Approche multifractale de la modélisation stochastique en hydrologie

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Approche multifractale de la modélisation stochastique

en hydrologie

Keltoum Chaouche

To cite this version:

Keltoum Chaouche. Approche multifractale de la modélisation stochastique en hydrologie. Mathéma-tiques [math]. ENGREF (AgroParisTech), 2001. Français. �tel-00005781�

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edvfxohphqw gh od Uìxqlrq +wurqfdwxuh ã 8(,= Pìwkrghv gx pd{lpxp gh yudlvhpeodqfh +PY, hw gh od IPGU1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <9

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ylll 6164 Hvwlpdwlrq gh od irqfwlrq gh vxuylh gh od vìulh ghv judqghv iuìtxhqfhv gh edv0

fxohphqw HSVDW +wurqfdwxuh ã 8(,= Pìwkrghv gx pd{lpxp gh yudlvhp0 eodqfh +PY, hw gh od IPGU1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <; H14 Olvwh ghv vwdwlrqv ghv vìulhv dqqxhoohv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 465

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d +Q @ qrpeuh pr|hq gh erñwhv qrq ylghv, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 64 519 Frpswdjh gh erlwhv vxu ohv grqqìhv Edglqdjh +S@ shqwh vxu ^8plq> 4k73plq`

hw S2@ shqwh vxu ^4k73plq> 4m43k`,= 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 66

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edvfxohphqw/ G @Gxuìh g*revhuydwlrq S @Shqwh vxu ^5=8plq> 9k`, 1 1 1 1 1 1 69 51< Uhyxh eleolrjudskltxh ghv prgëohv pxowliudfwdov 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 73 614 12/ srxu txhotxhv orlv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7; 615 Pr|hqqhv hw yduldqfhv ghv hvwlpdwlrqv gdqv xq prgëoh JY H + @ 3> @ 5=3:> # @ 3=78,

+2; = Pd{lpxp gh yudlvhpeodqfh hw 25 = prphqwv srqgìuìv,1 1 1 1 1 1 1 97 616 Hvwlpdwlrqv pr|hqqhv gh hw sdu ohv pìwkrghv ghv prphqwv hw gx pd{l0

pxp gh yudlvhpeodqfh gdqv xq prgëoh S J+> , vxu 83 ìfkdqwloorqv vlpxoìv gh wdloohv 833 hw 4333 gh S J+5> 3=64,1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98 617 Hvwlpdwlrqv pr|hqqhv gh hw vxu 83 4333ìfkdqwloorqv vlpxoìv gh SJ+5> 3=<3,

+sdu ohv pìwkrghv ghv prphqwv hw gx pd{lpxp gh yudlvhpeodqfh gdqv xq prgëoh gh Sduhwr jìqìudolvìh, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 98 618 Pr|hqqhv hw yduldqfhv ghv hvwlpdwlrqv gh sdu od 12/7 vxu 83 ìfkdqwloorqv

vlpxoìv gh orl Do+6=5, + @ 3=64,gh wdloohv 833 hw 43331 1 1 1 1 1 1 1 1 1 1 1 1 :8 619 Fdudfwìulvwltxhv ghv vwdwlrqv1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 <4 61: Hvwlpdwlrqv gx sdudpëwuh gh gìfurlvvdqfh dojìeultxh At vxu ohv vìulhv gh gìelwv

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Mh uhphuflh hqq wrxv fhx{ txl rqw irxuql ohv grqqìhv k|gurorjltxhv = PP1 W1 Oheho/ D1 Edufhor hw D1 Fdvwìdqx1

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(16)

6 ghv vìulhv qh frxyuhqw txh txhotxhv gìfhqqlhv/ hw uduhv vrqw fhoohv txl v*ìwdohqw vxu soxv gh 433 dqv1 Srxu dffìghu ã ghv lqirupdwlrqv soxv dqflhqqhv frqfhuqdqw oh folpdw rx ohv uhfrugv pìwìrurorjltxhv klvwrultxhv/ glyhuvhv yrlhv rqw ìwì sursrvìv whoohv txh ohv pìwkrghv gh sdoìr0 k|gurorjlh1 Fhshqgdqw fhv surfìgìv qh shuphwwhqw g*dffìghu tx*ã ghv hvwlpdwlrqv jurvvlëuhv vxu ohv xfwxdwlrqv folpdwltxhv klvwrultxhv/ hw qh irxuqlvvhqw mdpdlv gh vìulhv whpsruhoohv k|gurorjltxhv deohv1

V*lo vh uhvwuhljqdlw ã xqh dqdo|vh iuìtxhqwlvwh/ o*k|gurorjxh vhudlw reoljì gh vh frq0 whqwhu ghv frxuwhv vìulhv olvvìhv glvsrqleohv dxmrxug*kxl hw vhudlw shx ã píph gh uìsrqguh dx{ glyhuv ghpdqghv ìyrtxìhv suìfìghpphqw1 Lo hvw grqf qìfhvvdluh g*ìoderuhu xq prgëoh/ f*hvw0ã0gluh xq hqvhpeoh g*k|srwkëvhv dlqvl tx*xqh irupdolvdwlrq pdwkìpdwltxh shuphwwdqw g*dwwhlqguh fhv remhfwliv juåfh dx{ grqqìhv1 Ohv frqqdlvvdqfhv txh o*rq srvvëgh ã sulrul vxu oh skìqrpëqh soxylhx{ vrqw ã idluh jxuhu gdqv oh prgëoh1 Fhv ghuqlëuhv shxyhqw íwuh lvvxhv gh od sk|vltxh/ pdlv dxvvl íwuh gh vlpsohv ìylghqfhv olìhv ã ghv v|pìwulhv rx ghv lqyduldqfhv g*ìfkhooh1 Fhshqgdqw/ o*ìoderudwlrq gh prgëohv gh soxlh vxu gh frxuwhv vìulhv vrxoëyh glyhuv sureoëphv g*ruguh vwdwlvwltxh=

Fhoxl gh od vwdwlrqqdulwì rx qrq gh vìulhv sdu qdwxuh qlhv = Od vwdwlrqqdulwì g*xqh vìulh gh yduldeohv hvw xqh qrwlrq uhodwlyh ã od orqjxhxu gh od vìulh1 Hq hhw/ oruvtxh o*rq frqvlgëuh od vìulh gh od jxuh 414 dydqw wurqfdwxuh/ rq shxw frqfoxuh ã od suìvhqfh g*xqh whqgdqfh rx g*xq vdxw dx olhx g*xq f|foh1

Oh sureoëph gh od txdolwì gh o*hvwlpdwlrq hq jìqìudo +ghv sdudpëwuhv, hw gh od frqyhu0 jhqfh ghv hvwlpdwhxuv1

Fh ghuqlhu sureoëph vh frqmxjxh ã fhoxl gh od judqgh yduldelolwì ghv vìulhv1

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Gh píph od uìdolvdwlrq gh wudqvihuw g*lqirupdwlrq vsdwldoh hvw shx dlvìh gdqv ohv prg0 ëohv vwdwlvwltxhv fodvvltxhv1

Dfwxhoohphqw/ od soxsduw ghv prgëohv k|gurorjltxhv vrqw gìyhorssìv hq xq vlwh hw ã xqh fhuwdlqh ìfkhooh gh whpsv/ hq dmxvwdqw gh idêrq vxemhfwlyh xqh glvwulexwlrq hw2rx xq surfhvvxv vwrfkdvwltxh ã xqh vìulh soxylrpìwultxh1 Od sìulrgh gh uhwrxu g*xq ìyìqhphqw hvw hq hhw irqfwlrq gx prgëoh fkrlvl1 Ohv prgëohv h{srqhqwlhov hw dojìeultxhv/ txl shxyhqw íwuh ìtxlydohqwv srxu o*hvwlpdwlrq ghv ìyìqhphqwv iuìtxhqwv/ surfxuhqw ghv uìvxowdwv irqgd0 phqwdohphqw glìuhqwv srxu o*hvwlpdwlrq ghv judqghv sìulrghv gh uhwrxu1 Hq hhw/ gdqv xq prgëoh h{srqhqwlho/ rq sdvvh gx gìelw gh gxuìh gh uhwrxu 3 dqqìhv dx gìelw gh gxuìh gh uhwrxu 43 3 dqqìhv sdu o*dgglwlrq g*xqh frqvwdqwh doruv txh gdqv xq prgëoh dojìeultxh/ lo

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7

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O*ruljlqdolwì gh fhwwh wkëvh frqvlvwh ã gìyhorsshu xqh qrxyhooh pìwkrgh vwdwlvwltxh g*hvwlpdwlrq gh o*lqglfh gh gìfurlvvdqfh dojìeultxh/ sdudpëwuh hqwudqw hq mhx gdqv ghv prg0 ëohv hq fdvfdghv pxowliudfwdohv/ hw ã hhfwxhu xqh fodvvlfdwlrq ghv iruphv gh gìshqgdqfh wkìrultxhv gh whov prgëohv1

Fhwwh wkëvh ylvh soxv suìflvìphqw ohv remhfwliv vxlydqwv =

Srxu sdolhu ohv sureoëphv olìv ã od phvxuh hw ã o*luuìjxodulwì ghv vìulhv/ lo hvw qìfhv0 vdluh g*dffhqwxhu oh wudydlo g*ìoderudwlrq gh pìwkrghv g*h{sorudwlrq hw g*hvwlpdwlrq vwdwlvwltxh1 Xq rxwlo vwdwlvwltxh dgdswì ã gh whoohv vìulhv hvw grqf gìyhorssì1

Od qrwlrq gh orqjxh gìshqgdqfh hvw gh soxv hq soxv derugìh gdqv od olwwìudwxuh k|0 gurorjltxh1 Od plvh hq uhodwlrq gh fhwwh sursulìwì vwdwlvwltxh dyhf ohv prgëohv hq fdvfdghv frqvwlwxh od vhfrqg remhfwli gh fh wudydlo1 Od gìwhuplqdwlrq ghv prgëohv gh fdvfdghv txl srvvëghqw rx qrq fhwwh sursulìwì shuphw/ g*xqh sduw g*dssurirqglu o*ìwdw ghv frqqdlvvdqfhv gh whov prgëohv hw g*dxwuh sduw g*d!qhu o*hvwlpdwlrq ghv sdudpëwuhv gx prgëoh +juåfh ã ghv rxwlov vwdwlvwltxhv dssursulìv h{lvwdqw gdqv od olwwìudwxuh,1 Fh prgëoh/ pxql gh fhv rxwlov vwdwlvwltxhv/ ghyud íwuh frqiurqwì ã ghv grqqìhv k|0

gurorjltxhv uìhoohv +soxlhv hw gìelwv, lvvxhv gh glyhuv vlwhv hw ã glyhuv sdv gh whpsv = ohv uìvxowdwv rewhqxv vhurqw frpsduìv ã fhx{ uhfhqvìv gdqv od olwwìudwxuh1

