ(6^F^%d.>MQ1=^6%(C%Ed.Q;JY M%(3.N;3 f=% Ic%(.Q1mQj'/k GQYG$ Y=^.C
=^/f=m% a.%(?cQ(kM=W;mNmJKQ'M[Q0D.;3/.C'^>F^Kmi=3.?i=^gQ:.?N._Y;N[JY/?m>d%EFUO3.CG
C .6j[ * (.j? =^ ;m.$Q(.SD%@%(<M%E Q(>F[. ;m[JaQ@d%EH aU.$ .? Q1 mCM%<Q([gQ
[f=>M6=^a%1C=%Ed? dm.MQ2g)'^MQ@=CEm _f=f=G3(Q].C* .kDkM?Q1 Q0Me^ .Q=^Wdj% H
^F[^ =SEgQK.C/=^ G.j%EFQ0IiC=%1.C=?i=^gQ =%(?ml=^l% Q1.3l7TF ".? !
QE^M? ;A=%(.<D? Ik=^Y.CMDg
T%N.^K`{O 9 i%(f03GNgD7CDmKf0f=3GU(Q a%(I =%(.NCD?Wf%1mJ =^/` ?.CD./.C=^@im>U f
gQ(Q=# & *K._?a \ 0c7G?+6K+ M7HKg m=^ # & *a f%(J jY$[J .S' /Mi
= $J .j%(M? k,DT>F 1'.M?,a.Q/;gQRj%0d? ;Ca .? - g=^W \ 0
fE3 dm%=^[email protected]%(. ;mCYNYI.? kg) Q1.J i[3A=^6JK.$3J MgJ [fM?Y?.CD.=^
# & *-a.Q fGD QEi%(.7F gQ(3?"M? QEHQ0DJcQ( Y^3^ Q#Y^H D^Q1 i[(Q .j%( 7
^-%(m[F[. %(?%S )'^ DCD";Q1%0d? ;H"=^ ` ?M%(F =^Q ij% [?" Q Q(^Ih.Q
QEHJ ;m[Q TFc.UQ*. f MSEcf .kDkM? Yk=^c^%EUD.g;.j%<Q Q(^Y-F=^ MU%0D.j7U0H)'^
.Cdm%(.F DCD i%(f03l%(C=%DGdm? f%(J `{O9 ;gQRj%0d.CDgQ ?M%(F =^ Q1._JK =JKf%(.J 0Q
QE^a fGMG37NP=^ QE^.N?[? .%1. Q(^ YF =^ QED.j?.%(? ?Cd3.CD .%(M? =^c.Cd%1.F) ^
.F%(N_Ja_U;Ca";=^ [Q==%0MJY(Q Q F[? ;Ca jg* .? $JY YE^h. .dj%(.F
?7f=fD%(U"[f g
×
j J ;SY i%(f=G3Q(%I^G^ JYiG3Q =^.C =^ aji `*dCDm.>F% =^J QI^eQD7-F .ii%(i% .CDWd.>MQ/f=m%
&/ jg* $JY [.C=m ;SY .>%R%1._fG
a.Q@/Q0Mf=fE3GU f=%/J i.%(Q(g) ^ 3?.% Q1UQ .%DFWd._MQ mf DCD Mi ="j J
? 6 jk $J Y^%(A=^6Q(7F.FC(QD.HW.CDCUM.CD? 0%(.N?.% ?.2D.6QD^ Q=^@M?I;m.QR a.Q
.CM.j7H J M^ a% SWT m% [N.CD? Ja.Q0M%(JK(Q1 =^ =JK ?fEfEj%( .? ^%(UD.U
?GQ0D.N ;SY .%(%(.fGZ.%( "jm%D%(.CDN? IkD^ ?m3f0fD%(U 7 DCD f=fE3GU(QS
EUDF%(.<=7-Fl;=^ `:O9 .? ` i%(f=73QImf]D7C=[ f0f=3GU/d%@=^ %E%(j.CD? %(FmgQ
jg*a5 Y$J *3U.?[Q=c%(QDiC=>d i=.'?i=^Q
τ
f6U> *c.?lU* E) .C;3 ( =^W`{O9)?%(>d? d.>M Q//. G.j%EF%=^.ja=^@`D?%(dm?adm.MNYE^ =^@JK.Q0M%(JKMj%0D.7U=3Q
f6=^ Y gQ0=%0MJa_U(QS*)'^Q ?mfEfD%(lQ FGGF>;3l7 %(.?G.SE>d D%(JcQ( Fdm =^l3GJYk1?
