Global Semi-Lagrangian Atmospheric Model Based on Compact Finite-Differences and its Implementation on a Parallel Computer

(1)

HAL Id: inria-00073612

https://hal.inria.fr/inria-00073612

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Global Semi-Lagrangian Atmospheric Model Based on Compact Finite-Differences and its Implementation on a

Parallel Computer

Mikhail Tolstykh

To cite this version:

Mikhail Tolstykh. Global Semi-Lagrangian Atmospheric Model Based on Compact Finite-Differences and its Implementation on a Parallel Computer. [Research Report] RR-3080, INRIA. 1997, pp.25.

�inria-00073612�

(2)

ISSN 0249-6399

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

"! $#%

& # ' !() &!* +,-./*#.01 !2 # .3

4 " 5'33"' ' " 6!2) 8793

Mikhail Tolstykh

N ˚ 3080

January 1997

TH ` EME 4

(3)

(4)

%* %+-,./01'.2)#%34' .5& " 678

&)%* "9:7#

;=<?>A@B1<?C$D#ECGF8HI7>A@$J

K$LNM

O8PQO#RS TVUWPXZY\[^]_Ua`cb6O8]*`edZ]fUWPQUhg_[^]fUW`cb

i

Ogkjlgk]

M

O8PQO&g+m`cPQdlYaO8noO&g

p/q

`&rfO8]0sut#vw K*x

y

[^dldz`

q ] i O q

O&m L O q m L

O{b}|V~cecS V[^boX[

q

j8eS e d[&cO&g

QA.&&ZcVK$L

OgkO8PQUf[&

q

[^bZeUh[^b[&]fPQ`gkd L O q

Uhm6PQ`

i

O8Y`cb]

L

Ogkd L O q

O:[cgO

i

`cbm`ePQd[cm.]bZUW]fO

i

UO

q

O8bmO&g*Uhg*d

q

O&gkO8bo]fO i1

b]

L

O]k¡+`^

i

UaP¢O8bgkUW`cb[&Y/m[cgkO£1]

L

Od`c]fOb¤]_Uh[^Y7¥V`

q

]_UhmUW]jQUhg*XgkO

i

[eg¦`cbZO`&§

] L O+d

q

`ecbZ`gk]fU\m¨¥e[

q

Uh[&ZYaO©g

/ª

`eX q ] L

G`

q i O q

m`cP¢d[cm]1«bZUa]_O

i

U1O

q

O8bm.O&gA[

q

O*XgO

i

]f`

i

Uhg_m

q

O8]_Ua¬8O/

q

gk][^b

i

gkO&m`eb

i

?`

q i O q i O q

UW¥e[^]fUW¥VO&g

K$L

O q

O&gkXZYW]g*Uabm.YaX

i

UWbZ

q

O&[&Y

i

[^]®[]fO&g]g¦d

q

O&gO8b¤]_O

i

§¯`

q

e°=g

L

[^YWYa`&¡±¡*[^]_O

q

¥VO

q

gUa`cb¡*UW]

L ` q

`c

q

[^d L j i

O8PQ`ebgk]

q

[^]_O*Ua]®g/[cm8m.X

q

[emj¡*Ua]

L ] L

O*]fUWPQO*g]fO8dggO8¥VO

q

[&YZ]fUWPQO&gN

q

O&[^]_O q ] L

[&b

Uab³²´XlYaO

q

Uh[^bµPQ`

i

OY

K$L

O¢~c°¶¥VO

q

gkUW`cbµ`^§*]

L

OQPQ`

i

O8Y/XgO&g#]

L

O¢[^g`cYWXZ]fOQ¥V`

q

]_UhmUW]kj:O&·VX[&]fUa`eb

TV`ePQO

q

O&gXZYa]®gUabmYWX

i

UWbZ[

q

O&[^Y

i

[&][§¯`

q

O&m8[cg]6[

q

O(d

q

O&gO8b¤]_O i1 K$L

O:d[

q

[^YaYWO8Y*UaP¢dZYaO8P6O.b¤]®[^]fUW`cbµ`^§u]

L

O~e°

PQ`

i

O8Y`cb[

i

Uhgk]

q

UWZXZ]fO

i

P¢O8PQ`

q

jd[

q

[&YaYaOYNm`ePQdZXZ]_O

q

U\g

i

O&gfm

q

UaO i

¸¹VºN»f¼½^¾c-¿

YWUaP:[&]fO$P¢`

i

O8YaYWUabZl£VgkOPQU_[^

q

[^blcUh[&b:gfm

L

O8P¢OV£cm.`cPQd[em]AblUa]fO.