Hqq/ fh wudydlo guhvvhud xqh olvwh gh uhfrppdqgdwlrqv dx{ lqjìqlhxuv srxu derxwlu dx gìyhorsshphqw gh prgëohv k|gurorjltxhv rsìudwlrqqhov1

416 Gìpdufkh sursrvìh

Fh wudydlo v*rujdqlvh hq ghx{ sduwlhv1

Gdqv od suhplëuh sduwlh/ rq frpphqfh sdu udsshohu ohv dvshfwv pìwìrurorjltxhv ghv suìflslwdwlrqv hw ohv olplwhv olìhv ã od phvxuh ghv yduldeohv k|gurorjltxhv1 Sxlv/ dsuëv xqh ghvfulswlrq gh o*ìwdw gh o*duw hq pdwlëuh gh pìwkrghv vwdwlvwltxhv g*hvwlpdwlrq vsd0 wldoh/ xqh uhyxh ghv sulqflsdx{ prgëohv vwrfkdvwltxhv xwlolvìv hq k|gurorjlh hvw guhvvìh1 Hqq ohv iudfwdov hw ohv prgëohv hq fdvfdghv pxowliudfwdohv vrqw suìvhqwìv vrxv ohxu iruph jìqìudoh dlqvl tx*xqh uhyxh ghv sulqflsdx{ dxwhxuv ohv d|dqw dssoltxìhv hq k|gurorjlh1 Xqh

(20)

: vwuxfwxuh iudfwdoh gh o*rffxuuhqfh gh soxlh hvw gìfhoìh vxu ghv vìulhv Vdkìolhqqhv +grqqìhv EDGLQDJH,1

Od ghx{lëph sduwlh hvw frqvdfuìh dx{ orlv gh w|sh dojìeultxh +txl dssdudlvvhqw gdqv ohv prgëohv hq fdvfdghv pxowliudfwdohv,1 Gdqv xq suhplhu whpsv/ hoohv vrqw gìqlhv sxlv rq suìvhqwh oh fdguh suredelolvwh gdqv ohtxho hoohv vh gìyhorsshqw +oh grpdlqh g*dwwudfwlrq gh od orl gh Iuìfkhw,1 Xqh uhyxh eleolrjudskltxh ghv glyhuv rxwlov vwdwlvwltxhv dgdswìv dx{ h{wuíphv hvw guhvvìh1 Xq rxwlo vwdwlvwltxh ruljlqdo g*h{sorudwlrq hw g*hvwlpdwlrq gx sdudpëwuh gh gìfurlvvdqfh dojìeultxh hvw ìoderuì1 Lo hvw frqiurqwì dx{ dxwuhv rxwlov vxu ghv vlpxodwlrqv/ sxlv dssoltxì ã glyhuvhv vìulhv gh soxlhv +sdv gh whpsv glìuhqwv hw 565 vìulhv dqqxhoohv ã wudyhuv oh prqgh,1 Fhwwh vrxv0sduwlh ghvfulswlyh frqfoxw ã =

Xq frpsruwhphqw dojìeultxh ghv vìulhv ghv h{wuíphv soxylrpìwultxhv

Xqh lqyduldqfh vsdwldoh hw whpsruhooh gx sdudpëwuh gh gìfurlvvdqfh dojìeultxh +grq0 qìhv gx surmhw IULHQG0DP\ gdqv oh fdguh gh o*XQHVFR hw orqjxhv vìulhv gh fxpxov gh soxlh ã sdv gh whpsv doodqw gh od mrxuqìh ã od plqxwh,1

O*h{sorudwlrq gh od shuvlvwdqfh gh fh frpsruwhphqw ã idleoh sdv gh whpsv hvw hhfwxìh ã sduwlu gh vìulhv ã edvfxohphqw g*dxjhw +grqqìhv HSVDW0Qljhu hw vìulh gh o*Loh gh od Uìxqlrq,/ vxlwh ã xq wudydlo suìolplqdluh g*dgdswdwlrq gh o*rxwlo dx{ vìulhv gh iuìtxhqfh gh edvfxohphqw1

Od wurlvlëph sduwlh gh fh wudydlo dqdo|vh od iruph gh gìshqgdqfh ghv vìulhv k|0 gurorjltxhv1 Ohv fdvfdghv pxowliudfwdohv vrqw ghv prgëohv vlpsohv txl uhwudqvfulyhqw o*lqyduldqfh g*ìfkhooh gx sdudpëwuh gh gìfurlvvdqfh dojìeultxh frqvwdwìh gdqv od ghx{lëph sduwlh1 Pdlv uhqghqw0lov frpswh g*dxwuhv sursulìwìv vwdwlvwltxhv frqvwdwìhv hq sudwltxh B Od sursulìwì gh orqjxh gìshqgdqfh hvw xqh dxwuh fdudfwìulvwltxh frxudpphqw derugìh gdqv od olwwìudwxuh k|0 gurorjltxh1 Lo hvw grqf lqwìuhvvdqw g*dqdo|vhu/ vxu xq sodq wkìrultxh/ oh w|sh gh gìshqgdqfh +ã frxuw whuph hw ã orqj whuph, ghv fdvfdghv pxowliudfwdohv1 Txhotxhv fdvfdghv sduwlfxolëuhv vrqw ìwxglìhv soxv hq gìwdlo +orj0Jdppd/ orj0Qrupdoh rx orj0Srlvvrq,1 Ghv rxwlov shuiru0 pdqwv uhfhqvìv gdqv od olwwìudwxuh vwdwlvwltxh vrqw dssoltxìv ã qrv vìulhv srxu o*hvwlpdwlrq gx sdudpëwuh gh orqjxh gìshqgdqfh1 Lov frqfoxhqw ã od suìvhqfh gh orqjxh gìshqgdqfh vxu ohv vìulhv gh ulylëuhv vxu fudlh1

Hqq/ gdqv od sduwlh Frqfoxvlrq/ xqh v|qwkëvh ghv uìvxowdwv hvw suìvhqwìh/ dlqvl txh ohxuv olplwhv g*lqwhusuìwdwlrq1

(21)

;

Fkdslwuh 5

Fkdpsv gh soxlh hw prgìolvdwlrq

vwrfkdvwltxh

Sdupl ohv sulqflsdx{ remhfwliv gh o*k|gurorjlh jxuhqw od jìqìudwlrq ghv grqqìhv v|qwkìwltxhv +sdu h{hpsoh srxu whvwhu od uìvlvwdqfh g*xq rxyudjh idfh ã glyhuv vfhqdull, hw od suìylvlrq gh grqqìhv ixwxuhv +soxlh rx gìelw,1V*lo yhxw h{sorlwhu oh soxv odujhphqw srvvleoh o*lqirupdwlrq grqw lo glvsrvh hw qh sdv vh frqwhqwhu g*xqh dqdo|vh ghvfulswlyh ghv grqqìhv/ o*k|gurorjxh grlw dx suìdodeoh ìoderuhu xq prgëoh1Hq jìqìudo/ xq prgëoh frpsruwh ghx{ yrohwv = gìwhuplqlvwh rx vwrfkdvwltxh1Sduirlv oh yrohw gìwhuplqlvwh hvw devhqw hw oh prgëoh hvw sxuhphqw vwrfkdvwltxh/ g*dxwuhv irlv oh yrohw vwrfkdvwltxh hvw devhqw hw oh prgëoh hvw sxuhphqw gìwhuplqlvwh +rx pìfdqlvwh,1Pdlv fhv ghx{ yrohwv shxyhqw dxvvl vh frpsoìwhu = gdqv oh prgëoh olqìdluh sdu h{hpsoh oh yrohw vwrfkdvwltxh hvw oh uìfhswdfoh gh o*huuhxu1

Ohv prgëohv sxuhphqw vwrfkdvwltxhv +rx erñwhv qrluhv, qh vrqw g*dxfxqh xwlolwì srxu od prgìolvdwlrq ghv fkdpsv gh soxlh rü o*rq srvvëgh ghv frqqdlvvdqfhv d sulrul vxu od fdxvdolwì gx skìqrpëqh +yrlu sdu h{hpsoh od klìudufklh gh vwuxfwxuhv ìwdeolh sdu Dxvwlq hw Krx}h/ :5 ^6`,1Ohv prgëohv sxuhphqw gìwhuplqlvwhv txdqw ã hx{/ vrqw vxuwrxw gìyhorssìv hq pìwìrurorjlh hw whqwhqw gh uhsurgxluh od g|qdpltxh ghv fkdpsv gh soxlh1Frpph ohv ìtxd0 wlrqv h{dfwhv uìjlvvdqw oh skìqrpëqh vrqw lqfrqqxhv/ fhv prgëohv uhsrvhqw vxu ghv ìtxdwlrqv dx{ gìulyìhv sduwlhoohv gh Qdylhu0Vwrnhv txl vrqw wurqtxìhv hw dssur{lpìhv srxu gìfuluh od g|qdpltxh gh o*dwprvskëuh/ sxlv lqwìjuìhv qxpìultxhphqw +vrxv k|srwkëvh g*krprjìqìlwì ã fkdtxh ìfkhooh,1Pdojuì fhv vlpsolfdwlrqv elhq vrxyhqw ìorljqìhv gh od uìdolwì/ ohv ìtxd0 wlrqv uìvxowdqw gh fhv prgëohv uhvwhqw frpsoh{hv hw ohv fdofxov qxpìultxhv wuëv orxugv1Gh soxv/ ohv ìfkhoohv vrqw ìwxglìhv lqgìshqgdpphqw ohv xqhv ghv dxwuhv1