iC=%(.C=Y[fg=^@`{O9 UEUDF%(.C=F =^@`{O9 D= i%([f=36d%=^6fGMG3.NHm%EjaD
$J 6F>dQY. JaM^ ^>F^%6dm.M [f
τ
g')'^ QIQY. dm%EH ^F[^ i=U.*?i=^lf=%I. G3?.%@D iC=%(.CD.?a?m3U.CDQ=^Ad.%(3.;G3k0Ha[fg=^ i%1mf=G A; .;M jg*/$J JK.HY;@?MADa.$Q(>F.*.? =^ [email protected]%0]mf*=^ci%(mf=G3 Q/i%(;.;7H M%(3.;g3')'^ ` ?CDS(QWQ1mJa
-ESE f0f=3GU(Q
α <
×
− J .C =^ =%Dmimi.CMQ1 d, $J .N%(?m-F D%(.?gQ(M?FgQ 3.CM^? .C@ f%(J ){.JYi.{*g*KAUg# =^.C/?-l].ii.%/ =^
G3?.%*%(S=%Ed.Q(0TF [=^Q( d.>MQ .j%(6d%EH gQRI =^Y` Q(W3d
×
− J ._?QE^M?Yg;@[Q(?[%1?Y.Q .CM.ji.%0DGUQS
+6Y+(MgH m=^ # & * KPf%([J SI$[J .C'aMiW l $J .C'm=^j? Ic.F.G
.C:S, %1? QEHJ ;[Q 7 TF !Sg` ;Q(%Edm.CEmgQ f-ESE.d%(.jF? dj% .kDkM? ;7gQ
?M%(FW=^3Q{ij% [? T7F* .%1aQD7JKG3.%'=K`:O9 %(C%DGSd.Q MQ(FW=^6`V@9 0O:X + ai `*mUdUC=[
.>F% =^J =^ 3.%EF %D%(m%/;.%<QY ` -ESEgQY.j%( ?M D =^ Q0DjU [fYQ(dj%(. ?.SD.
i7U(Q 7K.6Q(FG/.kDkM?]; S`*gQ(Q0DUak=^ TF -^>F^K$-=C=N[f=f033_U(QE3.%EF%=^._
j
J .j%(@;Q(%Edm?g &]=^ i%(f03Q .%(@YF[? .F%(N_Ja_U'f%(J _M?6=i Y$J ? 6D
G3?.% ;gQR%=d.CDgQ .C SK$[J Q@?M6D D.'Q(7F.P.CDM.S=m.Q*%(.?.j% ;Q(j%0d.C=gQ6Q(^ .
Yj%*M?;.Q1[V Q*=^ +(Mg>H gA.QR`{O9%(=%Ed.Q*.%1a^F^7Hcdm.%(G.;3 .C: .kDkM?Q
EFg; j $J ( ?MW= YN.$ QE>F. ._? =^cGGJKkD?lQ0D.S;GG0H [f=^cd%<Q([ ._F%Ek=^J
EUDF%(.<=m mf DCD i%(f=G3Q@3.?gQAD dj%1H ^GF^ mi=U. ?i=^Q E) .C;3j * .j? [-
%(QDiC=>d7HKf=% =^6`{O9.?a=^6` )'^Q1 d.>MQ.j%(6NmQ( Q=D =^a=^6fGMG0i%(f0336i=U.U
?i=^ f=m%*+(MH g S) ^ Q(3F[^UE>H Yj% i=U.?i=^ f%1[J `:O9ZD7CDmgQ Q [Q(Q0D
Yk=^/=D.G3?.%Q(>F..CDUM.C=g
5. Discussion and conclusion
)'^QcQ=M?H i%(UQ((Qa. [J i.j% Q1m ;Caldm[kMJK D7CDmN[f=fE33_U(QY;gQ1%Ed? f%1[J .
` (Q(kM i%(; .?%(C=%(d.Q*f%([J 3G?.j% ;m.$gQRU.C3D%EFci%(f=G3Q RX[NCR<)'^%(Im_3?
;gQ(j%0d.CDci%(?[Q .%(YJ i.%(?^F[^37F^DFc=^6d.j% 3.;Gk=H YkD^ .kDkM? <X2RS\]Q=Mgk(Q
QE^ .@d%EHYF[?.jF%(JY;CaW;m=^K7gQ==%0MJK(Q1gf=m%: DCDK[f=fE3GU(QAQ1[JYCDJKQ
.Q: .QIj
J TF2) ^Q*3JWi3Q'=^ `AV@9 EOX+ ai `AdC=m ._F%(k=^J Q:?[-F .
