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- ΓαпїЅα Κούνδουρος
- 6 χρόνια πριν
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Transcript
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
19 7F (/+= 'BB'' ' + (5 >F )'5 (> 5 7G U / ' 5 B B + '' ''G( 7 7C+ = G( L 7(C7 ( E ((E>GE+ = '' ( E (7C+ 4 '' G( ( '' B (7F+ = B '((C 7B( (C BB+!#!#422$ *%'*$'2 %)*+ )5'$'$&% $6&7 = E '' (C B( 7(C 7 )> B /+ = ( 5 '' ' 5 '' (G '' ' ( + = B ( (C B (>F8+ =''G(G(7(F '+4''&'' 0+=( ('' G( B ( C ( F G( ' BF '(+ = ( )5 / ( G( + 4 BF ( '( ' G( BF 7''((7CO 7 + = 7(7CBF(' B (5 F'' 7(CB'(+ 4''5&''(- 05 ( + B> (F '' (CH*^'' )6(75.**/+
20 =B( ((G> '( + =( BF ( ( G> + 4 '' ( 5 F?(B ( + =( B ' C+4 ''5FBF'(' 5 ( '' + 9 &'' 0 + =''''J'(G>GC( (F 5(.***P1*)9445.**/+ L'.&!!J '(G GC( (F.*** P1*)9445.**/+ =''' B(-*+- "+( -. *-."+( -. +='J'> '''E''5 (Y.+"+( -. Y.+ "+( -. + = > '' ' ( F > 'J '+ '' F >' 'J ' E '' (F ( F 'J ' 5 >' ( 5.*
21 >F 7''( B+ 4 ( ( F B ' GC( (F+=( B I>(I (+ # B 85 (7C (C C 7C(+9((B )FF I (/ F 8)_** /5 F '' ' ( '' ( >F 7GF 7(F F '' (7C5 (( ( + ='J ' BK C( ( C ( O (>(+ = B ( K C B5 (7F)7(C /+ = 7C+ ='' ' ( > B + 4 '' ('( 5 '( ( 7(F + 9 ( (' B '' ' 7F ' B ( ' ( B 7( (+ = > '' ' >F ( (' 'JB(C+''' ( (5 '' ( QT'( +5.**R+ ='' ( L F (7F 7 F+!#40 1*$'% *+ ) #!#4#!'22+$ $3 %+$-%).' # =(7 BB +=G((''B B(7C' += F7GF 7(F.
22 )5'(5 (/ '' + #5 ( F G( '' (7C5 ' 55 C ' ( 5 B+= B(C( B+ ( -CG(F + B 5 (F + 4 G ( ( B ( '' (+ B'' 57(C+4(( (C C (7F+4G( ('(C ( B B (C 7(-+ B '' (7C )( /5 B + 4 ( G + = ( ( ( FIBCB+=B'' (F ( ( '' B ' ) (F5 ( 7(F CB(/+ =(7 B(+ ((7C ( (F ( F - ''+ = )7 / GC( F '( B + 4 G ( ( (( ' '( 7 ('' + =B 7 ( '' ' + ( 7 CB( '' ( (7 B..
23 (F+= K5 B(7F5>(F - ' F -' +!#4#40 1*$'.)0*)% *+ ) *&9% & % +* # =' F5B 5 ( 7'-+='>G(' B)/ B( ( (5 ((C' - +=(7 - ' F B Q!5 PH` $E T5,` 6 +5 ` <I( 75 R+ = ( ( ( F( F G( ( ' ) >/+ = ( F F 7 (7F+ > > G( B)*+,*-*+*a(/+ 4 ( B C( B - ( - + = &0 ' )#9/5 > (C 5 7 Q(+5PR+ =(B 'F( ' '' '+ Q 7( +5,R ( ( ( 'F (( 5( > B 7-' )*+,,-*+Ha(/+ = ( ( 7((B(K( ' '' + = F (C5( B 5 '( F B ' (7C+ =( ( (C '' F.
24 ( ( +(( 5'( ' [E+5`27 7<+5 P]+ = ' (C F F ( ( 7(F+=7(B(@=65-5( (F '' #b( F (C [E [( +5.**1]+ =( 2@9 [( +5 ]5 -'( 66##$%#5((( )*+11-.+c(/ ( 7F )( '/ )( /+ ''5 ( ( '' (C [ +5 H]+ ='((G'( ( B (' F + =7( B ( 2@9' ( F G '' ' [ +5 P]+ =( 296 )2-9( (/ 7 ( '( ' + ( ( F - F "!@29QT+5R+=( F > ('F''(C- + = ( >7B(' B ( (7 (F+ = G7C 7 ( B '' ( 5 ( ( B ( B F ( '' (2@9269+%( ( (( ( E E E + F 5 ( B5 B K '' >(.,
25 + = ( F ( F+ 4 -'()/ # =52- (-P52-5 #5 75 $ <@2 9W99 #9W99 45## 2@9 5#F ## 296 ## 269 B9 # P-I 6 )<(/ +d,+, P-.** 1* H-P.** -I.***-I.**.-I P H * *+d+. G( 3 *+11-*+P1µ( *+H-+.µ( )%A/ *+,-*+µ( *+,,-*+Hµ( 2 )A9-296/ *+,P-.+µ( *+,,-*+Hµ( 2 *+,,-*+µ( )/ τ τ)*/5 9 τ)h1/5α5η τ)λ/5''5η5α τ)h1/5η5α τ)h1/5α #B)Y/W =()-/ Y3 -( -4(B + Y#%A -! )4( / Y2K( B '' Y ' ) /'( Y + Y6' Y2F> Y'( Y6'+ *0)*&! 4 F > ( - B+ = ( τ α B( F '' #b(+ = ( η F('F+4 F'(+=B&''0 G'' ' )µ(/+=(& 0 ' +!#4#:0 1*$'.)0*)% *+ ) *&9% & % $ # +.++(F+ #- 5 (7 B ( F (7F+ 9 (K(-' + 5 '' B B ' 5.1
26 C( F ' B )'' G BE7F/()(' ' B B 5 B U /+ = ' B ( (C C ( G ' +4 F'F( ( ' 7 + 4(( ( - )5EU /5 - + ''(7B (F ''(7('+ (7 B ( B - (+ G ' 5 ( B B> )'K/5 ' ' 5 F ( ' 7 & ((=999 2 )2/5B' ' QT'(R+ ((5 7 ( 2@ =( 2@9 ( '' (7 ( (G '+ '' 2@9( (' '.+µ((' ' >B(F5 B(*+,P *+HPa(QT'(+5PR+=7(B2@9- ( F QT'( +5 PR+ =( 296 '(( ' +=(7' ' 7 (C ' ' Q2 7 < 5.R+ #- ' F5 7 ( F B ' *+* Q2 7 < +5.**,R+#- ' ' 75 ( (7 B ( 2@95 8=9 "!5 - > ' ' ( Q +5.**,R+ ( 2695 F ( -.H
27 (5 '> ' ' ( (7 B' ' 7 B()7CA+ D/+ 7F5'7(F5B F IF '' ( + = ' 2@# )*-.+1 a(/ Q= +5 5.**R ( > ' (#A66)+P a(/ Q# <( +5 R ( ( '' F ' 7(F+ ( F Q= +5 5 # <(5 P5 +5.**,R+ = ( B ( '' ' F Q +5.***R ( Q +5.**.R+ =(7 B '' ( '( 7 F F' (-FB+ (7B5& 0( 5 (( B (#A66 QT'( D75.R+ 4 7F ( B ' ' ) -(/ (7F ) /+ +.++= 7(5(@=6+ = C( -Q(+5P`E+5`4 +5PR+4((> ' ' +='> ' 5 '' B( (' F ' + = ( ( F (7C5 (B (( + =7( B '( (*+HP*+Hµ(Fτ5(C #b(α5f #9eτα' P+.P
28 *+1 * B ' ( 7F(F' -47 9) / ( B( '> ('>'K)2>F5#'F /+ = ( ( F ' (B 7-')*+,,-*+Ha(/+@=6' (' B ''' ' +=()Gf *+H µ(/ C '' ( B (7+ ' '5 - K5 ' 7 +''(C ' B (( (C ' B B B> Q6> (+5 R Q3 +5 1R+ =(C ' ( 7? ( (C(-(F5G((@=69Q 3+51R-''(+ +.++,4(''(75B(+ (1('5B5&0 -(+=.(''( B+F( B( 7 B+ = (C - F(.
29 Fτ '' #b(α5' ' τ)*+h1/5α 2@9 ' (5 τ)*+11*/5α 296 ' ( τ)*+11/5α 269 ' ( τ)*+h1/5α =()-/W#B)Y/ -9'((-FB Y>%A)C(5 \/ -2C' (-(F -!>F Y ' Y>7F -6' ' (F Y2 ' (G-' Y27' ' 7 (F+ -6' ' ('> -2C' Y27' '( + -6' ' ('> Y27' ' 7 (7F+ *0)*& 4 ' > (' - + B((7+ 4(7 (C5 (F 7G7C ( ' + = F - ' ( F- ' F+ 2@95 F B ( ±*+*±*+*1τ - (5 11* (5 ±*+*1±*+.*τ - Q6(+5.**1R+ F*+.5 >' (+F')τg*+*1/5-5BF**^h 5' F( ' ' += '' #b( F( >+= (C ( ( ' Q47+5.**.R+ 4(7 ( 7 ( (5 F GG' +.
30 % 7 B( (B '' B (7 + 4 ( B G ( 5 ( ( B (G-' ('+!#:+ $*$'%)*$-; # 2B> B >B C( -(+4B7C (@=6B> ' +!#:#! '$'3+' %)+$&%5 )''$*$' %)' $&$# ( ( ( 5 - ' + 45 ( - *+H1 µ( (C' (-(F('( (C ' + 9 ( X (( ( 2@95 ( (G '+ #- ' 5 ( (G- '5B.+.µ(5O (7F C('5B '( ' 5'B( C+ =I ' B (7 (7(+ #- ' F5 '( ( ( ) ' +.+./+ 7F >( ( K ( 5 ( )@969/ - Q47:7G+5.**.R+ *
31 B B (75 =@# B 45 %= ( B (5(5 ( +% BG5(- 5((2946@@=5 7B D.**+ ( 5 I I 7(FFF( (#+!#:#4''3*&706$'2 %)*$-; # =(2946@@= J'' ( ( B (G-' )*+,-.+.µ(/+ =I ' ( (' +@=69(F ' ' B 7- ')*+,,-*+Pµ(/+ = I ' B B' B B(G-'5IF.+.µ(+ # 5 5 (C >(5 F (7C &0+ 4 >( I (7 B ( 2@9 ) ' /+ ' B' (G-'5 ( 5.+. µ(5 ( ' ( >@=6+4 7 C(B ( '' 7' F 7( -' + =I '(I 7C ( (7 ( -+4I ' (' B(7( (( (2946@@=+!#:#:+*- '$'2'/&# #B-' 5 ( F (+ = I ' (C 7C 5 / (
32 - (5/ >B+ #- 5(7 ((C 'J + =I ' ( B 2946@@= >( 7(C #6@ B ( (+ =I ' '( ( - + % 7C ( FC B5 ( B '' G (7F ) /+ 4 B B ( ((''G' 'B (' +=(2946@@= '' ( ( - ' ( F+(BB)7 ((/ F-(2 (!64+ # 5( 2946@@= ( =#6 Q +5 *R5 = #( A99+ B ( '' --4G (-(+4B ( ( B 7F G ' B)' /+ 7C5 I > '' (C+D(B 7? ( ( ( 2946@@= 7( B > ' F+D(( C(B( (!64+= ('( ' ' > > G C F ((+ = 5 FC(5 C((( (I+ 4 B ' I Q"F+5.**1R+.
33 = 7C B ' (+4 (>'' (I = ' ' F F '( (B(2946@@= ( + ( 5 'J ''(7C ' + % I ' >( ( B B >( ( (( ' + =F( 7 B7(B5 '(( + =I ' B 7 B (7(C ( (7>7(+D. (7(F- ' )@=6/ 7 ' (5 (7 &7 0 )2@9/+!#:#=.*' *$'%)*$-; # = 7B)99/ '7F( (7 ( ( F 7GF B+ = C( 7 >( 7C+ 9 ( F 7F ( 2946@@=5 '' ( ( + = FC( 7 - ( ( 2946@@= ( ( ( 7(F5 + B5 75 7( B 2946@@= >+4(( Q"F +5.**1R+ ' FC( 7 B > - ' B ' ' + ( ' (7 B (.+.µ(+ = (7 F>''((2946@@=+
34 = B ( B (7 ) ( /+#B 5( > 7C '( (G-'(@=6+,
35 -*3'$4 ++*)'$+ 4#!-+; %%'22& '%*0 3$'$%+2)7'# 4#!#!'22& '%&*$3*)*$ 3-;# =F 7(C ''5 ( (C ''5 '' (5 B)'' (/+ = '' (5 7F5 ( 725B6G7F (5 B( ( 5G''G G( + 5 ( '' ( ( + = ''( F ' ' F CB( '' + = G( (> B 5 (C + 4 > B( ''+ => G( (( > + 5 ' '' ''5> 5' (( 1
36 = = = )99-/ O (F )π. 5 µ(/5 '' 5 > '' B(''5> + = '' > > '' '' B = + )99-./ ((''i * 5F '' '' ω* = )99-/ 7(C ''5 G( F'' F '' 7F (+ 5' 7 )Θ/( (( ( Θ) Ω =, π )99-,/, π 4 F G( B '' L Ω Θ5 ' ''+=Θ''+=G('' H
37 (C B > ( Θ) = ( Θ) ( Θ) 5OF)Θ/' 7+ =(CG( ('(' 7 B(G (C'' = ( Θ) ( Θ) π,, π Ω )99-1/ =' G(B''BB5-'' BC*''G(FBSC+ ' ' F 5 ' 7 )Θ/ '( (GL(=5 (( B ( Θ) = ( Θ) β )99-H/ = *. + β =. ( µ ) ( µ ) )99-P/ µ ''( )Θ/GL(=+ % '(((7(F ' 7E '' + = '' 7F ( G( '' 2+ = ''. π+ F((C2 ' λ + '' 5 P
38 (?(+> ' + 9 ' + = ' (>( = )99-/ 4 ( 7(F += B(5 ( ( ''+=GF( (+,*+11)7F F/+B(''B'KB )5 ( f+h*/ '( 7G )((5( g+,*/+g7ff5 (''B*+*+ 5 (''B'*+) \/+= ( ' (' B 5 5 (,,* *.*(QB<+5.***R+ 8(+ = ( 5 B(5 G ( Y e)/+b)/ D5F / ν ) = )99-/ O (C j 4 ((+
39 =D(F ( '' (C+ '5 ( ( (5 GF( B + '' (( ( QB5P,` 45.***R+ 5 ( &- (0F ( ) [ ( )] > σ+. π. σ =.. )99-*/ O * ( B( )µ( - /5 G ( σ -GF + 4 ( (( ( (( (-(+ 72+ = 7 2 ( '' ''5 > 7FQA51PR+(( 5''(C (5 -C+ =Fδ 5 7 (7F5 δ. = π+ + * * ( 5) + ( 5) )99-/ =' 7 )Θ/(''i * >
40 ( Θ) = *. π+ + *. π+ + ( 5) + ( Θ55) + ( ) ( 5) + ( ) )99-./ ω * =. π+ + * *. π+ + ( 5) + ( ) ( 5) + ( ) 7F )Θ/'( )99-./(J(()Θ55(/F)Θ55(/+ =G'' '(5 ''5 π+ + ( ) * =. π+ + ( ) * )99-,/.+++''(( + =F CB)( /5 7(C'' ''6G75F ( 72+=> 7' 7 ( B. ( Θ) = ( + Θ),. ( Θ) = ( Θ), )99-1/ )99-H/ 5 ' ( QB5P,R+=' >(B( *+*+# '5 '' ( 6G7,*
41 BH^( +4'' ( ''+ =F( δ ( >(B((λ -, (7F ( 7( ) '(/+ =''( (B ' G( G( + F ),*( /5 λ -, +' ' (B ' ( ( δ ( Q B5P,R+ 4#!#4'22+$ $3 %+2)7'.++.+='> + 4G'>F()!!/' + =' B ( +>(5' ( ((' ( B ( -) FF (C/+ =F ( ' ( ' (FG( 5(C ' 7(C '> + ' 5>(> ' '' C 5 G( ' 7 G(F( (' 5' ) '+'99-/+,
42 θ θ. L'.&9! 6'> ' G ' + O θ 5 θ θ B( 5 '> ' (C. > ' >(>+ = ' 7 K!5 F '55( 7( F' 7 + F5 B 7( F ( > ( 5 B(C += F 2>: F > B 7( F 7((F ( ( '' '> C 5 B( + ' (7C-5 B>(B() e/ ' ). e/5 F' (( µ µ = )99-P/ µ + µ µ µ = )99-/ µ + µ Oµ µ > B( ' + = ''!! F (C ' (C '( '> θ,.