Ohv prgëohv ã od irlv vwrfkdvwltxhv hw gìwhuplqlvwhv uhqfrqwuìv gdqv od olwwìud0 wxuh vrqw kdelwxhoohphqw whpsruhov hw frqvwuxlwv dxwrxu g*xqh vhxoh ìfkhooh +gh w|sh vìulh fkurqrorjltxh,1Ru ohv olhqv frqqxv hqwuh uìdolvdwlrq gx skìqrpëqh ã glìuhqwhv ìfkhoohv uhqghqw lqdgìtxdwv fh jhquh gh prgëohv1Ohv prgëohv vsdwldx{ hw vsdwlr0whpsruhov lqwëjuhqw soxvlhxuv ìfkhoohv hq vh edvdqw jìqìudohphqw vxu od klìudufklh ghv vwuxfwxuhv gh fkdpsv gh soxlh gh Dxvwlq hw Krx}h ^6`1Pdlv lo q*hvw sk|vltxhphqw sdv mxvwlì tx*rq grlyh suly0 loìjlhu fhuwdlqhv ìfkhoohv glwhv fdudfwìulvwltxhv1Gdqv xq hruw g*lqwìjudwlrq gx pd{lpxp g*lqirupdwlrq/ oh prgìolvdwhxu vh ghyud gh phwwuh hq mhx xqh jdpph g*ìfkhooh dxvvl odujh txh srvvleoh1

(22)

< Gdqv fhwwh sduwlh/ rq suìvhqwh eulëyhphqw o*ìwdw ghv frqqdlvvdqfhv txh o*rq srvvëgh d sulrul vxu oh skìqrpëqh soxylhx{/ ohv gl!fxowìv ã oh phvxuhu dlqvl txh ghv rxwlov vwrfkdv0 wltxhv shuwlqhqwv srxu od prgìolvdwlrq gh fh ghuqlhu1Hqq / rq suìvhqwhud ohv prgëohv iudfwdov hw pxowliudfwdov +Pdqghoeurw/ :8 ^8<`/ Vfkhuw}hu hw Oryhmr|/ <6 ^:9`, txl rqw frqqx xq gìyhorsshphqw uìfhqw1Lov ruhqw xq fdguh irupho suhqdqw gluhfwhphqw hq frpswh xqh iruph g*lqyduldqfh g*ìfkhooh gx skìqrpëqh/ shuphwwdqw dlqvl xqh uìgxfwlrq gx qrpeuh gh sdudpëwuhv hw xqh h{wudsrodwlrq gh o*lqirupdwlrq hqwuh ohv ìfkhoohv1

514 Ohv fkdpsv gh soxlh

Dydqw gh gìfuluh ohv surfìgìv gh phvxuh gh soxlh/ qrxv doorqv eulëyhphqw udsshohu o*ìwdw ghv frqqdlvvdqfhv vxu od vwuxfwxuh ghv fkdpsv gh soxlh hw ohv jdpphv g*ìfkhooh vxu ohvtxhoohv lo hvw srvvleoh gh phvxuhu fh skìqrpëqh1Xq wdeohdx irxuqlud hqvxlwh ohv ìfkhoohv srxu ohvtxhoohv fhv whfkqltxhv gh phvxuh vrqw vxvfhswleohv gh frqgxluh ã ghv hvwlpdwlrqv deohv1Qrxv whuplqhurqv sdu txhotxhv uhpdutxhv jìqìudohv vxu od shuwlqhqfh ghv k|srwkëvhv vwdwlvwltxhv gh frqwlqxlwì hw gh vwdwlrqqdulwì ghv vìulhv soxylhxvhv1

51414 Pìfdqlvphv jìqìudwhxuv ghv fkdpsv gh soxlh

Ohv sulqflsdx{ w|shv gh suìflslwdwlrqv

Rq glvwlqjxh sulqflsdohphqw wurlv w|shv gh suìflslwdwlrqv txl shxyhqw vxuyhqlu hqvhpeoh hw vh frpsoìwhu =

Suìflslwdwlrqv olìhv dx sdvvdjh g*xqh shuwxuedwlrq iurqwdoh = Hoohv vrqw gxhv dx{ uhq0 frqwuhv gh pdvvhv g*dlu gh whpsìudwxuhv glìuhqwhv1Od wudfh dx vro gh od iurqwlëuh hqwuh fhv ghx{ pdvvhv g*dlu hvw dsshoìh iurqw1Ohv iurqwv fkdxgv +suryrtxìv sdu xq gìsodfhphqw g*dlu fkdxg dx ghvvxv g*dlu iurlg gdqv od píph gluhfwlrq, rffdvlrqqhqw ghv soxlhv gh idleoh lqwhqvlwì hw gh orqjxh gxuìh1Ohv iurqwv iurlgv +suryrtxìv sdu o*dydqfìh g*xqh pdvvh g*dlu iurlg txl vrxoëyh gh o*dlu fkdxg, vrqw pdutxìv sdu gh iruwv slfv g*lqwhqvlwì1

Suìflslwdwlrqv olìhv ã xqh frqyhfwlrq orfdoh = Xq uìfkdxhphqw ghv edvvhv frxfkhv gh o*dwprvskëuh fuìh xq ìtxloleuh wkhupltxh lqvwdeoh1O*dvfhqgdqfh gh o*dlu fkdxg grqqh qdlvvdqfh ã ghv fhooxohv frqyhfwlyhv +}rqh lqwhuwurslfdoh hw }rqh whpsìuìh hq ìwì,1 Suìflslwdwlrqv rurjudskltxhv = Hooh vrqw gxhv ã od suìvhqfh g*xqh eduulëuh prqwdjqhxvh

txl/ vrxv o*hhw gx yhqw/ suryrtxh o*ìoìydwlrq gh pdvvhv g*dlu kxplgh1Lo hq uìvxowh xq uhiurlglvvhphqw gh fhv pdvvhv g*dlu1Lo shxw doruv | dyrlu xq ìtxloleuh wkhupltxh lqvwdeoh +lqvwdelolwì frqyhfwlyh, rx elhq xqh lqvwdelolwì hq dlu vdwxuì1

Vljqdorqv gëv pdlqwhqdqw txh vhorq oh w|sh gh suìflslwdwlrq/ ohv k|srwkëvhv g*xq prgëoh gh soxlh vhurqw glìuhqwhv = o*k|srwkëvh g*lqgìshqgdqfh ghv ìslvrghv soxylhx{ vxf0 fhvvliv vhpeoh soxv sodxvleoh gdqv oh fdv gh suìflslwdwlrqv frqyhfwlyhv txh gdqv oh fdv gh suìflslwdwlrqv iurqwdohv1

(23)

43

Hfkhooh Vsdwldoh Whpsruhooh

v|qrswltxh A43 333 np2 _{Soxvlhxuv mrxuv}

Judqgh pìvr0ìfkhooh 4 333 ã 43 333 np2 _{Soxvlhxuv khxuhv}

Shwlwh pìvr0ìfkhooh 433 ã 733 np2 _{Hqylurq xqh khxuh}

Fhooxoh gh soxlh Hqylurq 43 np2 _{4 plq ã 425 khxuh}

Wdeohdx 514= Rujdqlvdwlrq ghv fkdpsv gh soxlh Klìudufklh ghv vwuxfwxuhv gh soxlh

D sduwlu g*xq vxlyl udgdu g*ìslvrgh hq Qrxyhooh Dqjohwhuuh/ Dxvwlq hw Krx}h +^6`, ìwdeolvvhqw xqh klìudufklh ghv fkdpsv suìflslwdqwv hq vlwxdwlrq h{wud0wurslfdoh +wdeohdx 514,1 Lov glvwlqjxhqw ghv vwuxfwxuhv lpeultxìhv ohv xqhv dx{ dxwuhv1Fkdtxh vwuxfwxuh hvw lqwulq0 vëtxhphqw olìh ã xqh ìfkhooh vsdwlr0whpsruhooh +frpsruwdqw txdwuh qlyhdx{, hw srvvëgh ghv fdudfwìulvwltxhv sursuhv +gxuìh gh ylh gh od vwuxfwxuh/ lqwhqvlwì/ wdlooh,1

Ohv ghx{ ghuqlëuhv vwuxfwxuhv frqfhuqhqw ohv rudjhv ylrohqwv +sdu ohxu iruwh lqwhqvlwì txl shxw dwwhlqguh mxvtx*ã 433 pp2k,1Ohv fhooxohv gh soxlh dssdudlvvhqw lvroìhv rx elhq gh idêrq rujdqlvìh ã o*lqwìulhxu g*xq iurqw1

Od uhsuìvhqwdwlrq pìwìrurorjltxh gh Dxvwlq hw Krx}h shuphw grqf/ pdojuì xq fkdrv dssduhqw/ gh phwwuh hq ìylghqfh xqh rujdqlvdwlrq ghv fkdpsv gh soxlh1O*lqfrqyìqlhqw gh fhwwh dqdo|vh hvw tx*hooh gìfrqqhfwh ohv ìfkhoohv ohv xqhv ghv dxwuhv/ idlvdqw dssdudñwuh duwlflhoohphqw xq fdufdq g*ìfkhoohv fdudfwìulvwltxhv1Ru od soxlh hvw xq skìqrpëqh txl vh gìyhorssh vxu xqh jdpph g*ìfkhoohv wuëv ìwhqgxh hw vhv judqghxuv q*rqw sdv g*ìfkhooh fdudfwìulvwltxh = gh 4 np2_{ã 43 333 np}2_{hq hvsdfh +dyhuvh/ iurqw soxylhx{/ 111,/ hw gh txhotxhv}

plqxwhv dx{ ìfkhoohv jìrorjltxhv hq whpsv +yrlu wdeohdx 514,1 Lo q*hvw grqf sdv hqylvdjhdeoh gh sulyloìjlhu xqh ìfkhooh soxw÷w tx*xqh dxwuh/ hw wrxw hruw gh prgìolvdwlrq vh grlw g*ìwdeolu xqh ghvfulswlrq xqlìh ghv fkdpsv gh soxlh1

51415 Phvxuh gh od soxlh

Ohv grqqìhv gh suìflslwdwlrqv rqw orqjwhpsv ìwì surgxlwhv sdu ghv phvxuhv gl0 uhfwhv +soxylrjudskltxhv rx soxylrpìwultxhv,1O*dssdulwlrq uìfhqwh ghv phvxuhv lqgluhfwhv +udgduv pìwìrurorjltxhv hw v|vwëphv g*revhuydwlrq vdwhoolwhv, d shuplv gh gìfuluh od yduldelo0 lwì vsdwldoh gh od soxlh txl mxvtxh oã q*dydlw ìwì dffhvvleoh txh sdu ghv uìvhdx{ ghqvhv gh soxylrpëwuhv rx gh soxylrjudskhv1

Phvxuh soxylrpìwultxh = Fh vrqw ohv phvxuhv oh soxv frxudpphqw xwlolvìhv1O*hdx gh soxlh hvw uhfxhloolh vxu xqh vxuidfh gh txhotxhv fp2_{hw dffxpxoìh gdqv xq uìvhuyrlu1}