F? (; .C Q1_CD7-F G3?.%/%(.C=gQ f=%/i.LM M?[QSY YSd%(=^QImMQ([ Y.Q/%(.^?
MQ(F"MQ(F `{O9 ;gQ(j%1dm.CDmQ Y^%( J MkD>i[3 QRN.CGD%D7-F f=fEUC(Q .%(F7F>;g3IX[l=^
f==i-%E]mf .SM._ `*V 9 =OX+ ;Q(%Ed.SE[Q(YG3{;%(MF^HZj DJKQ Y3?% =^._#YkD^l`{O9:
J MgEiG Q(U.C3D%EF fEfDC(Q YG ^.d D ;m .NMDN? f=m% MQ(F . .ii%1mi%E.CD J6MkEi3
Q(N.CDC%D7-F %E%(<= f=.UC=% L[ Sc\@<=%Edm._ f5=^Q"i.%(.JKCD%h?i?[Q .??kE[.U
.>F% =^J QK.? ;Q(%Edm.CEmQc.?^lQKM(Q(? =^lQ(i mf6=^ dm._33?.CEm[f@=^ YNi
`*mUdC=Y.Fm%(k=^J k(Q1_3f(
+ d%(.3W=^"DCD _f=f=G3 i%(f03Q %(C=%Edm? f%([J `{O9 ;gQ(j%1dm.CDmQ Q(^ ^7F^j%
Q(JK.7 QRN._3 dm.%(3.N;3k0H EW=^ jEJKCD%<Q %(.jF'=^. =^ ` ;gQ1%Ed.CD[Q1eJaeQ=E>H ?M]D =^
Q(>F. D0GQ(l%1.CE *)'^ `{O9 dm.%(G.;G0HhN._ ; i[3.?Z;H =^ M[Q0D.S;G .SM%( mf =^
-ESE %(C=%Edm._ .F%Ek=^J Lgg@.<^tF[^ mi=3.P?i=^[Q1Y^3_^ %([email protected]%EFf0>MCM.S=mgQ
;.$gQRN.CGD%D7-F"f0f=3_3Kf%(J i%(f03G =5=^ Q(JY.G Q(N._3 dm.%(G.SE[Q 7Z`:O9
%(C%Ed.Q Q(^M?W=^%1_f=%( ;m =%(.<D?%Ik=^cN.CMEm .UQ{=^H J.H ';6i^HQ(GN._=+ d%(.G`
;gQ(j%0d.CDgQh.%( mfGD D.? YkD^7 =^ Q0D.?.%(? ?[d3.CD [f `{O9 %(S=%E3Ndm. Q2 VWQ
d.j% 3.CD[Qam3.%EF%Q1.3Qa.%( W_*%(i%1[?MN?: ^ %1C=%(d? i=.@?ji=^ QamH"Q(GF^=7H
.f0fDCDN? .?"/. ?fEfEj%( ;mCa =^ I gQ0=%0MJY(Q I^_ [Q(3?%(F D%RQ(CDF
;gQ(j%0d.CDgQ S'E =^lQ(Nm? N.Q1 0+(MgH ({=^ =CD_f=f=G3(QI%(C=%E3d? f%([J =^
G3?.% a%( Q(GF^D>Ha%=^.6=^gQ(@;gQRj%0d?2Q(0MY;H D^/` -)'^ Q:.Y;/$i[3.?a;HIE^
G3?.%@Q(F. ;m_F fM7H .CDUM.CD?;H=^Yi=N._37Hc=^3$ .NHm% mf'=^YdNCE>dm QEHQ0DJcQ(.?
=^MQcM.;3 D ijC=%(.<D =^ Y^[_M? 3.NHm% JY.Q0M%1? ;H"=^ ` + d%(.G@=^ 3G?.j%
i%Ef=%(JQ*%(.UQ(.;7H a7' Q=M_^ -=%(JK ?kD[Q Ed%EHK=^Gj$ mdmCD>dQEHgQ=D_J(._?
.Q ka.Q/Q(^ i%(dMQ(7Hc=^gQ(Y?Gf=fEj%(Q].%(>HlQ(FfE3.U* Q(JK._3QEi.CD.Q(N._3Q .?