43 ' (>(C+! >(F)99-/)99-.*/F.. ( θ ) = ( ) ((.. ( θ ) = ( ) " +. )99-/ )99-.*/ 4 '' ( = ''!! F 5 θ ' ' +='99-.B ''!B +'99-.-5B! B ' ' + Coefficient de Fresnel F P F Coefficient polarisé de Fresnel n= i Angle d incidence (en degrés) Angle d incidence (en degrés) (a) (b) L'.&94 )/A ''!B 5)/B ''!B ' + ' F ''!(B ' += ' ' G )5 7U / (+,+H5( B,
44 (G-' Q < +5 PR+ ' B5 (C ( +15 (G5 ( B 7-' QA +5 1R+ = ( ' ' (' ( + B '' ( ' (>+,-*+.) '+'99-.-/+ F'' ( ' ' '! += ( ' ( (C ='>''+ F (FCB ( ) '+' 99-/+ = C ' ' 7-7+ = ( K (( ( ( '> ' + = G( ( G( + 4 7(C ( '>B(+ L'.&9: 6'>''+ ='>''(' 7 + ( '> (' (5( ' + =( B 7(C '> 7(C '> '' G( Q!5 ` 85 PR+ =F ( ' ( ( F G( 5 (C ' 7 (C + =F 5,,
45 G(' 7(C''+=(CB ''G( ''6G7+ = ' 7 ' (( ' 7 (C '' + B F ' 5( B(G- '5(( ('> + 4#4*%& *%'*$'1 %0* # 4#4#!**;$ % $> # =(CK (( (F ( 7(F) /+% (F B5 B 7( F # (F$ +C2>:5( 7( F'' +C) 5 5% /5O ' > % 5 7( F# K ('JB ( ) ( ϖ ψ # # # ) = ϖ + + )99-./ O k '' 7 > ( 7 7( Fϖ (F+ 5 >( B 7( F 5 B5) '+'99-,/+,1
46 m l # L'.&9= 6F) 5 /+ = l5f > ) 5 /(Cm B( + % 'J F'((<Q47<751*R+9 ( (C (C 7( G( F (C+4(C>() 5 / (( & # + # ' =.. = )99-../.. = )99-./ # #. # # ( ) ψ )99-.,/ ( ) ( =. # # ψ )99-.1/ 4B(G(+=F(C< ( '5 K'(K( + = (C 9 ` $5 % A +=(C<>(C FB & = + ' ( )99-.H/ (.χ ) = ' )99-.P/,H
47 (. β ) =. ( + '. )99-./ G(5 B) e /5G 7''F C (G (5 ( χ ) ( χ ) + 4 G( F( (C 9+ 4 G( B (( (7C+ B (7C ' )7(C '' '>/5 G( ( K (((((C(C(+=B> T:5P5(F (C C '+ 5 G( K (( ((C95%5$'' + = F B ( F ( 7( G( & = & + & )99-./ &.. + ' = = )99-*/ & & (.χ ) = ' )99-/ O & & (G(5> lf > =( (' + = ( B( G( '' S ' 7 GC( -(7C+ 4 ( F ( G( ( + 4 ( 5 ((+4F5(' B 5( "+( `(F'5,P
48 (( "+( µ( - += ( (=F ( θ 5θ 5ϕ 5ϕ ) ) ) ( θ 5θ 5ϕ 5ϕ ) n π ) ) = )99-./ # O=n( 5 (7(7C>( "+( -. +µ( - 5θ θ B E7>B5ϕ ϕ B E(+ =F5=5KB((C<9 ( ( ( )=e= Y= /+ => ( (= (C<$%>( (( + ' = π )99-/ # =(C +5 ( 5BF 7( F '')' B/B F C+ 5 ( ( ( '' >F== + # 5 ( ' +47GF(' ' 5 ' ' 7 ( F J+% ' ' ( G( F' 7+ # (( (7C5 > ' 5 ρ5 B ρ ( θ θ 5ϕ 5ϕ ) ) ) n. n. ( θ5θ) 5ϕ5ϕ) ) ( θ ) 5 = )99-,/,
49 >(' ρ 5 F ρ ( θ θ 5ϕ 5ϕ ) ) ) ( θ5θ) 5ϕ5ϕ) ) ( θ ) 5 = )99-1/ 4F( ( (+ 5( > + 4#: '&)*$'%&*$?&3*&*3$&# = ( GC( o- -(7Cp (' (7C+ G( F '' S 5 ( ('' (I + 5 B >( ( ( + '' 7GF (C ( ' F + '5 '' + 4#:#! $ (( µ ) ω*, π ( δ5 µ 5ϕ ). π * δ ) ) = ω * ( δ5 µ 5ϕ ) + ( µ 5ϕ 5 µ 5ϕ ) +, π ( δ5 µ X5ϕX) ( µ X5ϕX5 µ 5ϕ ) ) ) ) ) µ XϕX ) ) # + δ µ )99-H/ µ5 µ µ B ) B( ϕ5 ϕ ϕ B / E7> ) B( E(>/ 5 B+ =,
50 C((F (''('' G('' )µ5ϕ/b B)µ B 5ϕ B /+ ''5 F ' > ( (7F(((((7C ( Θ5δ ) ( Θ δ ) = ( Θ) 5' ((5 δ ω + µ µ µ ) 5 )99-P/, µ + µ ) Θ'' B+)Θ/' 7 (o-( pδf5f5δeδ Yδ ( + F ( = + '5 F µ µ (>5F)99-P/B ( Θ) ) ( ) ω* δ Θ =, µ ) )99-/ O=( ((7F' >( ''(+= (((( 5= 5 ( 5= ( 5' (( ( Θ) ω* δ = ( Θ) δ =, µ ), µ ) ( Θ) ( Θ) 5(J' 7)Θ/' 7F)Θ/+ '(5 ( F F (' (7B+=( ( ' + 5 ( 1*
51 >( (( ( (+ B F >( I' 5 O ( ( ''FB+ 4#:#4%+)' *$'% &2* #.++.+' F+ ='>G(' 5 7(C &0+ = ( ( ( I '>!+ (C ('5 (C ' K I> ' ' 7) ' (/ F+=' B' (4>2<51,+(C) LF(7/5' FF( B7E B B+ =( ' 5)/ ''!!! 5)/(B)θ 5θ B ϕ -ϕ B /)/ + = B B (C ( (C+ =F BB'5' G(' 7 + =F (C ( )( /5 G(' 7'( ( ( ( B+ = ( F (B 7I- (+ = ' F( ( (' +4- '' ( '' )7G 5 77G5 ( U /+ 4 ' '' ( (( ( + C( ( > `(( 5'' (,* (5-1
52 (+4'' )HP*-..**(/5 F(B> F LC+=' (( ((CT<5,+4' (F(BB+F (C F' ( ' = A9+ 4(( B 7 5 ' ' 'BG(' +4BC'' ( ' 7+''G5 ( BA95' (( *(& H1 HP* = )99-,*/ H1 + 4 '' (( B5 (B)HP*(/ 7-')H1(/+ ' B5 ' B)5B B ' /+ = ' B A9 )f*+/ F G(F( ' B` B' B)> 'K/+=B ')g*+/ G B ( )> B55/+'99-15 F ''' + HP* 1.
53 0.60 Surface végétale Sol nu 0.50 Reflectance de surface Longueur d onde (nm) L'.&9" ' B+ = ' > - B ' ' H QA( +5 PR ' B F+ 4 G (( ( ( '> ' (G ( ( B+4 7(('' CF ' )( G( '' (/+ = ' + = ' B B ' B5 HP* H1 (5 (B 77G+=' +,.+*µ( +5 B B ( '+ = ' > B(K'' Q8G+5R+ = '' (7C B A9 - F '' (7C ( HP* ( F H1 (+#- 5 (CC+A9 '' (7C5 B C ( B - + = ' C'HP*H1(5 B 1
54 ''(7F+=A9 7E ) /+ 5 A95 ' '' ' FB' ' + 6' + '' ( F ' 5 ( 5 K (( ( 7GF Q"'5 P1` A A 5 ` +5.**1R+ =F 99-, ((' ' 5ρ5 (( )/ )./ ) >./ ) ρ = ρ + ρ + ρ + ρ + ρ )99-,/ )/ O ρ ( ('> 5 L! ) '+.++.+/5 )./ ρ 7(C & '> 05 >C( '> ' ' (5 ρ ) >./ 7(C'>(5 ρ ) '> '' B() ' / ρ ( G( ''F(BI( ' + 5((' '' ( G( ' ) ( - > '> /+ (( ' ' (( (( ''+ = '( ( F ( ' ' C( (>+''(C 5 >5' B QA +5 *` 6I +5.` 67( +5 R+ ((5 (C 6I 67( ( Q2 7< 1,
55 +5 P` PR+ 9> B (C5 > (B ' (C Q= +5.**` 2 +5.**,R+ C = +5.**5(C4747('(F( ( B> ' ' B ' *^) ( B 7-'/+ B5 (7 5'( ( + F (C+ 6' + (' 5 (' (( 7(C ' 5 G( '' ) 5 'U/+= BC '>5 F '>. +%( ( ' ' ρ = ( ρ )/ ρ = ρ + ρ + ρ )99-,./ )/ )./ ( (' B( )B # ''/+ % F (F ' > B)B ' (F =G5./+ '')Θ 7 *Z/5 ' ' ((( '( '+ 4 7(C B ( ' )B5 )./ F5 ' ( U /+ = F ρ ρ (( 7(C+= ( '> 5 ρ )./ 5 F (F ' (BQ"''5P1R+"<+5P 11
56 ( ρ ' >F 7 B B'+ = F ' ( '> G( ' ( (' )'B>5U /5 > B 7''+=7G7C(C F ' F( ( (+ = ' ' 5)/ 7F ' ()!/5)/ F(F ' )' ' (5 ' B5 7 U / )/ ( B) ( B/+ B B>5 (( (C B QA 851RQ6>(5R+4(C ( G ' 7( B5F''(+ '( '5 > (' ' ' 6 Q3+51R5 Oγ7)γeπ-Θ/+! " ( γ ) ( µ + µ ) =, )99-,/ %(CQ3+51R+%( ' 5 ( ' (5 (C +=''(G( (( (C' B+=>' ' 6 5! ( γ ) ) ) = ", µ + µ )99-,,/ 1H
57 %(C ' (-(F ( B B Q 3+5 R+ 9 (C 71) 1++./+ =(C -5( B 7-')HP*-H1 (/+ ( B 5 ''!! F( ' ) '+'99-.-/F' 'B QA+51R5 F '((@=6-9Q+5 R+ 4#:#:% %$* 2$*%'*$'2# ''(7BF'') '+ F99-H/+ ''')@/B QE +5 R+ 4 ( (C < G( '' GC( ' -(7C E>+ 9 ( (( ('' ' F )8/5F'>''' (+ (( ( (5'B5-(+#- ' 5 ( ( ( >( ''(+(5((5 ' ' H QA( +HR5 '' E (7F((+ = ( (5 F ((((I 7B+ 1P
58 1
59 -*3'$: '3$'' $&$*)9*3*. % % %+ 4 C( 7 >( + G B F 7F ( 2946@@=5 '' (( (( + = ' (C (( ( 2946@@= G( '' GC( -(7C) ( '' /+#- F'(CF((F(( @@= '' ( 5 F ( B B '' (5+ 5 K(( B ((+ (C 75 ' 7F 2946@@= F(( + ' (5 '' (C (> ( F >(+ =(7 (B(B(+ B ( (5 > I ' B5 (7F '' G 1
60 ( + ( :#! ( ' - ( $ '3$' CB ( + ' $ & :#!#! B 5 F >.5 ( C / ( H*Z) *+.Z /+ L 7 F ( ( + = 999- / F ' F..** (+ = ) 5 > L'.& (.+ + *) # ( ' > ( +, *5 HP*5 H15 H** = F F ( # ' G '' 9! A ( 5 5 G 5 ' ( C ( G C( F 5 B F )B + ' ' B ' 1 ( ( 1 G H* B F )./ + 7 F
61 Transmission nm 670 nm 2200 nm 1600 nm 490 nm Longueur d onde (nm) L'.&94 = F (2946@@=+ =('') '+>999-/ ' 7C (C + 4 L ( B '5(-7+ = >,*5HP*H1( (7 (+ 7 98# ' dz4 > H**..**(+= ((- (+ = 75 ( (> 98#5 7 F 7 ( ( C ' 5 ( ( F +=''(((CF ()+.++.+/+ = >,*5HP*H1(G).,*HP*(PH1(/+%G'')6/5> ((G'5 >H**..**(+=( > L5 )+.+./+ = 7(B()9!@A/ (5 5+1.Z5 F *((C <((+ H
62 =( > '' B F ( ' I L + 4 (( ( B' 7( B ()+.+,/+ = F1() </*(5*51(B+ = FBX(K(X B5 'J((B+%I (( *(5 F BHPF + :#!#4''3%)* &# &052>( (5. + ( α ) = )999-/. O= = ( ( B( ( G( α 7( F G+ &(C0)= e*/5b ( (G (B+ = (C 7( FX (F )'999-/ F G H* Q8 +5.R+ 4 ' (( ' (5 ( 5 ( Q65R+ H.