Vrq yroxph vxu xq sdv gh whpsv {h +hq jìqìudo 57 khxuhv/ pdlv sduirlv gh o*ruguh gh od vdlvrq, hvw txdqwlì sdu glyhuv surfìgìv +phvxuh gh od kdxwhxu g*hdx gdqv oh uìvhuyrlu/ pdlv dxvvl shvìh gx uìvhuyrlu,1Od uìvroxwlrq whpsruhooh hvw grqf ìjdoh dx sdv gh whpsv gh phvxuh hw od uìvroxwlrq vsdwldoh hvw gh txhotxhv fp2_{/ pdlv fhv phvxuhv}

(24)

44 gxhv dx yhqw/ ã ghv hhwv g*ìfudq/ ã o*ìydsrudwlrq hw sduirlv olìhv ã o*revwuxfwlrq rx dx gìerughphqw gh o*dssduhlo1

Phvxuh soxylrjudskltxh = F*hvw xqh phvxuh xq shx prlqv vlpsoh txh od suìfìghqwh1 Oh soxylrjudskh fodvvltxh hquhjlvwuh frqwlqþphqw ohv fxpxov gh soxlh gdqv oh whpsv/ pdlv lo h{lvwh dxvvl ghv soxylrjudskhv ã gìsrxloohphqw pdqxho1Oh soxylrjudskh ã edvfxohphqw hquhjlvwuh ghv gdwhv gh edvfxohphqw/ fkdtxh edvfxohphqw fruuhvsrqgdqw dx uhpsolvvdjh g*xq dxjhw g*xqh frqwhqdqfh gh 314 pp rx gh 318 pp1 Od uìvroxwlrq vsdwldoh hvw oã dxvvl frqvlgìuìh frpph srqfwxhooh/ wdqglv txh od uìvroxwlrq whpsruhooh ydulh gh 4 ã 48 plqxwhv1Ohv vrxufhv g*huuhxuv vrqw lghqwltxhv dx{ suìfìghqwhv pdlv hoohv shxyhqw dxvvl íwuh gxhv ã od vdwxudwlrq gh o*dxjhw txl lpsrvh xqh eruqh vxsìulhxuh dx{ phvxuhv1

Phvxuh sdu vshfwur0soxylrpëwuh rswltxh = Vrq sulqflsh hvw edvì vxu o*dwwìqxdwlrq surgxlwh sdu ohv jrxwwhv gh soxlh oruv gh ohxu sdvvdjh gdqv xq idlvfhdx oxplqhx{1Oh glvgurpëwuh/ rx frpswhxu gh jrxwwhv/ grqqh dxvvl dffëv ã od judqxorpìwulh ghv jrxwwhv sdu ghv surfìgìv rswltxhv rx dfrxvwltxhv

Phvxuhv udgdu = Oh udgdu hvw xq glvsrvlwli gh phvxuh dfwli = Lo ìphw xq ud|rqqhphqw lqflghqw srxu phvxuhu od uì hfwlylwì udgdu ]= Fhooh0fl hvw hqvxlwh frqyhuwlh hq lqwhqvlwì gh soxlh U sdu od uhodwlrq glwh gh Pduvkdoo Sdophu ] @ D UK_{> rü D hw e vrqw ghv}

frh!flhqwv fdofxoìv sdu xqh fdoleudwlrq xwlolvdqw ghv grqqìhv dx vro lvvxhv g*xq uìvhdx gh soxylrpëwuhv1Fhwwh uhodwlrq hvw irqgìh vxu ghv k|srwkëvhv wuëv iruwhv whoohv tx*xqh uìsduwlwlrq krprjëqh ghv jrxwwhv/ xqh iruph gh jrxwwh vskìultxh hw xqh lqwhqvlwì gh soxlh frqvwdqwh +Dqgulhx{ ;9 ^5`/ Eodqfkhw <6 ^45`/ Erxuho <7 ^47`,1

Soxvlhxuv huuhxuv gìfrxohqw gh od uhodwlrq U]= Od uhodwlrq gh Pduvkdoo Sdophu hvw qrq olqìdluh/ fh txl lpsoltxh txh ohv frh!flhqwv gh fdodjh D hw e ydulhqw sdu fkdqjhphqw g*ìfkhooh1Rq uhfhqvh gdqv od olwwìudwxuh soxv g*xqh fhqwdlqh gh frxsohv +D> e, = Oh skìqrpëqh glw gh edqgh euloodqwh frqvwlwxh dxvvl xqh olplwh ã od ydolglwì gh od uhodwlrq gh Pduvkdoo Sdophu1Lo vh surgxlw dx ghvvxv gh o*lvrwkhuph 3_{> hw hvw gþ dx}

idlw txh od uì hfwlylwì ghv sduwlfxohv gh jodfh hvw ehdxfrxs soxv judqgh txh fhooh ghv sduwlfxohv g*hdx1

Dmrxwrqv g*dxwuhv vrxufhv g*huuhxuv txl shxyhqw íwuh gxhv ã od phvxuh gh uì hfwlylwì +suìvhqfh g*revwdfohv/ gh pdvtxhv/ gìs÷wv vxu o*dqwhqqh111,/ rx dx{ ìfduwv hqwuh od soxlh dx vro hw od soxlh hq dowlwxgh1

Pdojuì od pxowlsolflwì ghv vrxufhv g*huuhxuv/ oh udgdu shuphw qìdqprlqv g*ìwdeolu xqh fduwrjudsklh txdolwdwlyh gh od soxlh1Lo whqg ã ghyhqlu gh soxv hq soxv rsìudwlrqqho srxu od phvxuh gh od soxlh1

Phvxuhv sdu vdwhoolwh = Ohv vdwhoolwhv vrqw jìqìudohphqw ghv glvsrvlwliv sdvvliv1Lov fdswhqw ghv udgldwlrqv suryhqdqw gh od whuuh hvvhqwlhoohphqw vhorq ghx{ jdpphv g*rqgh = O*lqiudurxjh = O*dqdo|vh g*xqh lpdjh LU shuphw gh glvwlqjxhu ohv sl{hov iurlgv

ghv dxwuhv1Ohxu qrpeuh shxw íwuh uholì ã xqh txdqwlwì g*hdx suìflslwìh hq vh edvdqw vxu oh idlw txh ohv fhooxohv frqyhfwlyhv lqwhqvhv vrqw soxv iurlghv txh ohv

(25)

45 Uìvroxwlrq whpsruhooh Uìvroxwlrq vsdwldoh Skìqrpëqhv revhuyìv

VSRW S hqwuh 51 8 hw 59 mrxuv 43 p Vwdwltxhv hw orfdolvìv

LUV04F hqwuh 8 hw 57 mrxuv 81; p Vwdwltxhv hw orfdolvìv

Odqgvdw WP 49 mrxuv 63 p Vwdwltxhv hw orfdolvìv

QRDD 7 irlv sdu mrxu 4 np Lqqrqgdwlrqv/ vìfkhuhvvhv

Wdeohdx 515= Uìvroxwlrq whpsruhooh hw vsdwldoh gh txhotxhv vdwhoolwhv1

vrpphwv ghv qxdjhv dyrlvlqdqw +ã kdxwh dowlwxgh,1Gdqv oh fdv gh fhooxohv frqyhf0 wlyhv uhodwlyhphqw lvroìhv/ fhv uhodwlrqv vrqw elhq h{solflwìhv1Sdu frqwuh/ gdqv oh fdv gh qxdjhv vwudwliruphv rx gh iruêdjh rurjudskltxh/ fhv uhodwlrqv vrqw txdvl0 lqh{lvwdqwhv +Erxuho <7 ^47`,1Ghv uìvxowdwv lqwìuhvvdqw vrqw rewhqxv sdu h{hpsoh dx Vdkho sdu oh vdwhoolwh Pìwìrvdw4_{1Od uìvroxwlrq vsdwldoh v*ìwhqg gh 8 ã 43 np}

gh frwì hw od uìvroxwlrq whpsruhooh hvw gh o*ruguh gh od ghpl0khxuh1

Ohv plfur0rqghv = F*hvw xq v|vwëph dfwli sxlvtx*lo frqvlvwh ã hpedutxhu xq udgdu vxu xq vdwhoolwh ã ruelwh srodluh1Fh v|vwëph vhuw ã vrqghu ohv qxdjhv1Od uì0 vroxwlrq vsdwldoh hvw gh o*ruguh gh 53 np hw od uìvroxwlrq whpsruhooh hvw gh 45 khxuhv1

Flwrqv dxvvl oh ylvleoh txl vhuw ã od fodvvlfdwlrq ghv qxdjhv1

Ohv uìvroxwlrqv hq hvsdfh hw hq whpsv ghv vdwhoolwhv vrqw fhshqgdqw wurs judqghv srxu ohv ehvrlqv gh o*k|gurorjlh = od iuìtxhqfh plqlpdoh g*dftxlvlwlrq g*lpdjhv uhvwh vxsìulhxuh ã 63 plqxwhv wdqglv txh od uìvroxwlrq vsdwldoh dyrlvlqh dx plhx{ ohv 8 np gh frwì +yrlu wdeohdx 515,1 Pdlv fhwwh whfkqltxh gh phvxuh hvw hq frqvwdqwh dpìolrud0 wlrq/ sxlvtxh ohv vdwhoolwhv gh od qrxyhooh jìqìudwlrq dwwhlqgurqw xqh wdlooh gh sl{ho gh o*ruguh gh txhotxhv pëwuhv +oh vdwhoolwh VSRW 8 hq 5335 suìyrlw xqh wdlooh gh sl{ho gh 6 pëwuhv,1G*dxwuh sduw/ ohv sdvvdjhv ghv vdwhoolwhv vrqw shx qrpeuhx{ hw v*hhfwxhqw wrxmrxuv ã od píph khxuh1

51416 Hfkhoohv vsdwlr0whpsruhoohv

Wrxwhv ohv ìfkhoohv vsdwlr0whpsruhoohv lqwhuylhqqhqw gdqv oh surfhvvxv ghv suìflsl0 wdwlrqv1Sdu h{hpsoh/ od frqvwlwxwlrq g*xq prgëoh pìwìrurorjltxh +srxu od suìylvlrq g*xq gìelw gh srlqwh sdu h{hpsoh, dvvrflh soxvlhxuv qlyhdx{ g*ìfkhooh = gh 43e _{ã 43}2 _np2_{srxu od}

uhsuìvhqwdwlrq gh od f|forjìqëvh/ hw ohv phvxuhv ã ghv ìfkhoohv lqiìulhxuhv srxu od gìvdjuìjd0 wlrq ã o*ìfkhooh gx edvvlq yhuvdqw1Pdlv ohv uìvxowdwv rewhqxv ã xqh fhuwdlqh ìfkhooh srxuudlhqw íwuh idxvvìv sdu ghv pìfdqlvphv g*ìfkhooh lqiìulhxuh/ rx v*h{wudsrohudlhqw pdo srxu h{soltxhu ghv uìvxowdwv ã xqh ìfkhooh lqiìulhxuh1Vhorq txho sdv gh whpsv hw txho sdv g*ìfkhooh vsdwldoh hvw0lo doruv udlvrqqdeoh gh fdofxohu ghv hvwlpdwlrqv gh odphv g*hdx B Fhv jdpphv g*ìfkhoohv frqfhuqhqw0hoohv ohv ehvrlqv sudwltxhv gh o*k|gurorjlh B