.%(@>HK.6Q1?.%EHYfE>[email protected]%EF%Q(N._3A=%(j?[Q .?WDjF%(.CD? %(Q=Mk(QS
Yf=fE%1_UQc-ESEK_f=f=G3(Q*Q0DGQ0D=^MF^.?JYF[^U;m6?M D[Q0=%=MgJYUD._.?
.>F% =^JW3"GGJKkD.CD[Q 7 ;=^ %(<=%Ed. QR_^JQ %lQEi.S=.c.? DJ i%(.JYQ<JK.CDj^g T m%
gQ0D.Ne=^WG3?.%*%(.SE GQ].QSQ=MgJK?D Q0D.SH gQ0D.U* . M? i%(f=G3Q(<XCRgg/D I^3_^ 0Q
M%1.GQ0D 3f63.%EF ^.FQI7 JK3%(i^HgQ(3U._:i%(i%0=UQ ^.ii m . Q(F3 i%(f=G3 ;.Q(QS V
Q0M?H [f 3"%EHgQ=D._KQ(^.i"3.QSQ(fE3.CDm f=%(J ?im.%(_.CEmh%(.CDeQ Q0MFFQ=(Q >H GGJKkDU?
^._-Fg J3%1mi^HQ(GQ ak=^ .kDkM?.;d S $J dSE>dcN.Q1Q/;gQ1%Ed? + M>H g
.?c?M% F `\ 'KX) V@9)TVI`: GK[jC:. ;(g^ YSd% Q(JK.G<Q(N._36d.%(.CD[Q .%1WQ0D
igQ<Q(>;3m\]F.%1?mFc=^`K.UQYkD^ JK.H =^%*i%(;Q1k^.QA;m .%DFM? =^.C*N%EHgQ=D.Q
.cQ(^.CDC% I^YJYi.CD?6;H =^@._%(j%(.fG'% =^ i%E;@k(Q1_f=[3U.?F D.a.%0=f033.g%(.Q(@G
`{\('X)'V 9) TVI`{ YHJ Q(fDG3? S . Q0MFFQ= =^.C ?M =^ Q i^_[JK
;gQ(j%0d.CDgQf%1mJ =^ ` JYF[^UYd%1Q0=JK.CD ^ -ESEf=fE3_3D*iDU=.GH ;H5.Q
J M^.Q:.6fD.CD% mf,/%0;j%0* :.?K,6.%D%(CG * ^.dm %(;-MD?6=^GQ Y%E$g.%DFM7-F=^.C
=^ fD%E%(N? %E%Dm%RQ a%( =^"%(Q=Mgk mf f=.CMk=H %l.jii%(mi%D.CD NmJ i.j% Q1mgQ2@C=^GUQ<QR
.??kDm.Y%E$ JYF[^U =^%(f=%(Z;m %(LM>%(N? = ?SD%EJY 7f =^ F? .F%(jJY f=M?
;SY %(UQ0Mk(Qlf%1[J ;=^ [Q==%0MJK(Q 7 =^ i%(Q(j Q0M?H Q =^ ;Hi%(?M2 f ?mQ0=C
;gQ(j%0d.CD..?.._HgQRQ{;3.Q(QcN.^K7gQ==%0MJYD I^3_^ aM?cJ i[Q(.SD6f=m%:.^K=^%
.? N[3?_UD.7H GN.? D5QEJKG3.%@%(Q=Mg(QS + =^ =^%@^.j?=^cf=.S=^.C %(UQ0Mk(Q/f%([J ;m=^
gQ0=%0MJY(Q1 MQ(F dm%EH ?fEfD%( DN^3LMQ( Q(^ . F? .F%(jJY Q==%(F=^[Q"=^
f03?N7 $-ECEm f0fDG3(Q %(C%E3Ndm? f%(J ;m=^ gQ0=%0MJYU(QS[!%(jdm%('Cdm =^
.Q1@[[email protected]=>d ;3.Q1=^ f=.UC=^.Cg=^]dm.%(3.C=[Q:mfDCDYf0fE33P.%(6Q(J33.% Yk(^
.kDkM? Q(.JK E?.Hi%(f=G3Qf%(J N.^ gQ0=%=MgJYUQ==736Q=MFFQ=(Q =^ dj%0=3. d.%(.;G3k=H [f
G3?.%:%(C=%Edm._Q .;m =%0MQ0DN?[Ec.jH .Q(Ne%1C=%Ed.Q*f%([J ;=^cgQ0=%=MJY(Q*.j%( [Q(Q0DU f=m%
dm._>MQ mfK=C= D;m j