63 # χ H*Yχ # χ # χ H*-χ. )/ )/ ) / L'.& 9:*0 7(F(+=B # 7( F χ >. + =2((( (= 7FB (( λ/ ). π ( λ) = + ( λ) + χ. ) λ/... ( λ) = + ( λ) ( χ ) λ/ ). π ( λ) = + ( λ) χ. )999-./ )999-/ )999-,/ = GC( F ( ( F 7 7 ) > χ/+ 5 (C FB.) +. + / = )999-1/.... = ( ) ( ) ( ) )999-H/ (. χ ) =... )999-P/ = ** )^/)999-/ H
64 :#!#:%+)' *$'3- '/&%& '.*) &+# = G 7 F+ 9 '( '> 7 '' ( FF+ 4 '' B ((F4+= ((F ( ( F B ( ( =+ = ( '> F ( ( ((F+1(5G(F ( 7E,(+ 4G 5 F'F'' BF J (C+47(C >F B 7(F+ % B ( F ( ( G(F( + 4(5 ((EF4 * 5'' >(+ ( F > 5 B 5 ( F 5 BEFX>E '+ =(EF '' ( 7GF >(+ 4( 5 7G7C I' > ( 7F B ( (( ( λ) *5 ( λ) + ( λ) = 5.5 ( λ) = )999-/ O 4 e5.5 )λ/ 4 *5e5.5 )λ/ ( (F E F ( ( 7F(# e5.5 )λ/ '' 5 -+ :#!#=**$+' *$'%)+$*)*.*0 )&# = ( '' ( B ( ( (( () ' 799/+=(( H,
65 G( ( 7C ) (/+ 7F5 '( )"S(. Sc(S/B 7C +>(C7C )=#36=-*,1-=-.**-/+,*(H**(5 B. ^ 5 F..**(5 CBP^+=>(()(G1*F / (( '' #)λ/f ( λ) ( λ) [ ( λ) ( λ) ] ( λ) # = )999-*/, π + * O 4 )λ/ 4 * )λ/ ( (F ( ( = 7C )λ/( B7C)"S(. Sc(S/+ =G(B7C)= e*/+c2)999- /5( ((B= 7C )λ/s.+f5 > 7F ( )999-1/ )999-H/ B.) '+>999-/+ =''(( 7(F5 ( )λ/ B λ5 '5 (' ')λ/)999-/+ # λ λ = λ ( λ) # ( λ) # λ ( λ) λ λ )999-/ = ( ' '' 7F B 5 '' 7F 7F+ '' F -B+2946@@= B'B7C+= (G (( ' + = '' -''JB H1
66 - ( λ) 5.. ( λ) *5 ( λ) ( λ) ( λ) = )999-./ O ( ` '' - B + => '' B + ( ) + ( λ) ( λ) λ. -5. *5. = )999-/ = '' '((( '4 -F( (BC ( )λ/q9f5r+ :#!#"$'$&% &)* &)'+C)+$*)*.# = (' ( ( '' + C '.** ) '+ > 999-H/5 ( '' *^..** ( ' H^ += '' -)999-./'F '' += '' - '.^) '+>999-H/+ :#4 **$+' *$' % 3''3*&7 3**;$ ' $&$*&7 $ $*'$$% & # :#4#! '0')'$+%)+$*)*.C)*$3+*$&# = ( '' ( ().1Z4/+ = ( ' ( 2946@@= ( ( 1Z,*Z4+ = ( 5 X(5 B( HH
67 '5 K ( 7(F (+ = ( >(5 ( B * *Z4 ( 7+ ( B ( B+ 4 7(F B B '' X X( 7GF + 5 ' 999-,5 B I E F (5 B '' (!64)B_.<(/+B5>999-.5(K( FB( F(( (''+ Zéro optique x nm 670 nm 1600 nm 2200 nm 490 nm Température de l instrument ( ) T1 T2 T :30 10:45 11:00 11:15 11:30 11:45 12:00 12:15 12:30 Temps d acquisition (UT) :30 10:45 11:00 11:15 11:30 11:45 12:00 12:15 12:30 Temps d acquisition (UT) L'.& 9= A E F B (5 L (5 B'' 7).<(/+ 4 B( E F B ( > H**..** ( ( K + 9 ( G B >,*5 HP* H1 (+ ''(H**..**(+ 5(('' ( '999-,+ (5 B ( B ( ' E F+ 4 ' B ' ' + '( (+ = X( ( 7C B '> )*+^/+(>E 7F HP
68 7FX+' ** (+ 5 E (5( (K(( * + 7 ( ( 7 ) * HZ4/+ = > P1 P2 P CN-CN 0 (T)/CN-CN 0 (T 0 ) Température de l instrument (en C) L'.& 9" (..** ( B + 4FFXXGX''C((X..**(+(FF ((() f1*z4/ B '' X^) H**( (/+45 5'' B B ( 5 F > + = '' B B B (''(''F + =' (( '' B ) '+>999-/+ >,*(HP*(5B(>( '' X(K(+C5H1( '' ( ( 5 (>( BC,+1^+ ( '' ( ( F '999-1' G(,+( H
69 ( F 2946@@=5 F ' ( ' '' ( ( 5 ( '' (F F+ :#4#4$D)%&$*&7%3)*' *$'# = L > ( ( '' ' ( ( G( ( 7C > QD+;+ 35 (( R+ 4 GC( F (. ( B + =('. ( ( I > ( B *5.^+ (>(2946@@=)*1*^/> &B0' '+='999- H+ Taux de polarisation MICROPOL Pmes 490nm Pmes 670nm Pmes 865nm y=0.97 x R=0.99 y=0.98 x R=0.99 y=0.89 x R=0.99 Taux de polarisation MICROPOL Pmes 1600nm Pmes 2200nm y= 1.00 x R=0.99 y= 0.69 x R= Pvrai Pvrai )/)/ L'.& 9B = > ( 2946@@= ' > B?>H**..**()/,*5HP*5H1()/+ >,*5 HP* H** (5 ( ( > B B ',^+# H1 (5 B *^+#..** (5 ( -( > C *^+ = L > '' 7F ( B B '' L 7C+ 4 B ( ( F F G B + 5 ' 5 H
70 >(+=( 5 > F999-5F= e=n + F 7G7C F G( ( (+ :#4#: $'*$'%&0&'$*%'+$'/&# = ( B ( ( ).1Z4/+% GC( 7 ( ( X 7F X+4 L7C+= G (G **F 7FB+=> (CF( = = >)999-,/+4> G >( = 5=. 5= + = B (F ( > BI?+ B5B(> *^+ 4 B B (I B F B (+ = )(/ =( (G (+ = =,* *5* * -1 H * -1 HP* *5. *5 * -1 * -1 H1 *5,, *5 * -1 P * -1 H** *5, 51 * -1 * * -1..** *5H., * -1 * -1 *0)*& 9! 3 (F ( @@=+ J ( B5 B '' ( 71Z41Z4+ (((5B (G 5 B B (' ' BB(+# (5B> (2@95 (.+* -,,+* -, B,P*-.*(QT'(+5R+ P*
71 :#4#=$D)%)*)'.$% $'3)$ # = ( ( B + B 7F B ( (K(5 K'+ B > ( B' ( B 7F F 5 5 ((( 7(B()9!@A/+ B B' ( > + =( F B (5 ' B 7C + ' B 2946@@=>F>+=qrC B () '+ > ( /+ B> E 7FB+ '999-PFH1( P1 P2 P P1 P2 P3 CN-CN 0 (T) CN-CN 0 (T) PHI ( ) TETA ( ) L'.&9( 4L H1(5> L+ = ( F B + =( B'(B) '+>999-1/+BB 7( B( (+1.+ DF 5B ( ((B '+>(2946@@=5((' (F( G( (+ 5 B (7 B ( B P
72 (+ ( (7 ' F (FB+ :#:++$'%0 1*$'%)' $&$%*+3$+# :#:#!+2''$'%.*%&.++$'/& &$') # =C( ( ((B ((B+ ( E7>θ Bθ B 5E(')ϕ /''Θ5'' % r B %B r % 2 Θ ϕ L'.& 9E5 8( B B 5 B = 2 B ' (+ = B ' 5 ' ) ' F B( 5B (' 2+= BE('ϕ (K(F ''F) ' 99-/+% E( B B &'' B0 F E(*Z B&''0 P.
73 :#:#4+$-%%*)&)# = BCQ#>GERB'999-+ > G %B # E L'.&98 4 BCQ#>GERB+ =CQ#>GERC7( +=# B B5 'B ' (+=>#E> B+ => #G > B B+ => #> > >. > B 7+ F5 B5 '> ( ' B ( > #G B5 (B> B(BC'F)*Z51Z5 *Z,1Z/+ 4 ( B ( BB+ =B ' ) >( CQ#>GER (( ' ) ') = * )999-,/ ') = BB ' '&B02 7 7? C FQ@V;MR )'999-*/+ P
74 M ' ) # ' ' 2 ψ ; L'.&9!< BC FQ@V;MR+ =CQ@V;MR C F+@V*Z *Z` L + = F ψ φ B(B+ %( ( >( B ' ) C FQ@V;MR+= B B ') ' ) =. Ψ. φ. γ.. * )999-1/ ') O2 ( ψ@m5φ@v5γ55 B(55 7F5+ V = 7F5 ( & B0+ = > #G B5 ( B((F+= > #E B5 ( B( 7+ '5 7F >#> B+ 9 ( *.π+ 4 F' B 7F((+ P,
75 = ' ) (F(FB C F +. = λ' ) )999-H/ 9''BλFs. sg) 7F/+%' λ (5 2 Q@V;MR += 7I'' ( B 5 B ( +5> B ( ( ( B+ ='(((7(F (7 Q+!J5 (( BR+ = ( B ( ( 7B G((+= E7>B E( '5 ( ( 5 ( 7( F ''+ = B5 ( + (' B(F+ :#:#:1$'.++$'/&%& '.%)*3)*' *$'# =F= '999-H F((+ ( &0+=χ B. ) ' ' 999-/+ ξ '' )' B/+= >7(C'> ''(C ('')ξ *Z/+4 7(C'> ''(( (I + 4 '' B ( G( C( '' )ξ *Z/+ 5 P1
76 (B(5 B+=' B (B(B 7 '')Θ *Z/+ BξF**ZBKB5>F7F( (+ F5 ξ χ () '+ F 999-P/5 ξ F (( = 5=. = +B 7FF G( ( B '5 F C( ( + F B B ( 5 *gξgπs,*gξgπs,5g( (( ( '' '5 ( '' '+= ξ>999-p F F(χ(B+ = ( ( ( ( B (F '+ '5 B ( ( '' E (7F ) 7GF/5 ( '' ()((7(F/+ 'FG((+ ( ( ( ( F.**+4' G (2946@@=+ :#= '3$'%)*0* %%+ *&&)+ %3&' 4<<!# 2946@@= FE B F ( ( + = > ( (!645! ( &05 (B'' ---4) (4/+ PH
77 =(( (( # +# '' (5( 2946@@= ((5( (!64+ ( 7(F G(F( B ( (F ( #6@S@@+ ( ( t '' 99+# (!645 =#6 ( ' ''( ((5I ' ( ( F > B > + :#=#! '3$'.++*)% *3*. % & # +,++= ((!64+ = I ' (!64 F ( B BB 7+4 ( ((B&0I ' - 2+ = (!64! 5+=B 7 7'J!#=4@-.*)!-.*/ (.P (.@.**+ 4 G B BB7).<(/+=B(G!-.*P* (S+=!-.*F(2946@@=5=#6Q +5 *R QE +5 R+ (5 * B '' = ( F * B (!64+ =75 G ' B5 F (7F 5 + PP
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
79 7(C' +4B t B -'( 66#)2@9/+ = B ( 2@ Latitude ( ) Photométres Longitude ( ) L'.&9!! I 7B (!64 5 7(C )/5 #--# )./5 )/5 #B )1/ 3> )H/ 7(C C 2),/+ +,++.= (4+ ( ( B '' 'B.** (.**,---4).**-.**,/+=I ' > ( / B ' / B(---4+ =B (!64B G#66@",-#.5(' (2946@@=+4B '' (, <( 5 B H* (S+ 4 ( B (F2! +=' KB F B F C BB+= B5 P
80 7E5 B ( 2@9+ (7F C ( 7 7' F ' += 'B'' B ( (K( >( ' C B (F ) (F =F/ B 7(F '' (+ = B ( ( 7C+ D ' B ' B ' '' B+ ( -C (C C B 'B (+ (B+ %B( 'F( B+ (!645 ( B > B( + 4 ( ( B B F I (F(B+ 7F>B5 7FB B('>' '( B7+ >(7(C#6@S@@+ (5 B '' ( >( 7(C #6@S@@ = )1*+H*u5 +,u/ <F )1+*,Z5.+PZ/+ ( 7(F ( ( 7(C)2946@@/+ G' B+ B 7 7 '' ( - ' B + >( *HS*S.**,5 > B - ' B G 5 ( ' + % ((F (G(F(((' ' B + + *
81 =E=5E()G/ =5 > <F)> 3-=/5 ((' B+ 5 7 B '' (7F B BC''+B(-5 <F5 7F+= FB C = A ' -+=999-''B (5 75 B (7FBG+ *$ S*.S* S*.S* S*S*.,S*S*.S*PS*,.S*PS*, *HS*S*, S*S*1 & NO +0&$P2' * P-.,1 **- 1, **- H * * **- 1* * **- 1 * **- *.* * *- * **- ** )$'$&% N>O *+1 *+. 3% &2* &1) *)' *$' <FS4 2 #>- = <FS4 2 #>- = <FS4 2 #>=-#( #>=F- A #>=F- A 0 1*$' *+3$+ '(5B 7'(<F`B C'5 FF B+ 4 (7F C B B` EB5 -B+ 4 7 B B` B (5 - B5 E()'B/+ #(7C 5. 7 ` FF #5 -B5 4('B E(+ C( 7F B ) ' /5 (> #5 B(+ =C ( B` - B5E (+A'' 7+ 4 (7F 5 +A'' *0)*&9: 4 FB (4+ = B.S*PS*, K ( I (5 ' C( 7FB (>+='(B
82 S*.S.** ( K( B B5 '' B5F '5-- B+' C' >B+ B ' I 7 B ' (B (5(7(C Latitude ( ) Calais Dunkerque Lille z=500m z=3.5km MICROTOPS AERONET Valenciennes Longitude ( ) L'.& 9!4 I 7 B ( 4 7(F+ = B S*S.** ' B )S*.S.**5 S*S.**.S*PS.**/+ B5 B '' ( >(EB()-(JC L/+ 4 7 ( ( (7 B 5 B 2946@@=5 - ' F + B ('' J-(5(B(K( C > B + 4 B ( ( ( B 7(+ = 7(C <F G ' ( B5 B '' B 7(F ( L7(C 2946@@+5BS*S.**.S*PS.**, ( 7F+.