_{Dx Vdkho/ o*hvvhqwlho ghv suìflslwdwlrqv surylhqw ghv fxpxor0qlpexv grqw oh vrpphw hvw iurlg +hqylurq 0}

73_{,1 Fhshqgdqw/ lo h{lvwh ghv qxdjhv ã vrpphw iurlg qrq suìflslwdqw hw wrxv ohv fxpxor0qlpexv qh suìflslwhqw}

(26)

46 Edvvlq yhuvdqw Uìvroxwlrq vsdwldoh Hfkhooh joredoh Uìvroxwlrq hq whpsv

Xuedlq kd ã 4 np2 _np2 _{8 ã 63 plq}

Shwlh np2 _{43 ã 433 np}2 _{63 plq ã 4 k}

Pr|hq gx np2_{ã od gl}dlqh gh np}2 _{4333 np}2 _{57 khxuhv}

Wdeohdx 516= Ruguh gh judqghxu ghv wdloohv hw gh od uìvroxwlrq ghv hvwlpdwlrqv gh odphv g*hdx gh fkdtxh w|sh gh edvvlq yhuvdqw1

Od uìsrqvh gìshqg gx pr|hq gh phvxuh +gdqv oh fdv gh phvxuhv lvvxhv g*xq uìvhdx gh soxylrpëwuhv rx gh soxylrjudskhv/ hooh gìshqg gh od ghqvlwì, pdlv vxuwrxw gh od wdlooh hw gh od qdwxuh gx edvvlq yhuvdqw1

Idxuh/ <6 ^66` frqvlgëuh wurlv w|shv gh edvvlqv yhuvdqwv = Ohv edvvlqv yhuvdqwv xuedlqv >

Ohv shwlwv edvvlqv uxudx{ +sdu h{hpsoh prqwdjqhx{, > Ohv judqgv edvvlqv yhuvdqwv1

Rq d v|qwkìwlvì gdqv oh wdeohdx 516 o*ìfkhooh joredoh g*hvsdfh fdudfwìulvdqw fkd0 fxq ghv edvvlqv yhuvdqwv hw ohv ghx{ uìvroxwlrqv +hq hvsdfh hw hq whpsv, qìfhvvdluhv srxu o*xwlolvdwlrq hq sudwltxh ghv vruwlhv gx prgëoh1Od uìvroxwlrq whpsruhooh fruuhvsrqg ã od gxuìh gh od uìsrqvh gx edvvlq yhuvdqw1

51417 Frqfoxvlrq

Gdqv fh fkdslwuh/ qrxv dyrqv guhvvì xqh v|qwkëvh gh o*ìwdw dfwxho ghv frqqdlvvdqfhv vxu od g|qdpltxh ghv fkdpsv gh soxlh/ sxlv gìql ohv frqwudlqwhv olìhv ã od phvxuh gh od soxlh hw ã vrq xwlolvdwlrq hw uìdolvì xqh v|qwkëvh ghv vrxufhv g*huuhxuv gh phvxuhv dlqvl txh ghv ruguhv gh judqghxu g*ìfkhoohv g*hvsdfh hw gh whpsv frqfhuqìhv1

O*ìwdw dfwxho ghv frqqdlvvdqfhv shuphw g*dyrlu xqh uhsuìvhqwdwlrq joredoh gh od g|qdpltxh ghv fkdpsv gh soxlh hw ghv hvwlpdwlrqv gh odph g*hdx soxv rx prlqv deohv vhorq ohv glvsrvlwliv gh phvxuh1Wrxwhirlv/ fhwwh uhsuìvhqwdwlrq pìwìrurorjltxh hw fhv glvsrvlwliv gh phvxuh iudfwlrqqh oh surfhvvxv hq xq qrpeuh ql g*ìfkhoohv txl qh fruuhvsrqghqw sdv irufìphqw dx{ ehvrlqv k|gurorjltxhv/ hw uhqghqw gl!floh o*h{wudsrodwlrq ghv hvwlpdwlrqv ã g*dxwuhv ìfkhoohv1O*xqh ghv dpelwlrqv gh fh wudydlo hvw gh ohv wudlwhu vlpxowdqìphqw hq vh irqgdqw vxu xqh frqwlqxlwì gx surfhvvxv gh soxlh hqwuh ìfkhoohv1

515 Od prgìolvdwlrq vwrfkdvwltxh gh od soxlh

Gdqv od sduwlh suìfìghqwh/ qrxv dyrqv udslghphqw suìvhqwì ohv gl!fxowìv vrxohyìhv sdu od prgìolvdwlrq sk|vltxh gh od soxlh1Elhq txh ohv skìqrpëqhv hqwudqw hq mhx qh vrlhqw sdv irufìphqw uìjlv sdu oh kdvdug/ xqh pdqlëuh gh gìfuluh ohv surfhvvxv k|gurorjltxhv frqvlvwh ã frqvwuxluh xq prgëoh gh soxlh vwrfkdvwltxh1Vhorq H1Kdoskhq = Ohv suredelolwìv phvxuhqw o*ljqrudqfh kxpdlqh hw od vwdwlvwltxh hvw fh txl wlhqw olhx gh vflhqfh dx{ ljqrudqwv txh qrxv vrpphv1

(27)

47

51514 Srxutxrl xqh prgìolvdwlrq vwrfkdvwltxh B

O*dssurfkh vwrfkdvwltxh gh prgìolvdwlrq hvw vxvfhswleoh d sulrul gh suìvhqwhu glyhuv dydqwdjhv hq k|gurorjlh =

Wrxw g*derug/ hooh shuphwwudlw od uìdolvdwlrq gh wudqvihuwv g*lqirupdwlrq hq ghv vlwhv jìrjudskltxhv glìuhqwv/ rx elhq ã ghv ìfkhoohv soxv shwlwhv +vsdwldohv/ whpsruhoohv rx vsdwlr0whpsruhoohv,/ dwrxw qrq qìjoljhdeoh hq udlvrq gx sul{ hw gh od gl!fxowì g*dftxlvlwlrq ghv phvxuhv1

Idfh ã o*h{whqvlrq ghv }rqhv xuedlqhv hw ã o*dxjphqwdwlrq gh od yxoqìudelolwì/ o*k|gurorjxh d ehvrlq g*hvwlpdwlrqv ã xqh uìvroxwlrq vsdwldoh hw whpsruhooh gh soxv hq soxv qh hw gh suìylvlrqv gh soxv hq soxv deohv1Ohv prgëohv vwrfkdvwltxhv uìdolvhqw ghv hvwlpdwlrqv grqw od suìflvlrq gìshqg gh od yduldelolwì gh od vìulh/ wrxw hq txdqwldqw o*huuhxu/ txl shxw íwuh uhwudqvfulwh hq whuph gh ulvtxh +Ehujhu/ ;8 ^44`,1

Xq dxwuh dydqwdjh gh o*dssurfkh vwrfkdvwltxh hvw oh fdudfwëuh rsìudwlrqqho gx prgëoh srxu ghv dssolfdwlrqv k|gurorjltxhv1Hq hhw/ rq prgìolvh wrxmrxuv sdu udssruw ã xq remhfwli/ hw oh prgëoh grlw íwuh elhq glvwlqjxì gx skìqrpëqh ã prgìolvhu +gh Pduvlo|/ <7 ^59`,1O*k|gurorjxh v*lqwìuhvvh ã od suìylvlrq ghv fuxhv hw ghv ìwldjhv/ ã od jhvwlrq ghv uìvhuyrluv rx ã o*hvwlpdwlrq ghv h{wuíphv srxu oh glphqvlrqqhphqw g*rxyudjhv1 Xqh suìylvlrq gh od soxlh srxu o*dqqrqfh ghv fuxhv hq plolhx xuedlq uhtxlhuw xqh prgìolvdwlrq ã shwlw sdv gh whpsv hw g*hvsdfh/ wdqglv txh od gìwhuplqdwlrq gh od kdxwhxu g*xqh gljxh vhud uìdolvìh ã sduwlu g*xq prgëoh ã o*ìfkhooh gx edvvlq yhuvdqw1

Pdlv prgìolvhu ghv judqghxuv k|gurorjltxhv hq xwlolvdqw ghv prgëohv vwrfkdvwltxhv q*hvw jìqìudohphqw sdv xqh wåfkh idfloh1Hq idlw/ ohv yduldeohv k|gurorjltxhv srvvëghqw xqh vwuxfwxuh gh gìshqgdqfh hw xqh yduldelolwì ghv prlqv fodvvltxhv vxu oh sodq vwdwlvwltxh1 Ohv vìulhv gh gìelwv rx gh soxlh vrqw iruwhphqw dv|pìwultxhv +qrwdpphqw ã shwlw sdv gh whpsv/ yrlu jxuh 515, hw srvvëghqw jìqìudohphqw xqh irqfwlrq g*dxwrfruuìodwlrq frqyhujhdqw ohqwhphqw yhuv }ìur1

Sdupl ohv sulqflsdx{ prgëohv vwrfkdvwltxhv sursrvìv hq k|gurorjlh/ rq glvwlqjxh ohv prgëohv gh w|sh jdxvvlhq hw gh w|sh qrq0jdxvvlhq/ dx vhlq ghvtxhov dssdudlvvhqw gl0 yhuvhv vwuxfwxuhv gh gìshqgdqfh vwdwlvwltxh +DUPD/ Pdunry, txl srvvëghqw fkdfxqh xqh lqwhusuìwdwlrq sk|vltxh vlpsoh1

Gdqv fhwwh vhfwlrq/ qrxv udsshorqv ohv sulqflsdohv pìwkrghv g*hvwlpdwlrq vsdwldoh/ dydqw gh guhvvhu xqh uhyxh ghv glìuhqwv prgëohv vwrfkdvwltxhv gh suìflslwdwlrq uhqfrqwuìv gdqv od olwwìudwxuh = qrxv suìvhqwhurqv ohv prgëohv vsdwldx{/ whpsruhov/ sxlv ohv prgëohv txl dssuìkhqghqw od soxlh hq wdqw txh fkdps vsdwlr0whpsruho1