JY=^.C aM?"Q0D73@%(JK._ Q(JK.G/.fGD% .lMJK%(GU.U
%0%1C=g )'^ %(Q=Mg(Q .j%( UQEiUG.7H GJYi%0D.CU Q(N %(S=%E3Ndm. Q f%([J =^ QEi.U;%E
`V 9 =OX+ JYQSQ([ #"$% S ._ #Y7 QRm"; .dm._33.N;3Y3.?7F .j -DgQ(>d
JK.ii7FKf3@M?YmiU=.g.?WJY3%(i^HgQ(3.[i%1mi%=Q2
! "# %$&!'")($!*,+-+./10 "2345+6$-106798:0; <>= =@?A$-4CBEDF G8)HI "# "$-!'"KJ6 "4L0 M*4-2 "N'M.4L0O$'C0
<>= EPCQSRCTURCV-W-X J6DF.-*2Y6#8U#F'Z>?[2-$-\I]+.4#.% "2^798_<6= =a`6H$-2$L0b\.4 'MF "4'M "Y#.MBUS$&c
$-4-2_798<>=
=d`fe$-10;_gh7i! "#jk4CB
8U%0b "cmlneg So
.Fp\p-b'M
X
`^% 3.N5!" `^i[fD%(* VY'Y3.d.3A!" Y.f=fE37AO: /M;M QSQ1m.? O:
'I.F' (J i%(dF \/C=%Dd.Q f `A%E%0MQ `AM? OP.%=3 X[U `AMiF 9:G?.j%/.?
)'^%($E^.\/.N?mJS=%EAD^3LMQ( .4L0]D8h "$L0] " HI MjM\ %( [ *
,/.%E%(C3:)A+ c,6j%0;%1e g,Y &].CMJ F.%1?m%(`@c) I^He g,Y &].CMJWF.j%(?m%(.?
] !"'#"gQ0D$* XmJa._33 ^7F^7H%1_fDGNCE>dmlU j%1HQ0D.Q EG.SEkM? >%E%=MQS
M.,+6#8U
X
HI "
X
?[ C0\0 ?=jgj, 9: g
,/.%E%(C3 )+N[VY+ YHJcQ(fE3G?[!Z+!N,6G3 & VY\]3?m3H[ ,W!&@.SMgJYF.%(?j%(g)*O:
&*MgP.? ` \I[#";Q0Dj%A g`*mUdUC=>d F%(.S=[ [f:7%D%0MQ .%=^6=%(ii.CMQ1
X
M.,+6#8U X HI Mj X 'S
,/.%E%(C3/)*+'* `mJYJKI S*f=fEUC=>d %(.N?m>MQYf/GN M?li.j%0E_3 iiM.CDmgQ
?%(>d? f%([J ._%(j%(.fG/i%(;mQ ;H YHJcQ(fE3G?CI.0 S
X
=50;c.
X
g'M "$-4
X
- M'"
X
.NiD?g
,/%0;j% c 'K ) .$.[")* +,6.j%E%(<G .? O K Y;;Q Ki[^[JKCD%
JK.Q0M%(JK(Q mf=^ VYQEHJYJKC=%EH i.%(.JKCD%( kMJ D7CDm f0f=3_3 .?
&].$gQ1.SGD%%(.2=7IV@%0E@_M?[Q1
X .\p =h0]c. X 'MX !
' E
,/%0;j% C .'* `*[JYJK m C*f=fDCDdm %1.?mMQImf/3 M? i.%0=33 iiM.CDmgQ
?%(>d? f%([J ._%(j%(.fG/i%(;mQ ;H YHJcQ(fE3G?CI.0 S
X =50;c. X g'M "$-4 X - M'" X
.NiD?g
a.%0=JY.{ 9 {.j? +/$% &]_{!ZP] .? !3^QR:!Z9 j')'^ f=f=UC/f
M? H-ig@Y.%==^"Q %DFmH ;m.G.Y-,6;...7HQ(Q(
X .\pJ6DFc5$L0
'Sg/j
aNHJcQ(fE3_3?[VY-+.?a!5NT .%(LM^.%(,W!Z j+ =^@^F[^K.>;?gQf'.jdG>%E%=MQG
=^ =%Ei. i.GfE3%a.%(J i[=JY3%(i^HgQ(3.1%Ei%(SD.2=[Q/f%(J `: O$# .? f%(J