83 =BS*.S.**5 '5B.,S*S.**'' B F+ => > B - 7(C=+=>( B5 (C B (7C ' '' (+ = ' B > ((K( 7FB+=B S*.S.**' 5 (7F C( + = B.,S*S.** -+ = B *HS*S.**, ( ( '' '' 5 F - (K( ' + 4F J - '' >'B=A 5B.*<(+% (J'' &70)+1<(/5F )1**(/+ 7F J5 ( B F B B *515*,1Z5'(B''+=J ( ('' ( ( E + =( ( F ±,*Z + =(& 0 '' ( B ( G B ' + B5 ' B F ' 7+ = ( +1 <( ( (7 B - ' C )'K5 B5 7(/ ( + = B S*S.**15''.**(5 FFB+ # B K '' D.** D.**, 5 (.**, #B.**1 5 B5 + +,++= ( ( ((( (2D.**+=I ' >/B(('(F
84 ) F5 ((F B( 5 7 U / / ( (7 7(C 7 7(F v)b (C 7G - 7(F5 EU /+# 5(>(G(>( (C(F 7G - 7(F (7C+% I ' ( >(F(>F +==@# B ('7(C#6@S@@ ) 6'5! / '' ( B ( 2946@@=+ (B (F ( B 2946@@= F B5.S*HS.**+ 99 ( ' ( B.**+ 4 B.S*HS.** F (B@=62946@@=+ :#=#4 '3$'%&%' 3 '$'2' $&$*)% *3*. # +,+.+=(7(F+ % ( B B ( 2946@@= (B (7(F F' + 5 B ( ( 7(C (F#6@S@@Q+5R+#6@' > B ( 7 7 8!4S## =@#+ 4 B 1* (F5 F +4('5 5F),,*5HP*5P* *.*(/((( )FF (/(C' (7F+% 7( B QB< T5.***R' (C #b(5 ' (> B(F *+*1µ(1µ(+= (>(*+*. F+ = ' (> K F (((*+,,,*(5 *+*,5 B (> ( B *^+ = '' #b( ( *+* F B*+.+ (,
85 7(F(B 7(C 4 (' F 1 )*5,,*5 HP15 P* *.* (/ B ( 7(C (F+ +,+.+.=(+ +,+.+.-=(2@9+ =(2@95 (-'(66#5 2.***+ = B (!64 4 K t B 66#+ =( 2@9' (( ( 5,1,.1(5''. +=> (.1*(.1*(<( <(+=' * <( * <(+% 7( [# <( +5 ] B ( 2@9+ =7( 5 ''.* 5 I > ( + =7( - ( > ( 11*.* ( > (C ) 9-/+ #- (5 (7 ' ( F HP*,P* (+ = (C 2@9 B ( 7(F #6@ Q6( +5.**.R+ 5 - (5 ( F δ H1 ( ) ( δe*+*y*+*1+δ/5g'' ' '' ) '' e*+µ(/' ηf B ( ' ) ηe*+.1 Q +5 PR/+ #- 5 F( F HP* ( ) δe*+*1y*+.* δ/+ = (7 B ( B( 79AA+ 1
86 = 99 #@ 99 (.**+= FB.**+=J **<(7G 7+=( H <( P <(+ =( ( F F 7( B5 B B±,Z ±1Z ( +% ( 44.,..P, > ( B (K( ' )IF,/5+%- '5B 5 ' 7F ' 7F ),,*5HP* P*(/+ = H*Z+ = ( ( ( ( ) ' +/+=7( >(C ) ' 7 /+ 5 ( F ( H1 ( '' #b(+ =.*<(.*<(+=(7B 71+ +,+.+=( (!64+ +,+.+-==#6+ = BG ( B (7C+ = ( (7F I ' '' + = 5 > F C I( 5 C 7(''BC)''/+='' ( + = ( ( ' + =( + ==#6-5B #(Q+5*R5' ( B (!64+ 9 H
87 -;(*H,1.(+='F (.E5*+=( **(D*H,(H* (D 1. (+ = (G ). / B B.**(+= =#6(C* ( B(+=F (' ''1.(.B BJ C( ' ( 5 B (+ =F G( ( ' '' )E/ ' (CGC(''(7CQMB+5R+. ) / = ( ) - ( 5). β )999-P/ ( ) 4 5β(( '' B(F'' ( )<( - - /+=()E5E/((7F5 ( )E/ )E /5>( (( { ( ) ( )} -) 5/ = > ψ X α ) X/ + α X X )999-/ α 5( )E/5 (5 > '' > ( + = ( ψ)e/ ( 7(C '' ( 7( B B Q2 75 R+ B '' (7C 5 ''(ψe + C F 999-P '' '' > '' ( (7F+ ='(('''( 5 'G(7C) F('' 7 4/+ = (5 ( )( P
88 (F999-P/5'7GF5B '' ''&0<( B + 4 F '' '' )( Y /((7F( 5'999-+ %- '' #b()& 0/5' '' ''1.*H,(5)999-/ β β 1. *H, 1. = *H, α )999-/ =?B 5BH ( 5BC+ ='' 7F( ' )C/5 F -7F ( Q+5.***R+=>' B1.(5 (( β = β SS ** )^/)999-.*/ => '( ''+%> B ( )( +,^ ( =#6/+#' B5 > - ''( + +,+.+-=(@=6+ %B(@=6( B 2946@@= (!64+ = ( F (((K(FB+= ' > ( B +% ( ( (2946@@=@=6'' B (!645-((7C-
89 )S*S.**/+ 4 ( ( F (C1*^( (2946@@=+4 ' ( '' B ( ( B )7C 3@B5.**1/+ =( 2946@@= B #6@ ( B 2@9 ) 7,/+ ( ( ( 2946@@=+=( F(@=6 > B( B+ ( (+B(5 ' '' ( 4 F>((@=6+ +,+.+,=B(F+ = 6 =G' (F((( 7( B GF+ ( B '' (5 ( -I ( 5 (C SS:::+++BSGS7G,+7(/+ '( (B B+ :#=#:';)* '2'*$'% 0 1*$' # # B 7(F #6@S@@5 (C ' B+F (,,*(5 '' #b(b(f+ ( ( '' B #6@QB<+5.**R+=B ' >( E ( 7 F+ '' >( B(F '999-+
90 Granulométrie volumique v(r) (µm) Rayon de la particule (µm) L'.& 9!: B(F B 7(F F 7(C #6@ = ).,S*S.**,/5 <F ).S*PS.**,/ #B )S*S.**/ )(7 B B<+5.*** 7F/+ = ( B ( ( 5 (('(+.S*PS.**,5 B( (' ( (F > ()4B'S4B.+/+= '' #b( B +5 F *+H+% B '' #b(')αf+h/ (I 7F (7C+ F'.,S*S.** &(>05 B( ('&>(B( > ( )4B'S4B +*/+=B F' ('+= '' #b(bb*+15 F *++ S*S.**5 (()4B'S4B *+,/+= '' #b( *++4B (I (7C+ = (( F '5 G(F( ' *+1+ = C ( I (7C F' C (+=F( *+5 F '( C(BS*S.**+ *
91 ' B '' '' ( F 7F )αf+h/5 &(>0 F >()α +*/ )αg*+h/5 (()δg*+1/c()δf*+1/+ :#=#=$D)%)*&1$&&*.& # B F ' + = L B B ( ( (+=BK'' t B - '( 66#+ (F > 2@9 L5 5 E (+ = (C <( <(+ =' 999-, >( (F >*HS*S.**,+ Vol du 06/09/ Latitude ( ) Longitude ( ) ((> > L'.& 9!= 6 7( ( 2@95 *7,*)%/5 *HS*S.**,)( '' 7* 7*%/+ = I B5'' =A 5+
92 >BF C F B )/5 ( 5 ( >5 > )/+4 C'') /''.* 2@9QT+5.**R+ # >( E (5 > & 0+ = > &( >0 ( > E EE +4E( Q <+5.**R+4'( '( - E(+= 7B>(B( *<(=5 '(B'' B) ' 999-/+ (K( (C5 B' ( B '' (+ (!645 ((=#6 ( B+ :#=#"A')*% 1) # ( 999-, F B F > + (( ( B B5 ( 5 F B 7(F (GIC)δα/+BS*S.**.S*S.** (!645BB(((>(B7(C I+ ( F B FB+.
93 #)<(/ 8( B ' B 7(C #6@ 7(C ' = =#6 )/ 2S δ H1 α HP*SH1 %)/B (F)/+ *S*S* S*S*..S*S* S*.S* +1 S*S* +1.,S*S* +..S*PS*, +1 *HS*S*, +1 *+1* S*S*1 *+.*.S*HS* + θe1z B Θe.PZ θe1*z B Θe*Z θehpz B Θe1Z θehz.b ΘeP.Z51Z θehpz,b HZgΘg*Z θe1*z 1B *ZgΘgH*Z θe,*z 1B 1ZgΘgH1Z θe,z B ZgΘgP.Z θe1*z B *ZgΘgP*Z θe,*z.b Θe151Z "#/ 2 )/ )./ 2 )/ δe*+*h1 αe*+1 *+gδg*+. *+gαg+* *+1gδg+1 *+gαg*+ ),/ δe*+*, ),/ )1/ - - ),/ - 2 ),/ - 2 &-## )H/ - - 2S δne*+*p αne+* δe*+. αe*+1 δe*+1 αe+p* δe*+* αe+1 δe*+*p αe+1 δe*+, αe+1 ((+ C F(+ C F- )' B ( (/+ C'F` ' ).B/+ 7F ( ' 7+ ` B &(>0 7F ( 7 ( 7F ' 7 ` ' ) B/+ ' ) B/+ ` B &(>0+ *0)*& 9= 4 F ( B > ( B)θe (G5 Θe ''/5 (5 F B)δ H1 ( α/+ = ( 7(F B ( #6@ )/ 5)./#B5)/3>5),/=5)1/<F6')H/( 7(C'492=)δn5αn/+ = 7 B B / (7F5 / G B (7C5/B( B/ G ' B+ = ( B B
94 ( +5 (>B ' (+=(B (5' 5 F( > ( B5 F B '' 5 (( C '')ZgΘgP.Z/+ = ( B )B5 B5 5 7(F5 5( 5 U / ( ' B >7F+=(I( F,*Z+= ( ' ' ( ' 5 (C IL(B+9( B BG&*HS*S.**,05+ ( >( ( F 2946@@= '' ((+ :#"';**) /&*)'$*$'1% & % # 5 >( ( B F2946@@=+I 'JB B F F((F(+ = ' ' 7A+((FG(F(>( '' &0+% (C(G '' F= 5=. = ) '+F999-/ B (> ( + = (G '' >(5 F ( 7 B+ 4 ( ( ( >(5 F B( '( + ( +. F+ 5 ( ( E5 ( B) '+>999-/5,
95 :#"#!*'*0')'$+% '.*& &% '0) 1*'+ # ' ( 5 F BA95*S*S.**+= A9 '' (7C+# B B B B( 5 F+ =I BF B*S*S.**S*S.** ) '+'999-/+4((B (!645B'' ( - - ().<(/+ =(GB1HZ(BI+' BEB)/()/+=(C ).1%/ L),+1,u5+u/+= ()' >/ B4),+HZ5+1Z/+= C)./5 '999-1-)'C 77E/5-(+ 1
96 L'.& 9!" B ( )/ )/5 BA9) /5B5 C(5 '' *S*S.**)J,.*<(/+ * H% B ' ` ( )' / F B Q 7( T5.***R+=( (>(H1(? )H**..**(/+#B( '> + = B B B *+. *+ B+ 4 B ( B ' B) 7(5 5 B (' /+ (a) (b) (c) Luminance totale normalisée Luminance polarisée normalisée NDVI N!ON:O N4O 865nm 670nm 1600nm 2200nm 490nm 13:15 13:20 13:25 13:30 13:35 13:40 13:45 13:50 13:55 14:00 Heure d acquisition (UT) 13:15 13:20 13:25 13:30 13:35 13:40 13:45 13:50 13:55 14:00 Heure d acquition (UT) 13:15 13:20 13:25 13:30 13:35 13:40 13:45 13:50 13:55 14:00 Heure d acquisition (UT) H
97 =B B E 5 7 B*) /+ FB 5 ' B 7(CFB ((+ (( + B) '' B *Z/5 B F ( 5 ' )(B Q8+5.***R/+ = B 5 &0 (( (+ A.* %5 (F B F B>+#.1%5 7 ( C( BB+=(BE B) /+5 CBB B)B /5 ''.Z,*Z.1Z+ ( ).*.1%5' /+ = -- BPZ5 '( '+ #,%5BB( +=>B ( '5 ( + = ' ( B ' (7C (5 ( ( F ( FB A9'+4B FG(+ #'>5 1, **%5BB4+B > F' A9'+=B'' (-( B L(+4(B( B BF '' ( ) '' /+ 4 ( F ( C( >(B( B F G K B F ( B P
98 + = B ( - B+ =G (C B ( F B 2946@@= (C 7GF (( ( ' > F57GF (( (C -- +=B-( L B F ( 7,*H1()(B 7'/+= L ( B(( )(7C( /+#C '' ( ) (/5F BY^,* H1 (+ 4 L( F 5 C'+ :#"#4'$;% +)$'% & # =(B ' B I ( B ) '' /+=( F7( B5 FB5 G(F(I+5 C (B' ( B+ I ( Z'>(A95 B ()A9g-*+/)A9 */+
99 :#"#:&'* 3)*' *&9% & % $ # +1++4(!645B.S*S*+ 5'999-H5( F B''.S*S.**5-! + Luminance polarisée normalisée nm 670nm 1600 nm 2200nm 490nm FIT (490nm) :45 8:50 8:55 9:00 Heure d acquisition (UT) L'.& 9!B B ( B )J.P*<(/5''.S*S.**+ = B )rehpz5 rb_*z/+ = '' Z+=B'' <(+=B (' (( CF) '+ +,+/+=FBI*+1+1) 3>/+= '' #b( 7E+(E+@ F (K( G I+ F 7 B (C ( ' 7I+
100 = > B C( 5 F F ( B'' -' +='' B ( ( B ' B)*+.gA9g*+P/+ (C 5 B >B'BFK ((B 7 += ( ( '' (7F5 '' ( F?+4(FB( B 7G7C ( ' 5 B BF(''(7F)( Y/+ #' ' B( > >5 '' (G( (+B5 ' 999-H5 (,* (+ 4(G ( '( > ( ( B B(G(7F+=(G'' 'K ( F (G! -.* B <(+ 4 ( '' ( ( (!64+ (5 B F( B + #' (( ( 55 B5B (( B'' ''B #G ((( + ' 999-P ( ( 5 F 5 > ( B C '')B.S*PS*,5 (/+ **
101 Luminance polarisée normalisée Q1R<S Q1R="S Angle de polarisation ( ) :30 8:35 8:40 8:45 8:50 Heure d acquisition (UT) 0 8:30 8:35 8:40 8:45 8:50 Heure d acquisition (UT) (a) (b) L'.&9!( A ( )/ )/>(BB).S*PS.**,/+ =( F F( )ϕ_*z/ E7B1*Z+=BB+1<(+=B > 5 > ( B C ''+ =( B(C>)Θe*Z/5,%5,1Z B )Θe1Z/+ = ' B ( ' G ) 7(5B5U /+= '' #b(+ F(H1(*++ 4( F B( )_*<( 7F J/+9CF (7F( '>+=BB)'999-P-/ B' B +#, %5 B ( ( F '' *Z 1Z+ 4 B B (( ( ' (7C QE +5.**R+ = ( B B 7 5 C( 5 B (( B,%5\B ' C()/+ 5(G(( ( 5'(>B' (7C+= ( F (G *
102 B.**(C)(C] 7 P1(C/+(G (' 5' BB>B+ 4- (7' B+ =5'999-P-5'' ( '' ) '+ ++/+ (C >5 O ( >('5'(( H15 H**..** (+ >5 +=BB>1Z+#-( ) /5 B GF( FF F F (B+ 5(GBB*Z ( B() ' ++/+ '' B5 (' 5( )(I / G( ( ''+ 5 +,* HP*(5(-(IC )6G7/+= ( ' +4 (B5 L 7 ( '' - ''B B (H1(+ =G > ( 2946@@= ( ( B > ( H1 (+ ' 999-P-5 B5(C>5FB( ( H1(>''+ >)''1Z/5 B ( B 5 > (B + = ' F ( 7(C+ = B*S*S.** ( E 7(C( ' 7+ >G' 5 (( ( ) ''999-1-/+(B5 *.