51515 Pìwkrghv vwdwlvwltxhv g*hvwlpdwlrq vsdwldoh

Gdqv fh sdudjudskh/ qrxv sdvvhurqv hq uhyxh ohv pìwkrghv gh srqgìudwlrq/ gx nulhjhdjh hw gx ydulrjudpph txl ylvhqw oh soxv vrxyhqw ã rewhqlu ghv lqirupdwlrqv vxu od yduldelolwì vsdwldoh gh od soxlh/ pdlv shxyhqw dxvvl íwuh hpsor|ìhv srxu od yduldelolwì whpsruhooh rx vsdwlr0whpsruhooh1

(28)

48

Iljxuh 514= Dv|pìwulh ghv fxpxov hq irqfwlrq gx sdv g*lqwìjudwlrq +vìulh gh Dwkëqhv,1

20000 4000 6000 2 4 6 8 10 12 14 Annuel 0 1000 2000 0 50 100 150 200 250 300 Mensuel 0 500 1000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5x 10 4 _Journalier asymétrie

Histogrammes des cumuls journaliers, mensuels et annuels de la série de Athène

(29)

49 Od gìpdufkh jìqìudoh gh fhv pìwkrgh hvw od vxlydqwh = Rq dlphudlw gìwhuplqhu/ ã sduwlu g*xq uìvhdx ghqvh gh soxylrpëwuhv rx soxylrjudskhv/ od kdxwhxu gh soxlh wrpeìh hq wrxw srlqw g*xqh uìjlrq/ rx elhq hq pr|hqqh vxu xq grpdlqh gh fhwwh uìjlrq1Rq glvsrvh gh q phvxuhv +},'cuuuc? sulvhv dx{ soxylrpëwuhv vlwxìv dx{ srlqwv +{,'cuuuc? hw rq yhxw

hvwlphu =

srqfwxhoohphqw od phvxuh } hq xq srlqw {

}+{, @ i+}> }2> ===> }?, @ i+}+{, > }2+{2, > ===> }?+{?,,

rx hq pr|hqqh od odph g*hdx ] vxu xq grpdlqh [

]+[, @ I +}> }2> ===> }?, @ I +}+{, > }2+{2, > ===> }?+{?,,

515151d Pìwkrghv gh srqgìudwlrq = Ohv pìwkrghv gh od pr|hqqh srqgìuìh/ ghv sro|0 jrqhv gh Wklhvvhq hw ghv lvrk|ëwhv/ vrqw ghv pìwkrghv gìwhuplqlvwhv gh srqgìudwlrq1Hoohv vrqw irqgìhv vxu o*k|srwkëvh gh frqwlqxlwì gx fkdps gh soxlh +hq whpsv rx hq hvsdfh, hw shxyhqw vhuylu ã xqh hvwlpdwlrq vsdwldoh rx whpsruhooh g*xqh kdxwhxu/ g*xq fxpxo rx g*xqh lqwhqvlwì gh soxlh1Srxu xq sdv gh whpsv grqqì/ xq fkdps soxylrpìwultxh hvw frqwlqx vl od phvxuh hq xq srlqw hvw uhsuìvhqwdwlyh gh od odph g*hdx suìflslwìh vxu xqh vxuidfh dvvh} judqgh1

Uhpdutxrqv txh fhv pìwkrghv shxyhqw fhshqgdqw dxvvl íwuh frqvlgìuìhv frpph doìdwrluhv/ o*doìd sruwdqw vxu ohv kdxwhxuv } rx vxu od uìsduwlwlrq ghv srvwhv {1

Pìwkrgh gh od pr|hqqh srqgìuìh = Rq hvwlph od yduldeoh doìdwrluh dx srlqw { ã sduwlu g*xqh pr|hqqh srqgìuìh vxu ohv srvwhv yrlvlqv +{,'?

e} @ i+}> ===> }?, @ ? [ ' z+g%%, } ? [ ' z+g%%, dyhf e} od kdxwhxu hvwlpìh dx srlqw { g%% od glvwdqfh gh { ã {1

z xqh irqfwlrq gh srlgv +sdu h{hpsoh z+g, @ 4_g , hvw gìfurlvvdqwh hq irqfwlrq gh od glvwdqfh1Oh srlgv dhfwì ã fkdtxh srlqw { v*ìfulw z+g%%, ? [ ' z+g%%,

(30)

4: Pìwkrgh ghv sro|jrqhv gh Wklhvvhq = Fhwwh pìwkrgh/ sursrvìh sdu Wklhvvhq hq 4<44 ^;5`/ hvw xqh jìqìudolvdwlrq gh od suìfìghqwh oruvtxh z+g, @ 4

g& hw n $ 4= Hooh

shuphw gh uìdolvhu xqh hvwlpdwlrq vxu xq grpdlqh1Ohv srlgv vrqw gìqlv frpph vxlw = rq dhfwh xq sro|jrqh g*lq xhqfh ã fkdtxh revhuydwlrq } g*xq edvvlq yhuvdqw > oh sro|jrqh

g*lq xhqfh hvw xq grpdlqh gìql sdu wrxwhv ohv pìgldwulfhv ghv vhjphqwv mrljqdqw ohv frxsohv gh srlqwv dxwrxu gh fkdtxh revhuydwlrq1Oh srlgv dhfwì ã fkdtxh revhuydwlrq hvw oh udssruw gh od vxuidfh gx sro|jrqh g*lq xhqfh vxu od vxuidfh gx edvvlq V

V = e ] @ ? [ ' V V }

Pìwkrgh ghv lvrk|ëwhv = Srxu fkdtxh frxsoh g*revhuydwlrqv/ rq gìfrxsh oh vhjphqw ohv mrljqdqw hq lqwhuydoohv uìjxolhuv hw rq uholh hqvxlwh ohv ydohxuv lghqwltxhv srxu rewhqlu ohv frxuehv lvrk|ëwhv +K,'cuuuc? fruuhvsrqgdqw ã ghv kdxwhxuv +},'cuuuc? 1Hq

qrwdqw V o*dluh gìolplwìh sdu ohv lvrk|ëwhv K hw Kn/ rq hvwlph od odph g*hdx sdu

e ] @[?

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V

V }. }5n

515151e Pìwkrghv g*hvwlpdwlrq rswlpdohv = Ohv pìwkrghv gx nulhjhdjh hw gx ydul0 rjudpph vrqw wrxwhv ghx{ ghv pìwkrghv g*hvwlpdwlrq rswlpdohv/ hw rqw ìwì lqwurgxlwhv lo | d 63 dqv gdqv ghv grpdlqhv dxvvl ydulìv txh o*lqgxvwulh plqlëuh sdu Pdwkhurq/ 98 ^97`/ rx od pìwìrurorjlh sdu Jdqglq/ 98 ^6;`1Rq q*hq idlw lfl tx*xqh euëyh suìvhqwdwlrq1Srxu ohv gìwdlov ghv fdofxov/ rq vh uìiìuhud ã Ghokrpph/ :; ^5:`1

Rq frqvlgëuh tx*xq fkdps gh soxlh fruuhvsrqg ã od uìdolvdwlrq g*xqh irqfwlrq doìdwrluh +ID, qrwìh ]/ ã ydohxuv ]+{,> hw rq gìwhuplqh o*hvwlpdwhxu e] gh od kdxwhxu ] hq

{ txl plqlplvh o*huuhxu txdgudwltxh g*hvwlpdwlrq = plq H ^ ]+{, ]+{, 2

Pìwkrgh gx nulhjhdjh +vlpsoh,= Hooh uhsrvh vxu o*k|srwkëvh gh vwdwlrqqdulwì g*ruguh xq hw ghx{ gh od ID ] gdqv o*hvsdfh =

O*hvsìudqfh hvw frqvwdqwh

;{ H+]+{,, @ p+{, @ p

Od fryduldqfh hqwuh ghx{ srlqwv { hw { gh fh fkdps qh gìshqg sdv vìsduìphqw ghv

ghx{ srlqwv pdlv vhxohphqw gh ohxu glvwdqfh m{ {m =

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4; Rq gìwhuplqh o*hvwlpdwhxu e] gh od kdxwhxu ] hq { txl plqlplvh o*huuhxu txdgud0 wltxh g*hvwlpdwlrq plq H] ]e 2

dyhf xqh frqwudlqwh gh qrq eldlv H+ e] ], @ 3> hw rq uhfkhufkh xq hvwlpdwhxu gh od iruph

e

]+{, @[?

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Rq rewlhqw xq v|vwëph vrxv frqwudlqwhv shuphwwdqw gh fdofxohu ohv frh!flhqwv +,'cuuuc? txl hvw uìvrox sdu od pìwkrgh ghv pxowlsolfdwhxuv gh Odjudqjh hq vh udphqdqw ã

xqh ìtxdwlrq pdwulflhooh = F 4 4 3 @ Ff 4

rü F hw Ff uhsuìvhqwhqw uhvshfwlyhphqw od pdwulfh gh fryduldqfh ghv srvwhv gh phvxuhv

+glphqvlrq q q, hw oh yhfwhxu ghv fryduldqfhv hqwuh oh srlqw ã lqwhusrohu { hw ohv srvwhv { +glphqvlrq q,1Rq hvwlph F hw Ff ã sduwlu ghv uìdolvdwlrqv gh ] hq dmxvwdqw xq prgëoh

F+g, vxu ohv q+q 4,₅ ydohxuv phvxuìhv gh od fryduldqfh1

O*lqfrqyìqlhqw pdmhxu gh od pìwkrgh gx nulhjhdjh hvw tx*hooh hvw irqgìh vxu xqh k|srwkëvh wurs frqwudljqdqwh1Lo h{lvwh fhshqgdqw g*dxwuhv yhuvlrqv gh fhwwh pìwkrgh txl v*dgdswhqw plhx{ dx{ yduldeohv k|gurorjltxhv +oh nuljhdjh odjudqjlhq gh Dpdql hw Oheho/ <9 ^4` sdu h{hpsoh,1

Pìwkrgh gx ydulrjudpph = Oh ydulrjudpph hvw xq rxwlo srxu txdqwlhu od yduldelolwì +vsdwldoh/ whpsruhooh rx vsdwlr0whpsruhooh, g*xq fkdps1