103 BI( G('''*Z+ = C( ( ( (' ( F C )1**(/+=>('+=(( K7' B(+ ( 2946@@=5 >( 7F B '' (C F ()w_+1( ( / (GC(F+B C( ( > F B + > F ( C5 > ( '' B > ( (K( +% ' ( 5 ( >F ( B+4''((('H1(5OG + 7G7C '5 B ( B '' (K( G H** (+# 5 ' (' 5 '' ' ( FH**( F H1 () '+' 99+1/+ 9 ( G B ( H** (5 ( - ' K + = L ( >FB'' ) '++.+,/5B (G +B ' ( > (+BB ' >H1(5 H1( C(+B 7( C (!64+=('' (9668(FC(+=( H1( (F(5 5B F F(+ *
104 :#B)& '# = ( 7 ( 7 B ( 2946@@=+ 4- ( 5 5(' F5( +$B(5 (( ( ( >5 > H1 ( 5 + B ( ( 7F>((G-' ( 7(?+=''( (FF ((( (-*ZY1*Z+ = (F (..** ( ( (K( F B B+ 4( 7C 5 (>(..** ( ( *^+ = ( (F5 (F 7GF 7 F ((2946@@=+ 2B5(H1(K>F +B' 5 (( '' B )P*ZgΘgP*Z/+ (5 5 B H1 ( 5 > '' ' *Z+ I ' ' B (G '+ =(,*5 HP*5 H**..** ( B ( '' (+ #- (5 ( ( F ( > ( θg*z+='bg(f( L + ( ( I ''+ ( 7( ( F >(5'B' + *,
105 -*3'$= **$+' *$'% *+ ) *&9% & % # #-' F5(7 ( (C 7'J ( > ' ) '+ 7 9/+ 9 ( 5 (C 75 ( ( (( L5 ' 7 '' G 5 B5 (5 7( > ' F+ 4( ' 2946@@=)(( ( /5B 5 5 7( B ( 2@9+ ( 7 ( ' L F ( ( 5 ' B5 (7 B ( B 2@9+ 5 B ( 5 ( B ( 'F(+ = (!64 ( I F5 ( BB5F(+4 > ( B ( B 2+ 4 ' I Q"F+5.**1RF (C ( B B 7F5 ( + = *1
106 5((5 B>( <F+B7(+ 7 7 (( ( B 7 2@9 > B (7 ( + C 75 'F( B ((7BB + =#!**$+' *$'% *+ ) *$&) +%'$*+# =#!#!$%&$'# = 5 C(5 C((( (I ( Q9445.**` T'( +5.**.R+ =I ' ( (!64 ( 2+ (5( BB(C( ( 2946@@= =#6-9+ ( ( 2@9+ (>B''!645BS*S**S*S* (F'B+I B S*S*5 (F GC( 7 -! 5 F GC(? 4+ 4 (F B ( ' 5 ( 7 C (5 > -+ = (F *S*S* FF'&05E( F' ((( += "F+5.**15 >IB+ *H
107 '' (( BB (7( ( ( QT'( +5.**` = +5.**R+ = F ( F (( B!64+ (C 5 B5 ( B F 7F 7F (+ 2946@@= - (+ (( 7F7(5 (C' (+% ((C(2946@@= 2@9( +C 5 B B ( B 2946@@= =#6+4((' 7(B 'G(2@94#=9@Q=+5.**R+4 (( 7B' (+ =#!#4 $')5 F*'$'*%%& $* ) $'1*) 2 3)*'G%*% &)$' 3$*) *$'1 *% 3* '1 H# ( * :1*55:;<83755=2, G '' 7 ( '' ' ' 7 ( BG ' 7 7G 7( + 2((7 '7 (7 +- 7(77 ( 7: G '' G ( B( 7B7 (+7 ' ' (( '( ' '( :G Q3 7 " <5 *R:7( '( 7: ' (- +7'( 7G 7( 7+7 '7(7G ''77'( 7 <5:7 *P
108 ( 7 '7 7G: ( <:7 : G G 7 '7BQ(+5`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
109 '7G ('(-Q2x+5`` +5.**.R Q!( **.R B : 7 GG : B )/ B )(/ B (B7B'QT'(+5.**`=+5.**R+9 ' ( 7'( ' 7 4-# = 9' 4#=9@ Q"< +5.**.R 7: 7 G.**1 : ' ' 7#$%# #=9@ )4#=9@/ 'F G- ;#8 :7 7 ( 7 (G 1. *H, ( - E 7 1. (+ 7 ( : B 77- B ' ' + 7 GG : 4#=9@7' G7 '7 + 4( G 7: B ' ( :7 B F (G :7 2@9 B: B5 7 # >(5 # Q= +5.**.`T'(+5.**R77#! #6 9B5#!#69 QT'(+5.**R+ 7' 7B'7' (((B'(B)2946@@=/ B)7 < =#6/ (+ B ( ' 7 (G B ''( 5: @@= B 7B'7(' 7 <'' B+37 (: G 7! 6 >( 4 7 5!64Q3E+5.**R>(5:7 7< B77'7 "2+7 '7'757B (7> +7: 7 G'72946@@=BB7 ' + 7 ' @@= B ( 7 2@9 B+9 7 5:GGG:2946@@==#6 7 E7 B '((+ *
110 ,++.+.!>(+ 7( ' 7!64 (: F ( B B 'B 7 E 77-B +7! 7 7 '!#=4@-.*)!.*/ 7 ('(.P (.@.**+ '7 : '( 7 (` ' ' 7( : 7 E B ' 7 '7 7 ( G ' ' B': 7 G ' B B !.* : F :7 7 < =#6-Q+5*R7@=6(QE+5R+ 7 : -:B 7:B ( 2946@@=: 7!.*+ 4( - B : B+ 2 ' 7 '7:'( 766#B+:G : G B ' (( ( 7 E+ 7 (( : F - ' G,**<(5:77 '! : '7:'(@ BG 1** *5,* **%+, (+ 7 - ' ),+.1u5*u/5#--#),+Pu5*+.1u/5 ),+1Pu5+Pu/5#B),+u5,+Pu/ 77'! 5 : F :7 ( 4( -7( ' #6@+ 7 B 7( QB< T5.***R5 B 7 7 <57 (>' B>7 E:*+*1 µ(1µ(+#(-7(:77z1x -,ZHX@ 7 + 2( ' 7 B ' G: '( 7 <- =#6-+7 ;B*',* *(D 7 1. *H, ( 7 BG+ 7. E5 :7 7(BB.75 7E'.**(+7((7(B ) (' *(7' :77 ''G'*<(/+7 B *
111 7('* (<7G( ( +7EB'( 7'7 -E @@=('B,*5HP*5H15H**..**(+! 7:B757 G( (' (5 5''5E +7:7 ' 77EH*Z+7 ' 7( ' B 7 ' E 7 E + 7 E (E B 7 7 ( ' 7 ((( Q( +5 PR+# ' E (E 71:B7(7P+1(+97H**..**( 757 E('-*Z4)98# /+97 7:77'' '(B (7.^(>((+ 7 G.- ^' 7:B7,*5 HP*5 H1 H** ( 7H^'7..**( 7+7FB'' ( ) =/ E ) =/ (E ( B(E +7FG >(G B B 7 ' ' E *^5 B'7 '7>(+7'E'7 ' 7 E 7 QE +5 R+ " 7B (7 FB'' 7 < τ..**( 7 >( 7( 'B Q +5 PR+ "7 '.*u5 τ F +* -.+* - 5 BG'((((Q7!5PR+ 2@97 'G 7 (## ' 2 7.***+ 7 ( '( (('(,1,.1 (. + 7 ' 7 >'(.1*(.1*(<( <(:77(B '*<( *<(+#7(5<- 75 7B'BB ' +77( H 7'(11*.*(+7 '7B7 ' 7 ( 7, ( B '( 2@9 7 7 < )#@/5 7
112 '' B'7E57' '7 7 < ('(7'()η/+2@9 7BB #6@ 7( (( Q6( +5.**.R+ 7 #@ B B:7 G '*+* ±*+*1 #@+ 7 G 7 '' B±*+µ(+#BGG7(7E7'' GB7 (η G5:7 7G (:7 G'± *+.1Q+5PR+,++.+.-@B+ G ( B B 77 B 7 '! 5 :- G( B 7 4G 95 7G B '('(#' G 7 +!9A-G 7 7 <)#@5H1(/B'(2@9@ 7 +# :77B5< G<GB7 5 ::7+4:7+7 <7 < ' 7!.* ' 7 '7 '( 7 ( G : %4+ # F('2@9* *%+7B '(5 :7#@B*+15>'(7#' 577:'72+7((((>((#@ BG7-7(: BG*+.*+1+7 G B #b( >5 ( : 7 HP*-( H1-( 7 QE+5.***R5:*+.1' *'+9 7 ' > 7 ' ( + 7 ' B5 7#@( G 7#B -7(: 7 :5 : *+ *+.5:7 7#b( >: : +* : *+ 7 G+# 7:!9A-57!.*7BGB'(7(+7 2@9#@(7!.* ' < '(*+.17 *+14.
113 N*O Latitude Longitude N0O Altitude (km) β 1000 km -1 sr :00 11:05 11:10 11:15 11:20 11:25 11:30 Time (UT) NO Altitude (km) Color ratio :00 11:05 11:10 11:15 11:20 11:25 11:30 Time (UT) L'.&9! 2@9 7 <H1(5@ 7 )/+7 < 7 '7-7(')/5)./5#B )/ 7 ' -7( 7 7),/+ = < '' 1. ()/ ( B 7 1.(*H,( < '' (:7 <'7 ) /+
114 N*O Latitude Longitude N0O Altitude (km) β 1000 km -1 sr :20 12:25 12:30 12:35 12:40 12:45 Time (UT) NO Altitude (km) Color ratio :20 12:25 12:30 12:35 12:40 12:45 Time (UT) L'.&94+2@9 7 <H1()/5@ 7 +7 < 7 ' 7-7( ' )/ #--#)./+ = < '' 1.()/ (B 7 1. ( *H, ( < '' ( : 7 < ' 7 ) /+,
115 =7> < - : ( + 7 (E - B 7 < ''! 9A- 9A-.+ 7 ' BG( 7'7( < '< '( ( + 7 ( < '' ( 7 ' 7 (75 I : 7 '+ 7 < '' 7 ' 7 )( / < '' ' B G 7 :-:G ( : 7 7B+7 < '' 7 B '7+!9A-7 < '' β (1.(@ 7 '(* 1%),+1 5,+1 / 1%), P+.H /7 '(4 7 7:!9A-+7' 7 1. ( 7 *H,( < '' )7' :7 7/ B'7(E' )!9A- / ' 'E 5FH'( *'7+#''B )'(*1<(/ '746' 7G7: )!9A-/BG:7' H<(77+B(>(7 < '' B:77(+ 7' +1 <( ( 7 ( B 7:7'7+ :(>(B BG:.,<(+#7 '(B B7) ( /57G( <( 77+ =: B ' 7 5 '( :7 7 (+# 7 < '' :77 746B7(GG7' ( ' 7 ': B ' < '' B: *P 1%<(77 :77 '7 + 7'7G :.,<(77)!9A-/:' < I '( ( )7 SS:::+++BSGS7G,+7(/ > Q(+5PR)7 SS(+' ++BSS+7(/+7 : ' B 7 ' " ' 7 1
116 2')7#/+7 5:7 7 B>B'(75 <: ' ( Q > 77:'@ 7 7B B# @9 F@ 7 * **%4!9A-.+" B ( (5 :*+1 B 7: ' #@ B 7 *+, 7 ' 7 (5 <+7GB#@( #--#: BG*+*H1 *+*P BG( 7 7 G5 :7 YS-*+*+ 7#b( >:*+1' 7-7( '7 '(7 7'(( ((E+ #(GGBB<(77B7' + 7 < '' 7(GG:7 777(H**( ( 7( (B)..*. *%/+!9A-. 9A-. B B'(. 1%),+,1 5,+.1 /.,1%),+P 5 +1 /5 B 7 (! 9A- 5 ' 7 (( < '' : : )++:...,%/7B G'7: (7 ( G G+# 7 < '' :7 ( B'7467:7'G' (' B 7(GG,<(77+7B46'B! 9A- G 7 ' H<(77@ 7 +7 (GG 7 EGB'7 77 GB+7467(GG77@ B7(GG 7G'' +7 '' B:@ 7 7 (G '' 7-7''' 7' : )(/+ 9 7 ( G G5 7 ( G(>'-' +7' 7 G'(7G(G7B B 7 7 ' : Q!( +5 R+ 7 B: )@### G/ 7 ' :*(+ - '("+ H
117 L'.&9:#A ''7 7 )/ ' E 7+ 6 < G 7( 7 :( 7 )/ E5:7-7 ('EQ+5.***R+#G 7 '( (()+,^7 'G(/ ' E+! 9A-, 7 B E ''@ 7 7 +#77((G5E,^B :77G:7EB7(GG+9 '( 7 7 7( G G+ 9 7 ' 7(( '5' EB+ P
118 L'.&9= E '' )7/@ 7 )/ 7, , @@=7((+ #7(7B'2946@@=5 7B 'B< ' Q85.**R+77(( 72@9Q+5PR772946@@=:B @@= ( 7 7 ' E ' 7 7 ' G7(7-' G(71B:B7+97':: :B 7(+7'(<' :77 E + 37 B < 75:7:7 B@'( QE+5R ' 7 ( ' 7 E B ' G( : G'( ' )4> 2< Q1,R(/+ 4( '(' B B ' 7 (7 7 < '( * ) 6G7 / ) (7/+7<''E7θ 5 B:E7 θ B 5BE(7φ+7<''(5:7 7
119 ',(1(+"(77E': -( E ( ' : ((+ 7 -( ( ' ')/B'( )/ = * σ.π >..σ [ ( )]. )9A-/ "7 * 7G() ( -. /5 ( 7('7(`σ ( 7 B ' )/+ 7 ( 7 ( 7 2@9 B Q+5PR+7(σ ( 5 ( 77G '7( B9A-+ %) &0 σ 22 σ ' ' $ *+*P +, *+* +P +,1-*+**1 ""G. *+*H +. *+1 + +,1-*+**1 ""G *+* +. *+ + +,*-*+**.* ":77(G, *+* +. *+., + +,*-*+**.* ":77(G 1 *+,* +. *+P + +,1-*+**1 "G H *+H* +. +,H + +,1-*+**1 "G P *+* +. +, + +,1-*+**1 "G *+H* +. +,H + +1-*+*** -<G *+1*.+...+H +HH +1-*+*** -<G *0)9! 2 '#2+ 7 ' B > 9A- B' 7( H1 (+ 7 ' B>7G:B7-+7' B> 7:B7 B6(+[.**.]+7 '7'( ( 7 2 7G+ 7( ('(, ' 7 ( (:7 '' B)'7'777 (('7E/5 '(*+**+1µ(5:7(('(1'7 (:7 '' B '(*+P.+H µ(+ 7( (( (' H5P(G7 7 G 7 ' 7 ' B >5 BG F +1'( +,1' (( G 7 B ' 7 '' B 5 BG '( +,H.+H µ( ' 7 ( 5 '( *+P +, µ( ' ((+#>(( 7 '-
120 7 QA+5.**R77'((+7 ('(G(('7 ' HP1(,,*( '('(+"(77 )E/' 7 >(( B 7( '..** (+ 7 7 ' '7-7 (77' '77 (1 B!9A-1:B7'H1(+" 77('' 7-7 7' BG' 7B7 < ( '77' B'7 + L'.&9" 7 7' '77 (72@9 7 77=%77(7(' G " 8[,] 7 7( '( : -(( >( G 7:7 ' 7 ' 7 B(' 7 ( 7 <+7(7> 7- >( (7 G 7 :7.-^ ' 7 <*+1*'B:* P* +'' (G :77G57 57(' B+ :B 7 F = λ 7(B:7('7( = λ.*
121 7 = λ 5 ('7( 7 <δ5( 7 <' +7( :7 G7(( η ( δ µ 5 µ 5φ ) η ( δ5 µ 5 µ 5φ ) + ( η) ( δ5 µ 5 µ φ ) λ 5 ) = λ ) λ ) 5 )9A-./!G57 7 <('( H1(G (75'B'7(( )*5*+1/'7,>H ( ( :B75 (G HP*5 H**..**((F)9A-./+7 ε 6 ': F)/ + BG72@97(7B7:7ε 6 '7FG'7BQ+5PR+ ( µ 5 µ 5φ ) ( µ 5 µ 5φ ), % ) % ) ε = )9A-/, % = % + *+* = < ( 7(E( '7 7<5= < 7( + 7',*(BG :7'(7 B+# (G 7 ( ' 7 5 7,*7B 7(+7( 7 I BG ((E ' BG,>H (+ 7 (7B7(ε 6 '7- B'η y6y :7y6y' +757B'#@η ( 7ε 6 7E 7':F),/+ ε ='(EE + = 1 ( µ 5 µ 5φ ) ( µ 5 µ 5φ ) 1 % ) % ) = % + *+** %.. )9A-,/.
122 7E'7 ' G(,*( Q47( +5.**R+ 7 (7 E 7 G (7:B7+75:7E 7,*(7B 7(+ 7 E 77 7 G : ' 7 E [=G+5P]+ 7"8>(> ' F )9A-./ B ( <G E ) ( /+ " I 7 ' :7 7 7 ε e )ε 6 Yε 6 /S.5 ('7E 57 1^+#7'G((Eε +7 y6yy+# '''(7'7z6{ B+" 7 y6yyg:77b>7' '' :77y6y+ "77'' (7 G 7B)7 G 2@9B5B +, /7 (+, @@=B+ 97 7B'7 '7)(( /B7 (5:7B :7 G+2 ' B (B7, E 9A-.9A-.'7E' 5 BG+7' '7'7(E 7 '7E7[E +5 ]+ 7. ' 7'7 : *. *P%5 1.*%@ 7 5:@ 7 :..H-..%. 1-.,*%+7B:(GG7('7G+7 E71Z)±.Z/'7GB'(+7 *Z+7B'7 ':+1<(*<( BG@
123 A*% T! T4 T: T= HP* +P±*+*. +P1±*+*.1.+,H±*+*1.+.±*+*, H1 *+H±*+*. *+P.±*+*.1 +H±*+*1 +1±*+*1 H** *+.1±*+*.1 *+*±*+*. *+±*+*1 *+P.±*+*.1..** *+±*+*. *+H1±*+*1 *+1P±*+*1 *+,±*+*1 *0)94* 26' > )E./@.**)E,/+ A*% T! T4 T: T=,* +,P±*+*, +1.±*+*.1 +H±*+*1 +,H±*+*1 HP* *+11±*+*1 *+1±*+* *+H,±*+*.1 *+1P±*+*. H1 *+.,1±*+* *+.H±*+* *+,*±*+*. *+.±*+* H** *+*P±*+* *+*1±*+* *+.H±*+*. *+±*+*..** *+*,±*+**1 *+*1±*+**1 *+H1±*+* *+1±*+* *0)940 2E6' > B' 7 +#B'(B 'G*<(+ 7E' 7:B7 7( '( 5> +97: 57 *E' *' +9B77B' ' 7 (( '( G 7 : (+ #' 7 7 ( (7' )(74>2<Q1,R (/5: 7B 7 E ' 5 (E H1 (5 ' '7:B75!9A-H9A-H5 BG+ Normalized Aerosol Radiance UT UT UT UT Normalized Aerosol Polarized Radiance UT UT UT UT Wavelength (nanometers) Wavelength (nanometers) N*ON0O L'.&9B (E )/(EE )/ ' ':B7+.
124 7,*( 7 7B 7( 7:!9A-H '7 G7(':B + 7 7B5' 5( (( F (+ 7 7 B E (' 7 G 7 (+ :B5 '' 7 B B : 7 : ('((G+7E G! 9A-H5 ' G ( ' '( 7 E '':''('G+ "'72946@@=B'7y6y:77 7'BB1 +!9A-P9A-P7:7 7 <H1(7'' BB'(2946@@=B '7GG5@ 7 + N*ON0O L'.&9( # 7 <H1()/'' B( ()/ BG2946@@=@.**+ 2 G 7 - )! 9A- 9A- / @9#@)! 9A-/ B @@=B#@!9A-P+7#@ '(*+.*+: 7! (7! 77 ) u1 5,uH 5 ' 9A-/ B#@ '*+ ±*+*1 : *** **%5:7 7> (:772946@@=#@+! 9A-P 7: 7 7 '' B ( B B.,
125 B 7 5 ' I ' 5 F *+, µ(+ ( ' 57*+*Hµ(B+7B#b(()7:/5 (B7H1HP*([E+5.***]5 *+H±*+.5:77 7(77 B'*+.+7 G >G7 ' 77#b((BGB7B '( 7 7 <5 G:77#b(>:+**+. [(+5R+#7B:'(7'7(5 : > BG7B '77:G7 (( #B+ 9 7#b( >( #B 7: '( *+. 7 G 7 G(B 7:+7 (( )η5 7:/ B'( 1 1* ^ (7E+7' ' (>'(,1)9A-/+7(H5 '7*^'7+4' :' E)ε 6 ε 6 / BGF.+^1^+7( B 7 z6y{ 7 z6{ > G 7 (+ 7 '( 7 7 ( 7G77(7E G7 +7 7(' B(, ( 7B 7 G (E '7(I ' 7 B 7 (: E G 7 :7BBG: G77(5:7 7(>'1*^'( 5 7 E G 7 B + 7 '(77 '7((7E( 7 '7(+:B5: 77( B 7': ( E : 7 G ' (>:77 7(7+! 9A- 9A- 7: 7 7 < H1 ( 7 '' B BG2946@@=@ 7 +.1
126 N*ON0O L'.&9E # 7 <H1()/'' B( ()/ BG2946@@=@.**+ 7( 7 ( G 7 +@B 7 (GG:7 7B'G)!9A-.9A-. /5 7 B 7 1^ 77 )*^-1^/+ 7 #@ B B 7 ((G:*+*,*+.+'' B 7G'(*+,.µ( *+H µ(:..,1%+7 '7#b( ('(*+H++7' '(.^^'( 77'7 +7 'E5ε 65 ^+ #(>'1*^'(,)9A-/1*^'(1'+7 7 '' B B :. *. % ( B'η):*+/ :77B(+9(:77( B! 9A-H5 7 B '' B :. 1d. %:..Hd..%(+7'' B '(*+ *+. µ( 7#b( ( +.+# ( ' (. :7(PB:7B 'P*-P1 ^+ 7 z6y{ 7 7 ( 7 <)'' 7*+**1/5 7 '( 7 '' B ''' 7 B- :..,1%)!9A-/+7 '' B7 ( 7'7z6{+7 77B( '7((7 7 <+# ('(,PB7:..,*%:7.H
127 (HB:.,*.,1%+7B )η/ (7'7z6{B7 '( *+P+! 757E H^5:77 :.+1+1^+, * **%@ 7 +7((: '(:7*('7B@ 7 5(7. 7@ 7 +72@9 B*<( *<( :77E'2946@@=G,**(7 '+9 ( 7 B @@= > :7 7 2@9 > B 7 (+# > * * (G2@9>+7 77 :7 '7 2@9>72946@@=>7(:7H<(+!9A-7: 7 ('7B2946@@=#@)z6{/B72@9' 7. G Standard deviation (MICROPOL opticalthickness) Linear fit y=x AOT AOT AOT Micropol Linear fit : Standard deviation : Correlation : 0.91 Slope = Offset = AOT Modis L'.&98 4(:7#@BG2@92946@@=H1 ( @@=#@ 7 BG:7 7 2@9 >+ 7 ( : 7 : > + " 7B ( 7.P
128 '' B5G((G(H1(57#b(( (BHP* ( H1 (5 7 (( H1 (+" ('57B2@9 Q+5P`6(+5.**.R+7 (9A-+"7B 7('7((B'75 7'G7 + *$!!P!<P4<<! <EP!<P4<<!.&.*&.*&.&.*& 32 )&$' $ +) $ *+H1± 22$'1*%'& *+,1±*+**, *+,±*+** *+*, $ *+P.± *+P±*+**1 *+H±*+**P *+P±*+* *+H1±*+*1 3**$ *+**H *))% *+,± *+,±*+*1 *+H±*+*P *+1P±*+.*& +) *+,*±*+* *+*±*+*P *+P±*+*1 *+P1± *+** *+1±*+1 *+1.±*+*1 $*$' *+*1. $U73$ *+H±*+*1 *+,.±*+ *+H*±*+ *+Hd+. *+H1±*+ *+H±*+ *))%)&0, -,, - *.%)&0 1 H - 1 P - '%&*)2'$$'. ^.d,^ d.^ +1dH+1^ *$$'.*.).Hu -*.Hu -* *0) 9:# 4( : 2946@@= 2@9 B )6 G B/+7B(B7 B 'G!9A-+9A-.++7BG'7B(7 B )B 7 /+ 2(( (>(( ' 7 5: BG(7'' BBG 2@9 ) / 2946@@=5 F BG *+, *+,1 µ( @@=BG((G((:772@9 :7 7 2@9 G )± *+*/ ' 7 (+ 7 '' : 7 2@9 B ' 7 '' B :7 7 (( 7#b( >5' 7 B 5 (( 72946@@=+7E'7(7('' @@= 2@9 B) 9A-/5 : 7 ' 7 ((7 7 <+:B7B#@'' B(+ 9 77BB7 7 <7'' B 7 5' B7BE( 7 BB''' BBG2@9'77B.
129 : ( 72946@@=+7' 5G 7: ' 9A @@= '' B >7 77 BG5 '(*+. µ( *+ µ(5 B B '*+,* µ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µ(+97'B@ 7 57'' B 7'7(GG5:7 7( 7 ': '(746 + *
131 L'.&9!< > '' 7 )/ 7 + L'.&9!! A '''' B)7/@ 7 ) / 7 +
132 ,++.+1 #B(7BB7:-( 7 '7G:((G B B ' 7 ( >7 77 '(G7'' BB5:7 7G *+1µ(+" B 7 7 '' B 7 G((G (5 B'( 7 ( B G 2946@@=5 G ( B B 1** <( )! 7 4 9/5: G 7G7 7EG+957> ('(7#+:B5:7B(7 '7B5 G7'7(+7G'7E '(7 ' -7 7 G+ :B5 7 E '' : G :5,^5 ( B G ' 7 ( (+ 95 2x +5 Q.**] 7B B E '' BG'( *.1^ 7B'7(B=E)8(G/5:@ 7, 7 +9 G 77E(G-'((:7 (+7'7'7GH<(G7 7( (B 7: Q2x +5.**R+ 7 '' B ' '( 7 GG :772946@@= :775:7 7 '(7: 7BB7(5:77 7BG(BG (+ 7(B'' :(((BG (7 7 <+95@ 7 5'7((B5 #@ *+:7*+7 '77+97(( 57 B 5 B G 7 7: 7 ( ' 7 > '7(GG:<(+:B5 B 7G.<(+# '' B'(*+.*+µ(B : 7 1*( 7 ' 7 G( G+# 77 7EG BG7B(((B+#7B 7'(B7(5> 7BG(- BG 7> B7' :+#>.