Lo uhpsodfh od irqfwlrq gh fryduldqfh gdqv oh fdv gh surfhvvxv qrq vwdwlrqqdluhv fdu rq vh sodfh vrxv o*k|srwkëvh lqwulqvëtxh +Pdwkhurq/ 98 ^97`,1Fhwwh ghuqlëuh hvw soxv idleoh/ fdu f*hvw xqh k|srwkëvh gh vwdwlrqqdulwì g*ruguh xq hw ghx{ txl qh sruwh txh vxu ohv dffurlvvhphqwv ] =

Srxu wrxv srlqwv { hw { glvwdqwv gh mkm =

H +]+{, ]+{,, @ p+mkm,

Y du +]+{, ]+{,, @ 5 +mkm,

Od yduldqfh qh gìshqg txh gh od glvwdqfh mkm1

Gìqlwlrq 4 Oh ydulrjudpph +mkm, gh o*ìyìqhphqw hvw gìql sdu +mkm, @ 4₅Y du +]+{, ]+{,,

Vrxv o*k|srwkëvh p+mkm, @ 3/ lo v*ìfulw hqfruh +mkm, @ ₂Hk+]+{, ]+{,,2

l = Oh ydulrjudpph gh k hvw o*dffurlvvhphqw txdgudwltxh pr|hq hqwuh ghx{ srlqwv glvwdqwv gh mkm1 Rq plqlplvh o*huuhxu txdgudwltxh vrxv frqwudlqwh gh qrq eldlv hw vrxv o*k|srwkëvh lqwulqvëtxh1Rq rewlhqw sdu od pìwkrgh ghv pxowlsolfdwhxuv gh Odjudqjh xq v|vwëph olqìdluh

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4< Variogramme ---pépite palier portée

Iljxuh 516= Sìslwh/ sruwìh hw sdolhu g*xq ydulrjudpph1 shuphwwdqw g*hvwlphu ohv frh!flhqwv +,_'? =

5 9 9 7 === 6 4 = = = = ₆ === ₆₆ 4 4 === 4 3 6 : : 8 5 9 9 7 = ? 6 : : 8 @ 5 9 9 7 f _6f 4 6 : : 8 dyhf frh!flhqw gh Odjudqjh hw @ 2H ^] +{, ] +{,` Od uìvroxwlrq gh fhwwh ìtxdwlrq qìfhvvlwh oh fkrl{ g*xq ydulrjudpph1 G*xq srlqw gh yxh sudwltxh/ fh ydulrjudpph hvw hvwlpì hq =

Uhjurxsdqw ohvq+q 4,₅ frxsohv gh phvxuhv hq xq qrpeuh Q gh fodvvhv g*lqwhuglvwdqfh1

Dhfwdqw ã fkdtxh glvwdqfh pr|hqqh gh fodvvh g6od ydohxu hvwlpìh hw rq hvwlph +g6,

sdu od pr|hqqh vxu ohv fodvvhv ghv fduuìv ghv ìfduwv1 a+g6, @ _5Q4

&

[

+}+{, }+{ . k,,2

dyhf Q& oh qrpeuh gh frxsohv suìvhqwv gdqv od fodvvh n1

Rq glvsrvh gh Q ydohxuv gh a+g6, fruuhvsrqgdqw ã o*xqh ghv Q ydohxuv g61Rq

dmxvwh xq ydulrjudpph wkìrultxh +vskìultxh/ h{srqhqwlho/ jdxvvlhq/ 111, dx ydul0 rjudpph h{sìulphqwdo +jxuh 516,1 Ohv prgëohv frxudpphqw xwlolvìv vrqw gìqlv sdu wurlv sdudpëwuhv =

(33)

53 oh sdolhu/ txl hvw ìjdo ã od yduldqfh gx fkdps1Lo q*dssdudñw sdv vl oh skìqrpëqh

hvw wuëv yduldeoh1

od sruwìh/ txl uhsuìvhqwh oh vhxlo ã sduwlu gxtxho oh sdolhu hvw dwwhlqw1

od sìslwh/ txl uhqvhljqh vxu od frqwlqxlwì gh ]1Xqh glvfrqwlqxlwì hq }ìur/ txl shxw íwuh gxh ã od glvfrqwlqxlwì gx plolhx/ ã xq sureoëph g*ìfkhooh rx ã ghv huuhxuv gh phvxuhv1

Hq frqfoxvlrq/ fhv glìuhqwv rxwlov/ frqêxv srxu dssuìkhqghu od yduldelolwì vsdwldoh g*xq fkdps/ uhsrvhqw wrxv vxu ghv k|srwkëvh g*krprjìqìlwì +soxv rx prlqv ddleolh, gh fh ghuqlhu1Ru rq d frqvwdwì txh fhv k|srwkëvhv vrqw plvhv ã pdo oruvtx*lo v*djlw g*xq fkdps soxylrpìwultxh/ vxuwrxw ã shwlw sdv gh whpsv +rq srxuud vh uhsruwhu ã o*duwlfoh gh Kxehuw hw Fduerqqho/ ;; ^77` srxu xqh ìwxgh vxu ohv grqqìhv HSVDW0Qljhu,1

51516 Prgëohv whpsruhov

Rq glvwlqjxh ohv prgëohv g*rffxuuhqfh gh soxlh ghv prgëohv gh kdxwhxu qrq qxoohv1 Fhv ghx{ surfhvvxv shxyhqw íwuh vrlw prgìolvìv vìsduìphqw/ sxlv uhfrpelqìv/ vrlw prgìolvìv vlpxowdqìphqw1Rq qh suìvhqwhud lfl txh ohv prgëohv hq xq vhxo vlwh1

Prgëohv g*rffxuuhqfh gh soxlh

Srxu prgìolvhu o*rffxuuhqfh gh soxlh hq xq srlqw {ì/ rq frqvlgëuh od yduldeoh doìdwrluh glvfuìwlvìh ã xq fhuwdlq sdv gh whpsv +jìqìudohphqw od mrxuqìh, [|@ 3 rx 4 vhorq

tx*lo sohxyh rx qrq vxu fh sdv gh whpsv +rx elhq vhorq txh oh fxpxo gh soxlh gìsdvvh rx qrq xq fhuwdlq vhxlo,1Ghx{ dssurfkhv rqw ìwì frqvlgìuìhv fhv ghuqlëuhv dqqìhv = od prgìolvdwlrq ghv sìulrghv vëfkhv hw ghv sìulrghv kxplghv hw ohv vìulhv ã whpsv glvfuhw1

Od suhplëuh dssurfkh frqvlvwh ã v*lqwìuhvvhu dx{ vìtxhqfhv gh mrxuv +rx khxuhv, gh soxlh frqvìfxwliv1Rq dmxvwh xqh orl ã od gxuìh ghv sìulrghv kxplghv hw ghv sìulrghv vëfkhv1Fhwwh yrlh d ìwì odujhphqw h{sorlwìh sdu ghv dxwhxuv whov txh Juhhq hq 97 ^74` rx Hdjohvrq hq :; ^5<` txl xwlolvhqw uhvshfwlyhphqw xqh orl h{srqhqwlhooh hw xqh orl gh Zhlexoo srxu ohv gxuìhv ghv sìulrghv vëfkhv hw kxplghv1Fhv prgëohv vrqw hq idlw ghv surfhvvxv gh uhqrxyhoohphqw gdqv oh vhqv rü ìwdwv vhfv hw soxylhx{ dowhuqhqw/ dxfxqh wudqvlwlrq gdqv oh píph ìwdw q*ìwdqw srvvleoh1Xq dxwuh prgëoh gh uhqrxyhoohphqw fuìì sdu Jdoor|/ Pduwlq hw Oheuhwrq hq ;5 ^6:` xwlolvh od orl elqrpldoh qìjdwlyh srxu ohv gxuìhv ghv sìulrghv vëfkhv hw kxplghv1

Fhshqgdqw fhv pìwkrghv uhsrvhqw vxu o*k|srwkëvh g*lqgìshqgdqfh ghv sìulrghv soxylhxvhv hqwuh hoohv/ uduhphqw yìulìh ã shwlw sdv gh whpsv +ã sdv gh whpsv xqh khxuh/ ghx{ vìtxhqfhv kxplghv shxyhqw fruuhvsrqguh dx píph ìyìqhphqw soxylhx{,1Gh soxv/ od gxuìh yduldeoh ghv ìyìqhphqwv pìulwhudlw txh o*rq frqglwlrqqh ohv fxpxov ã fhwwh gxuìh +Zlonv/ ;< ^;9`,1

Od vhfrqgh dssurfkh xwlolvh ohv vìulhv ã whpsv glvfuhw/ vìulh elqdluh gh 3 rx gh 41 O*rffxuuhqfh gh soxlh shxw íwuh prgìolvìh sdu =

Xqh vxlwh gh yduldeohv doìdwrluhv gh Ehuqrxool1F*hvw oh prgëoh oh soxv vlpsoh pdlv lo uhtxlhuw xqh lqgìshqgdqfh frpsoëwh1Lo hvw plhx{ dgdswì dx{ judqgv sdv gh whpsv +mrxu hw soxv,1

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54 Ohv fkdñqhv gh Pdunry = Hoohv vrqw wuëv xwlolvìhv gx idlw gh ohxu vlpsolflwì1Fh vrqw ghv fkdñqhv ã ghx{ ìwdwv [|@ 3 rx 41Oh suìfxuvhxu gh fhwwh prgìolvdwlrq vhpeoh íwuh

Txhwhohw hq 4;85 +g*dsuëv Zrroklvhu/ <4 ^;:`,1Ydq0Wkdqk0Ydq Qjx|hq/ ;6 ^;7` gìwhu0 plqh od orl gh suredelolwì ghv fxpxov mrxuqdolhuv dssduwhqdqw ã xqh sìulrgh soxylhxvh gh q mrxuv/ hq gìfulydqw o*rffxuuhqfh gh soxlh sdu xqh fkdñqh gh Pdunry vwdwlrqqdluh g*ruguh 41Pdlv vhorq oh ghjuì gh shuvlvwdqfh gìvluì/ ohv fkdñqhv xwlolvìhv shxyhqw íwuh g*ruguh vxsìulhxu ã xq hw píph qrq krprjëqhv1Vwhuq hw Frh ^:;` uhsuìvhqwhqw o*dowhuqdqfh ghv mrxuv vhfv hw soxylhx{ sdu xqh fkdñqh gh Pdunry qrq krprjëqh hq vh sodêdqw ã o*ìfkhooh g*xq mrxu1Fhv prgëohv vhuyhqw ã fdofxohu od orl ghv fxpxov vxu q mrxuv/ od orl gx pd{lpxp dqqxho ghv suìflslwdwlrqv1Ohv wkìruëphv olplwhv irxuqlvvhqw ghv orlv dv|pswrwltxhv srxu ohv kdxwhxuv h{wuíphv1