133 7 ' (( 5 :7 7 > 7 5 ' E:B:77(GG+ # ( : 2@9 2946@@= ( 7 '(+ 7 B 7( (5 > 7 2@9 H:B7 '( 11*.1 (,' 2946@@= '( HP*..** (+ 7 ( ' 7 B G 2946@@= 2@9 7 < BG + 7 B #@ '' (:2@92946@@=(F+7#@' G :7@ 7 +7G'72@9BBG'( 7E G7+#77 7 <57 '77((7B G( [6( +5.**.]+ 7 : B 7 777BG7B(5G ' G72@92946@@=B- (+7'' 7 F().7/5 (' 5 ( 7 '7 (+ 7 E (( F G 2946@@= 7B B G7:B7 '7E G7G' +:B7E G((( : ( G B ( ( 7 (' 57@ 7 (>'1*^'-7 (":77(G()(,5 9A-/+7( ε 6 ε 6 BG+1^^ ( 7 '7B ' 7 B (G+ 7 :7 7 :< B E + :B : ( B 7 ( 7G E7'7BG'77'7 7(7+
134 =#4**$+' *$'% *+ ) *$-3'/& %&%# =BS*.S*5S*S*.S*PS* 'F( B ( <F )( 7F/+ '5 F B S*S*.S*PS*,5 7( 2@9 2946@@= F E S*.S*+# B5 B '' ((7(FB 7(C(+(5 B.S*PS*,5 B 7(C C B <F (7F>( 7FB+ (' (C7(C >B 7(B 2946@@=+B 7 ( ) & 605 G 2@9/ Q +5 PR5 ( (( )&6Y05G 2946@@=/Q"F+5.**1R+ =#4#!+ $*$'% 0 1*$' 3-$+$'/& $% 1) #,+.++4 F(G<F+ ( DB.** (.**,5 F(+4( ) ((/ ' +.**.**,5( ('' (DB(+ BDB#B+45.**-.**,)_**IB/ B (C 7 >( <F+ ('9A-.-5B(F '' #b(+ ' 9A-.-5 7(( F((IB+,
135 Epaisseur optique à 865 nm δ 865nm α 670/865 07/03,4j 08/03,17j 09/03,10j 10/03,5j 11/03,6j 12/03,2j 07/04,8j 08/04,11j 09/04,14j 10/04,4j 11/04,5j Coefficient d Angstrom (%) Epaisseur optique à 865 nm (a) (b) L'.& 9!4 )/ A ( F H1 ( '' #b()α HP*SH1 /5(7(C(F<F5 I.** B(.**,+ )/ (( F (IB+ 9A-,5 (C (G 7 '(5F >'('+ V $ EB" α NB(<PEB"O µ V 2 PV $ EB" µ *+ *+*n +1 *+,1 *+, *+1 *+P* *+1 *+1 *+*. *0)*&9= A(G(C 75' ( )/ (')'/ 5 B <FI.**B(.**,+)n/ -G+ = B ' 9A-.- 9A-.- ( BB(.**.**,+= F '' #b(5 ' 9A-.-5 -G B(G(+=(I I F'9A-.-) /+=B 9A-, B(GIC+ ' 9A-.-5 B F F (G ( ' B )D (/ F ( ( )@ (/+ = (F ( ( F 5 ( 1
136 ( + = B(G F ( *+)*+*/H1(+%FB F' (*+*1*+*P1) '+'9A-.-/+ (FP*^ F)H1(/ (7F ) '+ 9A-,/+ (G5 (7F B <F5 >( 5 B K F' '( 7 + ' 9A-.-5 ' B ( (C #b(+ = B(G (C ( +1)*+,1/ > 5+H5)\ (.**,/+4 (C (( ((.**, B *+ )*+,/+ 4 B C ( ( F + B F (F B 5 ( B ( 7 IF Q"F +5.**1R+ = C!645S*S*5((BIF-! #(5 B(.S*S*S*S*+F ( '' #b(5<f5(#\b(.**,5 ' ( 5 ( 7 C (+ ( B <F5 '' -I ('J` + = B 9A-, F ( F (C 7 ('5'B ( > (+=G'' '(G( ('B*+1*µ()*+*1/5 *+,*µ()*+1/( +4CF F(' B <F ' B FF + '5 B E ( + ( >( 7(F I(>B+ H
137 ,+.++.AS*S*.S*PS*,+ '9A-.-9A-.-5I 7BS*S*.S*PS*+B(>7(C(F O ( 2946@@ '' Vol du 19/03/2003 AERONET MICROTOPS 51.2 Latitude ( ) Calais (c) (d) (b) (a) (1) Dunkerque Lille Longitude ( ) (8) N*ON0O Latitude ( ) (7) Dunkerque Axes de mesures (28/07/04) AERONET MICROTOPS Lille Longitude ( ) L'.& 9!: I 7 B S*S*.S*PS*, 7(C+ > (5 F>((5 >)/5)/) /5IS*S*) '+'9A--/) /)/ I.S*PS*,) '+'9A--/+=>)/S*S*)/.S*PS*, (B(7BB- ) '+ 7 1/+ I S*S*5 ( 7(C (F <F+ I5 ( 7(F ( <F ( (2946@@)(5'9A--/+=B.S*PS*,( 4+ B5B'' (7(F >B>( L)(P5 '+'9A--/+ B > 9A-1 9A-H B 7(F '' B(IS*S*.S*PS*,+ (c) (d) Calais (e) (f) (b) (a) (1) P
138 F )%/ δ HP* δ H1 δ H** )./ α HP*SH1 1 **-H * *+1gδg*+ )/ *+*gδg*+ )/ _*+*, +1*gαg+P* )/ 2946@@, 1*)/ *+ *+*H1 *+*..+*1, 1P)./ *+ *+. *+*1.+* 1 *)/ *+1 *+* *+*, +H* 1.),/ *+* *+*H *+*..+** 1 )1/ *+*1 *+*H1 *+*. + 1,)H/ *+H *+* *+* +1 H *,)P/ *+P *+ *+*1 +P* H.)/ *+1 *+* *+*.+** 2946@@5S*S*+= (' 9A-.-+ )/ B>K(B7(C=B+ )./ FH**(> '' #b(+ F )%/ δ HP* δ H1 δ H** α HP*SH1 #6@)<F/ P **- ** δr*+ *+*.n δ R*+ *+*n δr*+*,* *+**1n )*+Hgδg*+./ )*+*gδg*+/ )*+*gδg*+*,/ 2946@@ P **)/ *+ *+ *+* + 1)./ *+H *+* *+* +,,)/ *+.* *+.1 *+*, +, *,),/ *+.* *+. *+*,.+** * 1)1/ *+.* *+. *+*.+** * 1P)H/ *+ *+* *+*. +*,)P/ *+11 *+*1 *+* +. α R+ *+*n )+P1gαg.+*/ (2946@@5.S*PS*,+= ( '9A-.-+)n/ -G+ = B 7(F5-5 ( B ( 7 > B+ 8(5 F '' #b('+h5 F F C ( (I 7F (7C+=F(<FFFBB (7FE S*S*)δ H1( e*+*h1/'(.s*ps*, )δ H1( e*+/+ B B 7(C (F B+
139 BS*S*) '+9A-1/5('' >( E <F+ = ( 7(F5 (.5 (((7C7C)('' B 7 B /+ 4 ( F B F '' #b(c'' ) '+ 9A-1/+ 4 '( ' B F B ( >( (+ = (C ( ' B (, 15 '' (7C 7(C B <F)( /+ 4( F ' F)_*+*H1/ ' B '' #b()_.+*/+ = F ( )( H / B ( ' ( B B 7(C =+ I.S*PS*,5 F( (G'F BS*S*+=F(>( B >( B 4 L)( 1/+ = B B(' )(5.5 HP5 '+9A-H/+ >IB5B(C 7 5 ( #6@5 '( B 2946@@+4BCF(K(G B E<F4+ =#4#4+ &)$*$ # I.S*PS*,+ I5 7'5 F( 7(+5B7(C(F5 <F+, S*PS*,+ B B (7 B 2@9 F( ( '' ( HP*5 H15 H**..**()&60/+'9A-,5F '' #b(.s*ps*,+
140 nm 670 nm 865 nm 1600 nm 2200 nm MICROTOPS Coefficient d Angstrom MICROTOPS (mesure) δ(λ) α 670/865) :02 9:03 9:04 9:05 9:06 9:07 Heure d acquisition (TU) 9:02 9:03 9:04 9:05 9:06 9:07 Heure d acquisition (TU) (a) (b) L'.&9!= )/F )/ '' #b( (7 2@9 ) &60/5.S*PS*, ( B ( 7(F2946@@+ 4(B ''PZ+=J5.*<(5>) /) '+'9A-- /5BP<( L+=(7(F ( Z 1) '+' 9A--/+ = F 7(F5 H**..** (5 > '' #b(5(f(hp*h1(+ ' 9A-,-5 ( + (G5FH1((*+)*+*./ *+.)*+*/ (+#,*(5 (5 F (G ( B B( *+.1 )*+*.1/ *+H )*+*/+ 'F(,*(7( ( + (F F C(>+(C >) *.- *,%/5F(GH1((*+.)*+*./5 (5 - B*+*)*+*/+ ' 9A-,-5 F '' #b('>(+ )*+*./5.+**)*+*./ 7(C+ B F 7(,*
141 F(C +=' B F5>5 7(F+ 5 B ( B ( 2946@@= F C B 7C+ = (!645 B B''G) '5 '+'9A-9A- /5 ( ( 5 } } ) '+ 9A-9A-,/5((C' B) B(Y^ Y.*^/+ 95 (C } } '( ) B(.^/+=7G7CB(5( F >K(('+%''' ) /( B) B '' P <( L/+ 7 ( 5 '' ' '' ( ( HP* (+ =7( (( F '' C(7(((C F + 5 B B ' B '' #b(5(c' > ( ) '+ ' 9A-,- 9A-1- /+ F B B F5 *. *1 %5 B (7C7C 7 7F+ ' 9A-15 G '' '5 (C G( ( ( (C (' 7(+,
142 Rayon effectif Paramètre d asymétrie Reff (µm) g (865 nm) :02 9:03 9:04 9:05 9:06 9:07 Heure d acquisition (TU) (a) Paramètre de concentration :02 9:03 9:04 9:05 9:06 9:07 Heure d acquisition (TU) (b) Numéro des modèles δf 865nm /δt 865nm Numéro des modèles numéro du modèle du mode fin numéro du modèle du mode large 9:02 9:03 9:04 9:05 9:06 9:07 Heure d acquisistion (TU) 9:02 9:03 9:04 9:05 9:06 9:07 Heure d acquisistion (TU) (d) (c) L'.&9!"5((C(72@9)(7&60/ F 2946@@=5 )/ G '' '5 )/ (C G(5 )/ (C ) /((C(' 7(+ =(CG( '9A-1-9A-1-5H1(+'9A-1-5BB ' F'' + =(C 7( 7)'9A- 1-/+ 5 7( F ( (I ( ' +=(C 5(.) '+'9A-1- /5 (C 7F)&":G0/ G'' '*+1* µ( ' +,1-*+**1 H1 () '+ 9A-/+ =(C (( (C ( 7F(B<F)*+1*µ( *+*.5 '+9A-,/+ ' 9A B C ' ' '' (C + F (C (*+5*+***+.15 B(G'' '5(CG( (C ) '+ +,+.+.-/+ 4( B 5 B B ' ' B F( 7(+# > F5,.
143 ( * *,%5B J+ ( ( 7(5 ( ' (&60 &6Y0+ ( 9A-P5 B (G5 -G 5''(C7()(6 6Y/>() /)/) '+'9A--/+( (C7(C<F+ = >) / )/ '' ( B5 9A-P ''+ F (7C ( 7>B5 ( 7((B+ 7 ) / )/ ) / )/ & NO P,* & NO *.S *P,S *.S *P,S V EB" *+ *+*n ΘNSO V EB" PZ HZ PZ HZ *+ *+*1 *+* *+* *+ *+* *+* *+**1 µ *+. W )& NXO W 3) NXO α B(<PEB". EB" η EB" % % µ 2'. ' N )&$'JKO *+H1 + *+11 *+ P)*^/. *+** *+*. *+**. *+* H +* +H * *+,1 *+P )^/ 1)^/ *+* *+ *+*1 *+1. P.+ +* N )&$'JYKO *+H +H *+1 *+* *+**. *+*.1 ** *+*. 1 + P+* *+1.+* *+1PH *+** *+*1 *+** * H N&>/&O α B(<PEB". EB" Z EB" µ µ. 2. +, *+*.n *+11, *+P *+,1.+,P *+1.* *+* *0)*& 9( 3 B.S*PS*,5 &60 &6Y0>) /)/B.S*PS*,5B7(F #6@ ) 7F5 (7 B</+)n/ 7(F+ ( &60 >( 7(F+ >) /5 > 7( 7(C <F+ = F H1 ( ( G '' ' ( (.1^+ (C G(5 B > *^+ =,
144 7( > ( B (C+=(( 5} ( 5 C ' ( ^ F '( F B + = ( ( 5} 5'( F( ^+= ((5 ( ( >5>9A-+= B5 5 > ~* -, 1~* -, 5 B(( + > )/5 7( '' ( (C 15 (C *^+ ( B B 7(F5.*^5 F H1 (5,*^ G '' '+ 5 B > (C ( ( F + = (C } ( (''(.^+ F 7('5F} (.*^+ B(B &6Y0+>) /5 '' ' B &60 &6Y0 ) '' B'> >(C/+= 7 '( 7 + >)/5 &60 &6Y0 B &6Y0 (( (C ( > > ) / > 7 ) '+ 9A-P/+ ='( ( 5 5 7( B ( B+ F (C } G(F('('^(G+, S*S*+ ' 9A-H5 F 5 '' #b(g'' 'S*S*&60+,,
145 δ(λ) nm 670 nm 865 nm 1600 nm 2200 nm MICROTOPS :49 14:50 14:51 14:52 14:53 14:54 14:55 Heure d acquisition (TU) Coefficient d Angstrom Rayon effectif α 670/865 α 670/865 mesuré (MICROTOPS) 14:49 14:50 14:51 14:52 14:53 14:54 14:55 Heure d acquisition (TU) (a) (b) L'.& 9!B )/ F 5)/ '' #b( G '' ' (72@9)&60/5>S*S*) '+' 9A-,-/ ( B ( 7(F 2946@@ <F+ =J5.*<(5'>BS*S*) '+' 9A--/+#,,%5B*<( L5B(+ = B, 1, 1.%5 (' B (5 Y*Z Y,1Z5 '' B (G *Z+ = ( 7(F(G('' <F)( 5 '+ 9A-1/5 ( (.5 '' (7C 7C+ ' 9A-H-5 B F (C >+ =B <F5 F H1 (? B(*+**+*H1+=BB' ( 7(C2946@@) H1 e*+* *+*./+=F B, 1.%B(G*+*H*H1(+4BC 7( 7(F '' ( <F ) H1( e*+*h1 *+* H1 (5 (,15 '+9A-1/+'9A-H-5 (C '' #b((+b(f (C7((>5G '' ' (*+Hµ( Rayon effectif (µm),1
146 ( 9A-5 B (G -G > ''(C7(&60&6Y0 >B'' S*S*+ 7 )/ )/ ) / )/ )/ ) / & NO,,P-, 11, 1-1 *H 1 1,- H **,,P-, 11, 1-1 *H 1 1,- H ** ΘNSO δ EB" *, P *, P *+*H1 *+* *+*H *+* *+*H1 *+**1 *+*P *+* *+* *+*1 *+*P *+* α B(<PEB" µ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e *+.µ(5e+,*-*+**.5&":77(g0/(c + 4(C (C. (C (.+H + *+ P+,H
147 F ' '+ F ( ( ( ( (( ) '+9A-/+=BB(C ' B G'' '(*+*, µ()w '' e*+µ(/+ '>)/5 ' 'F5( *+*5&6Y05*+*P&60+>) /5 &60 6Y0 7 B F *+*P+ >)/5&6Y0( (CC(F+= 7(' I F (7>(7(F+, B (+ = F B <F ( F ( (( ( '+ = B B.S*PS*, S*S* (I(G7F)αf+/+= (5B E5 +>I B5(FH1((C #b((cc'5 B(*+**+C+7(( F G '' ' ( *+1 *+H µ(+ I.S*PS*,5 (CB '*+µ(+ =(7B2@9( += F C F (C 7( 'B+'5 F (C ( ( ( ( 2946@@= > B)} _*^/+=( ' (C'> 7+# '5 I.S*PS*,5 B 7(F F ' +,.- *+* HP* (5 +,1-*+**1 (C + ( 5' (C+ 7 ''5(7 '()&6Y0/( '7(B (B+,P
148 =#:)& '# 75 B 2946@@= - (+ B 5 (5 (7 B 2@9 B F ( ( '' (+ = ( B B 7(B@@S#6@5(F2946@@= (C ) 75 5 U / B ( 2@9+ 4 ( B ' ( ( (7 + 5 B ( ( ( ( 2946@@=+ B F 7 ( 7( B--B ( B+ 5 '( ( ((( '+'5 'F)g*+H1(/5B B7(+4- C(( (75 ( > (+ B ( ( 7 ( F' F ' '( + % 5 B (( ('( -7 - Q( +5.**1R+ '' 7 >(7F('(( 5 Q4 +5 P` 2 7< +5.**R+ = ( 5 - (5 ( ( '( + 5 CB5 7( '( -+,
149 -*3'$" 3'+$+ *%'*$'1 % &2* 33)'*$' C )* **$+' *$'% *+ ) *&9% & % $ # = ' ( (7 B-) '+ (-(F ( - H1 (5 ('( (7 + B B5 2946@@=5 7 5 ( (G-'+ 4- ( 7G7C F ' ' ( B(G-')HP*-..**(/+#..**(5''(7C ((5 (B(( ' ( 5B5(CB@=6+ 75 > I ' '> B5 )/ ' B(G-'5)/( '( (G-' -+,
150 = (C 7 B ' + ' +'' ( (..**((+%C 5Q+5.**1R5( > ( ' +=> - 5 ( + (5 B (7 B ' B ()G&7 0/5 (+=I '5 5 ('( > 7 '' 2946@@=+ = (7 &7 05 B 2@95 (( (F ( ( ' ( )47 /+ ' ( ( 2946@@= B' GB+ 75 7( (C -+ (7 ( >( ' + ( ' '( > 7 )&( 0&7 0/''B' B 7+ 1*
151 "#!$&%% 33'+$+ *%'*$'1 % &2* %&1' '0)*& 5 B F B (7F + B *HS*S*,5 S*S*15 S*.S*(.S*PS*,) '+999-/+=>(B( '' FB(')'*+HP*(/5 ( ) B( 1**.**(C/+ 4 >( ( (5 5 (7C (+ 4 B - '' G ' ( B B+ B ' ' ' ' + ' ' + (( B '' 7 )+1<(/+ = (7F BS*.S*,C F' ' + I5 F > B5Y,1Z)''/5 7' BB+ 5 ((5 B.S*PS*,5 FB5 B '' '' C+ (5 ( '' ( (..**((5( ( +5'5BS*.S**HS*S*, (F(7&7 0+ "#!#!$&%%)*+3 3$*)% &2* 3)*' *$' =7G7CB >F ' F ' ('> + 4 7G7C (F F ' K ( ( C B ' ) '+ 7./+ ( ' B 7-')HP*-H1(/+= > 5 + = ' 1
152 ( B 7F 'F (7FC +#C ''(7C5( G ' ( B+ F' '' >B5 7 (B(G ' ' 5,,5 HP* H15 ( ( ( B/+ 4 ( '' 7FBI+% (( '' ' GBF+ 5 (B FE7>B ' ''+ 4 ( ' '' > ' ' HP*H1(+=(( B G(F+ >( Q4+5.**`+5.**1R( C( ' 5( '( B(G-'+4B (6 Q4 +5 PR5 ( ( 7 5 (,*..1* (+ = 'F ' (C ( -+ (5 ' 5> ( B 7 + = B> ( (( '' ( *ZH*Z+= ((C ' + =( ' F)_.**(/5 E7.*Z+#C '' (7C5 ' ' B'' '' B C+ 4 ( ' '' > '' B ''(F''C5 5 5'' H*Z+=''B F'+ ' (B( FFB(+= ' ' (( 1.
153 ''+ ' 5 ' (B''(7C+ '(( ( ( 2946@@= ( +4 ''(7F+ ( ( (5 >( ''() '+ 7./+''7F>(( F ( '' F ( Q=G+5P54+5PR+ >(5( BK(+( ( ( B 5 ' ( 5' 5 ((5 λ ( )= δ λ ( ) λ ( Θ) + δ λ( ) λ ( Θ) ω λ > α δ 5λ + δ λ,µ ),µ ) µ > αδ 5λ + βδ 5λ + αδ λ ( )+ βδ λ ( ) µ µ) ( ) µ ) + µ! ρ )A-/ = C B( F B > ( > +=(µ µ B B(> E(> B+=(δ δ)e/ B(F F(' B)/+=(F ω ' 7 ( ''+ = (Cαβ((C(F+! ρ ' ' + = > ( ( F > > ( ( ( ( 5 >( >( '' (+ = ( > (5 B(5( ( 5 ' (7C)( Y/+ ='(( 1
154 &(0FG((I' B)E/+=F (BF + = F5 E5 F>5 ((5 δ ( ) = δ > )A-./ δ)e/δ B(FE F+'5E 77+= 7 7( '> B(.<(+ 5 ' B '' ' F G(''F((K( F' +4'' (G(+=(Cα β(f( +=(Cβ'>' (C )*+gβg*+h/+% ' (F ( B (C ' '' #b(q=' 5PR+=( G((C' (C α ( *++ 4 >( ( B F '' '',* (5 (+ 4'(( B HP* H1 (+ 7( )δ *+.1HP*(/B'H*Z5 >A- 5(.+* -, HP*(+* -, H1(5' ' '( Q=' 5PR+ 5 C 5 F B(' 7 *+*,5 *+*P5 *+* *+1 ) HP* (/ B( I S*.S*5 S*S*15 *HS*S*,.S*PS*,+ ' ' 5 5( ''(7C5FA-+ 1,
155 ρ = µ - ( λ) ( λ) ( λ) - ( λ) )A-/ =>(FA-+ B (C'#6@) '' #b(/f (+ 4 ''(BB+= ( (7F (K('J ' ' '+ 4 F (B2946@@= #G5( '5' BF'(( (( 5>( B' +B'' ''B C5 ' ' (7 + ''B) '+'A-/+ ('A--A--5' B( HP*(H**('..**((B '' '' B 5 B S*.S*5 *HS*S*, S*S*1+ ( + = B 55' '' (GB+ =(('' 7 (P*Z1Z) '+ 999-,/+ = E7> B B B(,Z H*Z5 Y.ZY,1Z+=( ('' >( )ϕ e*z/±,*z+ 11
156 Reflectance polarisée à 670 nm y=x y=a*x+b a= 0.97 b= R=0.93 Reflectance polarisée de surface à 1600 nm y=x y=a*x+b a= 1.03 b= R= Reflectance polarisée de surface à 2200 nm Reflectance polarisée de surface à 2200 nm (a) (b) L'.&9!56' ' HP*()/H**()/'..**(+(B''B)r B *Z/5 B*HS*S*,5S*S*1S*.S*+ ' A-- A--5 B '' B5 *++ = '' > '' ' '^+B'B(( ( + ( F (HP*..**()'A--/+4 '( > F ( ( (C + 4 (+4 (B ' B ( ( Q5 R+ = (G' (HP*H**( (..**(B B(*+*,~* -. *+*~* -. +B5B 7 ±*+**.1)_*^(/+=(( > '' ' +@=65 (G HP*H1((*+*P1~* -. *+~* -. 5 ' B5*+~* -. *+.H~* -. 5' F+='' > B 5HP*5H**..**(5 ( > B@=6+4(F ' (B(G-'+4( B (CB (65F ' 5 (K(( B'' ''B+ 1H
157 H**-..** (5 BC > B( (5 B Y+1~* -, )' A--/+ 4 B >F (('F'' (G' H**-..** (5F HP*-..**(+ 5B B BBF''( -.+1~* -, + (C7G7C>F ( (+B( F > HP*5 H**..** (5 B( ^5 H^ *^) '+ 7 /+ F '' ' *+, > ' H** (5 BY+~* -, B*+P+ F '' ' +* *+* > '..** (5 B( *+ +*P5 )/ B B( Y+~* -, Y+*~* -, + = '' B( H^+=( F (>F(B+5 '' 7 B ''5 F ( F( B (C ( + B ( C( '' (7C+=( (7FB (7F )FG / B+ 4- ( ( B + = '' (7F ( B 5 ( (7F ' ' H** ( F HP* (+#..** (5 (7F ((C'K ) ^/+=> HP*-..** (5 ( F '' (7C HP* (+ => '( ' C C( '' += (7F H**(> CH^5('' +B (> 7G7C(B ( '' (7C >F + 5 K>F F C( ( P
158 B BF F ( H1 (5 K ( B5 ((5 H** (+ 4 7G7C ( >F > ' G(F + G( (BB B + ( '' C B *HS*S*,5 S*S*1.S*PS*,+ ( ' A-.- A-.-5 ' B((HP*H**(' (..**(B''C+ Reflectance polarisée de surface à 670 nm y=a*x+b a= b= R= Reflectance polarisée de surface à 1600 nm y=a*x+b a= 0.30 b= R= Reflectance polarisée de surface à 2200 nm Reflectance polarisée de surface à 2200 nm (a) (b) L'.&94 6' ' HP*()/H**()/'..**(+(B''C)r B g*z/5 B*HS*S*,5S*S*1.S*PS*,+ = (( '' 7 (,Z P.Z) '+ 999-,/+ = E7> B B B(,*Z 1*Z5-1Z -,1Z+ = ( *HS*S*, S*S*1 ( '' >( )ϕ e*z/ϕ e±,*z +=E('.S*PS*,.*Z+ =B>5(G'F B '' B) '+' A-/+ 4 B B (( ' 5(B '' 1
159 QE +5.**R+ ( F ' ' B B+ B 5 F ( B 7 - )ΘfH*Z/+ (C 5 B C'(+ HP*-..** (5 B )' A-.-/+ 5 B ((F?+4''( B) ' /+='B ( ( ( + = (G' ' HP*H**(..**(5B B(-1+1~* -, -*+1~* -, +4 '5( ' ''B+>( ' A-.-5 B '..** (5 ( * *+**,5 ( B HP* ( ( -*+** *+**+ 4 B ( > '' > (F '' C+ 7 7 F' '' ' ( BG' + = ( B B B 2946@@=+ B '' B5 B G(F( ''+(G5 '' > B '+ B '' C ''5 ' ( (( B ( + ( (7F '' G ' 7 F B B(+ 1+++#G5 ' 5' (F (( ((5(5 B B ( 2@9+ = ( B *HS*S*, S*S*1 B + B A-5 1
160 F ( 7(C =5 F F (G ( B *HS*S*, -G + => B 7 7(C 2946@@+ 4( F B > (+ ' A-5 I 7B5F (+ F )%/ δ,,* δ HP* δ H1 δ *.* #6@)=/ P ** *+. *+11 *+* *+* *- * *+±*+*P *+±*+*. *+±*+* *+**±*+** 2946@@ P **)/ *+* *+H *+* *+*P1 1)./ *+ *+H *+* *+*P1 *)/ *+.. *+ *+* *+*H 1),/ *+..1 *+ *+*P *+*,1 *.*)1/ *+. *+* *+*H1 *+*, *0)*&9! F7(F(=)#6@/> B7(C2946@@*HS*S*, Lille (1) Latitude ( ) (5) (2) (3) (4) Vol du 06/09/04 MICROTOPS Valenciennes Longitude ( ) L'.&9: I 7B*HS*S*, (7(F+ =()/ 7(C=+ = B(G F '' #b(( = B B( *+ +1+ (7C'( +B ((( H*
161 B 7(C#6@) P **%5 '+ A-/+ HP*5H1*.*(5 (>(F( 1+* - +4 ' )*+*/5 F(F 7(C '( + =,,* ( ()*+*./F (+ B5 F >( > B), 15 '' A-/5 ('F B=) *+*,/+=B '' #b(b)(1/5 5C 7 =+ = B (( (>( B( +P1 +*+ I5 (C ' #6@ F((2946@@+ 5 F*+5F >B+4B BF(B) '+A-5,1/+ I5 ( ( 7(F H1 (+ 4( '' (C #6@ + B ' ' ' ( (C += ((( ((F(C( (((('' ( * *Z) '+ > A-/+ B5 H1(B ',^5 F(FF (C 5 5 ' B) ' /+ = B S*S*1 ( (K( F *HS*S*,+ = B ).**(/ > B + = 7 ( '+ = B 7(F '' = > B5 F ' B ( 7 + =F(G(7(C=5' B) *%-* **%/5(*+*HP*( '' #b((g B +P*+ I 5 (C F'7(C@@S#6@+ H
162 B ( 5 '( B (7C+ B5 F (' B5' F (5**+1<( *HS*S*,)δ *+1<( Sδ /+ >( ( ''5 ( F ) '+ 7 9/+ = ( '' ' ' + 5 B( C ( C ' + = (I( 7 ( (7F+ = 7 7 (BFF (CFF<(C' (F+=7 7( ' ( 7 + I *HS*S*,5 (( '' C E ( )/(('' )(C #682-! /+=( 7(5 5K ''B (+%B'( F 7 ( (F+ = B ( 7+ B5(?B (C +=7 7( (' B+ = (&$%9!0)($%9! /5 FF '( ( B 7F+=I ' ( B( B+ # 5 ( )( B5 (7F5 CB( G U/5 F ( 7(F )@@S#6@/5 += > (47E5.**1+ ='B >''(FB ( *+ +1 <(+ = ' B > '' > >I)D.***/5( ''+ = B ( ( H.
163 (F+4B(F ( B5 B 7F (7C '' ( (B + ' > 5 ( B ) '+ F A-./+ 4 ' F ( B 7 7.+* <(+ = 7F B <(+ = F δ)e/sδ ' F (' B+*+1*+.<(5 77+1<(5 ' F B(.^.^+ 4( ' F B S*S*15 '' 7 (7C B+ I *HS*S*,5 B B (7C5 '' (' 1*^)E e*+p.<(/.*^)e e.+*<(/ ' ' ' + =B*HS*S.**,S*S.**1 ( J ' + > G ' 5 ( E'C5 G ' F F' ) 7(5 B/E)BA /B+ 'A-,5( (+1<(*HS*S*, 'A-15(GB+ H
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