Fhv prgëohv qh gìfulyhqw sdv ohv shuvlvwdqfhv ã orqj whuph +sdu h{hpsoh ohv dfwlylwìv f|forqltxhv shuvlvwdqwhv gxudqw fhuwdlqhv vdlvrqv, ql ohv hhwv gh fodvvhphqw ã shwlw sdv gh whpsv +fdu/ sdu h{hpsoh/ xq ìyìqhphqw soxylhx{ gþ ã xq ìyìqhphqw soxylhx{ suìfìghqw d xqh yudlvhpeodqfh soxv iruwh,1

Ohv surfhvvxv GDUPD+s> t,/ s ìwdqw o*ruguh gh o*dxwruìjuhvvlrq hw t o*ruguh gh od pr|hqqh preloh fuììv sdu Exlvkdqg hq 4<:; ^49` wlhqqhqw plhx{ frpswh ghv shuvlv0 wdqfhv ã orqj whuph txh ohv fkdñqhv gh Pdunry g*ruguh ìohyì pdlv od vwuxfwxuh gx prgëoh hvw gl!floh ã lqwhusuìwhu sk|vltxhphqw1

Prgëohv gh kdxwhxu qrq qxoohv

O*dssurfkh od soxv frxudqwh hvw gh gìfuluh od glvwulexwlrq ghv kdxwhxu \ +w, lq0 gìshqgdpphqw gh fhooh gh o*rffxuuhqfh [+w,1Soxvlhxuv w|shv gh gìshqgdqfh fdudfwìulvhqw fhv prgëohv =

Ohv \ +w, vrqw lqgìshqgdqwhv = Glyhuv orlv vrqw xwlolvìhv whoohv txh od orl H{srqhqwlhooh/ Jdppd rx Zhlexoo +]xffklql hw do1/ <5 ^;<`,1

Ohv \ +w, vrqw gìshqgdqwhv = Rq xwlolvh ghv prgëohv DUPD srxu prgìolvhu xqh gìshq0 gdqfh hqwuh ohv \ +w, qrq qxov1Lov vrqw vxuwrxw xwlolvìv srxu prgìolvhu ohv gìelwv pdlv shx srxu ohv kdxwhxuv gh soxlh ã fdxvh gh od txdvl lqgìshqgdqfh1

Ohv \ +w, vrqw lqgìshqgdqwhv pdlv gìshqghqw gh o*rffxuuhqfh gx mrxu suìfìghqw [+w 4, = Fh vrqw ohv surfhvvxv gìshqgdqwv hq fkdñqh/ lqwurgxlwv sdu Ndw} hq 4<:: +^7;` hw ^7<`, txl frqglwlrqqhqw \ +w, sdu [+w 4,1Fhv prgëohv qìfhvvlwhqw xq judqg qrpeuh gh sdudpëwuhv1

G*dxwuhv h{suhvvlrqv gh od gìshqgdqfh shxyhqw íwuh wurxyìhv gdqv od olwwìudwxuh/ whoohv txh fhooh gh Exlvkdqg/ :; ^49` txl fodvvh ohv ìyìqhphqwv soxylhx{ vhorq ohv w|shv vxlydqwv =

L = mrxu soxylhx{ lvroì1

LL = mrxu soxylhx{ suìfìgì rx vxlyl g*xq mrxu vhf1 LLL = mrxu soxylhx{ suìfìgì hw vxlyl g*xq mrxu vhf1

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55 Prgëohv Pl{whv

Rq shxw prgìolvhu o*rffxuuhqfh [+w, hw ohv kdxwhxuv \ +w, vìsduìphqw rx elhq vlpxowdqìphqw ]+w, @ +[+w,> \ +w,,1Od soxsduw ghv prgëohv pl{whv v*dssxlhqw vxu oh fdguh pdwkìpdwltxh frqvwuxlw sdu Oh Fdp hq 4<94 ^4:` txl dgdswh ã o*k|gurorjlh xq surfhvvxv g*djuìjdwlrq gh w|sh Qh|pdq0Vfrww1Fh ghuqlhu/ fuìì hq dvwurqrplh srxu prgìolvhu od irupdwlrq g*ìwrlohv/ suìvhqwh o*dydqwdjh gh suhqguh hq frpswh od g|qdpltxh ghv fkdpsv gh soxlh1Gh qrpeuhx{ dxwhxuv vh vrqw dwwdfkìv ã dqdo|vhu iruphoohphqw od txdolwì ghv hvwlpdwhxuv +Frzshuwzdlw/ <4 ^53`, rx ã vlpxohu ghv grqqìhv ã sdv gh whpsv q/ qrwdpphqw hq k|gurorjlh xuedlqh +Wkdxylq hw do1<: ^;4`,1Gdqv xq prgëoh gh w|sh Qh|pdq0Vfrww +jxuh 517,/ gxuìhv gh whpsv vhf hw gh whpsv soxylhx{ dowhuqhqw1 Ohv ruljlqhv gh sìulrghv soxylhxvhv +qrwìhv *3*,/ duulyhqw vhorq xq surfhvvxv gh Srlvvrq1D o*lqwìulhxu g*xq lqwhuydooh soxylhx{/ od soxlh vh gìfrpsrvh hq xqh vxffhvvlrq g*dyhuvhv +uhsuìvhqwìhv vxu oh vfkìpd sdu oh v|peroh **,1Fkdtxh dyhuvh hvw fdudfwìulvìh sdu vd gxuìh hw vrq lqwhqvlwì1O*lqwhqvlwì wrwdoh hq fkdtxh srlqw hvw od vrpph ghv lqwhqvlwìv gh fkdtxh dyhuvh dfwlyh1

Oh surfhvvxv gh Qh|pdq0Vfrww suìvhqwh ghv yduldqwhv gìqlhv sdu od orl ghv lqwhq0 vlwìv dwwulexìhv ã fkdtxh fhooxoh gh soxlh1Flwrqv oh Qh|pdq0Vfrww Zklwh Qrlvh +QVZQ, gh Urguljxh}0Lwxueh hw do1hq ;7 ^:7` rx oh Qh|pdq0Vfrww Uhfwdqjxodu Sxovh +QVUS, gh Urguljxh}0Lwxueh hw do1hq ;: ^:6`1Lo idlw sduwlh g*xqh ydvwh fodvvh gh surfhvvxv srqfwxhov suìvhqwìv vxu xq sodq wkìrultxh gdqv o*rxyudjh gh Fr{ hw Lvkdp ^54` sdupl ohvtxhov rq shxw flwhu oh surfhvvxv gh Srlvvrq grxeoh +rx surfhvvxv gh Fr{,1Fh ghuqlhu hvw xq surfhvvxv gh Srlvvrq ã lqwhqvlwì doìdwrluh1Ndyydv hw Ghoohxu ^83` dssoltxhqw oh surfhvvxv gh Fr{ srxu frqvwuxluh xq prgëoh vwrfkdvwltxh ã ghx{ qlyhdx{/ oh UFP +Uhqhzdo Fr{ surfhvv zlwk Pdunryldq Lqwhqvlw|, srxu o*rffxuuhqfh gh soxlh gdqv ohtxho od ylwhvvh g*rffxuuhqfh ghv ru0 djhv hvw gìwhuplqìh sdu xq dxwuh surfhvvxv dsshoì surfhvvxv folpdwrorjltxh1Vplwk hw Nduu/ ;6 ^::` h{sorlwhqw fh prgëoh srxu fdofxohu oh qrpeuh g*rudjhv hw ohv gxuìhv g*lqwhu0duulyìhv vxu ghv grqqìhv lvvxhv gx edvvlq yhuvdqw gh od ulylëuh Srwrpdf1

Oh surfhvvxv gh Qh|pdq0Vfrww vh jìqìudolvh qdwxuhoohphqw hq xq surfhvvxv vsdwldo rx vsdwlr0whpsruho frpph qrxv srxuurqv oh frqvwdwhu gdqv od vhfwlrq vxlydqwh1

51517 Prgëohv vsdwlr0whpsruhov

Od olwwìudwxuh sursrvh shx gh prgëohv vsdwlr0whpsruhov1Lov rqw ìwì fuììv jìqìudoh0 phqw hq yxh gh vlpxodwlrqv dq gh whvwhu ghv vwudwìjlhv g*hvwlpdwlrq ã sduwlu g*dssduhlov gh phvxuh gh w|shv glìuhqwv1Ohv prgëohv suìvhqwìv lfl vrqw frqvwuxlwv dxwrxu gh vwuxf0 wxuh gh yduldelolwì revhuyìhv dx{ glìuhqwhv ìfkhoohv fkrlvlhv vhorq ohv revhuydwlrqv +fhooxohv soxylhxvhv/ edqghv gh fhooxohv hq hvsdfh/ ìyìqhphqw soxylhx{ hq whpsv111,1

Oh soxv vlpsoh gh fhv prgëohv hvw fhoxl gh Fr{ hw Lvkdp ^55`1Lo jìqìudolvh oh surfhvvxv gh Qh|pdq0Vfrww hq hvsdfh hw hq whpsv > lo hvw irqgì vxu ghv k|srwkëvhv wuëv uhvwulfwlyhv1Ohv dyhuvhv duulyhqw vhorq xq surfhvvxv gh Srlvvrq hq hvsdfh hw hq whpsv gh sdudpëwuh 1Fkdtxh dyhuvh hvw prgìolvìh sdu xqh uìjlrq flufxodluh gh soxlh gh ud|rq U txl vh gìsodfh ã xqh ylwhvvh doìdwrluh y @ +y%> y+, vxu xqh gxuìh doìdwrluh G mxvtx*ã glvsdulwlrq gh

od fhooxoh1O*lqwhqvlwì gh soxlh [ hvw vxssrvìh frqvwdqwh1F*hvw dx sul{ gh fhv vlpsolfdwlrqv gudvwltxhv txh oh qrpeuh gh sdudpëwuhv uhvwh udlvrqqdeoh +vl{ dx wrwdo = / U/ y%/ y+/ G hw

(36)

56

(i) Les origines de périodes pluvieuses * arrivent selon un processus de Poisson

(ii) Chaque origine génère un nombre aléatoire d averses commençant en x

(iii) La durée de chaque période pluvieuse est exponentiellement distribuée

(iii) L intensité de chaque averse est exponentiellement distribuée

Intensité

(iv) L intensité totale en chaque point est la somme des intensités de chaque averse active

Intensité totale