i

UO

q

O8b«mO&g£ed[

q

[^YaYWO8Y

m`cPQdlXZ]fUWbZ

ÀaÁ6Â

ÃÄÅ8Æ

Â

Ã*ÇÈÄÊÉÌË.Í

Î¤ÏÐÒÑuÓÕÔ&ÏÔ8ÖlÓ®×0ØÚÙÓÕÖ¯ÙÜÛ.ÔoÝcÞhÔ&ßÒÖ¯ÙÜÖ¯à^Ö¯Ï1ÛáeâAà&Ñ0ÏÐÒÙÜã_ÓØ&äÓÕÖ¯å&ÏÑ#ÓÖÒÙÚãkß_æçNà&ßÒß¯ÙÓÔèã_ÓÕé&ÏÑ*ê/Ûáë©ãÙÜÏÔ&ãÏßfæ&ä#Û.ßÒãÛì¢ç1í/ë&ë8Þhè

î ÏÑuÓÕÙÚØhÝVÖÒÛ.ØÜß¯Öhê8ï8åeðAÙÜÔ&ÑñÐGÓß_ñÐÒà

Unit´e de recherche INRIA Lorraine

Technopˆole de Nancy-Brabois, Campus scientifique,

615 rue de Jardin Botanique, BP 101, 54600 VILLERS L ` ES NANCY (France) Téléphone : (33) 03 83 59 30 30 – Télécopie : (33) 03 83 27 83 19 Antenne de Metz, technopôle de Metz 2000, 4 rue Marconi, 55070 METZ

Téléphone : (33) 03 87 20 35 00 – Télécopie : (33) 03 87 76 39 77

(5)

/9 '2 #%3 %* %+/ , ¦ & " 678

/9 $'^/9- ^

¹¤¹

O6PQ`

i M

O8YWO

i

O6m.U

q

m.XZYh[&]fUa`ebµ[^]_PQ`Vgd L

O q

Uh·VXZOcYW`c[&YaO6~c° dz`eX

q

gUaP6XZYh[&]fUW`cb

i

O6mYaUWP:[^]0O8]

YaO&gO8]_X

i

O&g

i

O&gd q

O i

Uhm]®[^ZUWYaUW]

OQO8]®[^UW]

i

O8¥VO8YW`cdZd

O

O¥V`

q

]_UhmUW]

O6O&gk]XZ]_UaYWUhg

Om`ePQPQOYWO(¥e[

q

Uh[&ZYaO:d

q

`^

cbZ`gk]fU\·XlO

OQPQ`

i M

O8YaO6O&gk][cg

OgkX

q

YWOQg_m L

OP:[:gkO8PQUf[&

q

[^bZeUaO8b)·VXZOQdO

q

PQO8]_]fO i

XZ]fUWYaUhgO

q

YWOQd[cg

i

O]fO8P¢dg#~©?R(§¯`eUhg#dZYWXg·XZO

i

[^bgYaO6gfm L

O8P[²/XZY

O q UWO8b

b³[(XZ]_UaYaU\g

OYh[Q¥VO

q

gUa`ebµc° gX

q

Yh[:gkd L M

O q O

dz`eX q i

O¥VO8Ya`edZdO

q

YWO*g_m L

OP:[$b¤XlP

O q

U\·XlOgkO8P¢U?UaP6dZYaUWmUW]kO´gkO8PQUf[&

q

[^bZeUaO8bO8bXZ]fUWYaU\gf[^bo]NYaO©g

i

U

O q O8b«mO&g

m`cPQd«[cm]_O&g¨bZUWO&g

i

OQRcU

M

O8PQO`

q i q O

w¨«b i

O8¥e[^YWXZO

q

Yh[:d q

O&m.UhgkUW`cb

i

X)g_m L

OP:[QgkOPQU_[^

q

[^blcUaObd[

q

[^dldz`

q ] M

[XZb:PQ`

i M

O8YWO i O

q

O§

O q

O8bm.O#²/XZY

O q

UWO8b:gkdO&m.]

q

[&YG£o`cb[§?[&Ua]+YaO&g]fO&g]g*[8¥VO&m

i

O©g

i

`cbZb

O8O&g q

OO8YaYWO&g

O&g q

O&gXZYa]®[^]g#PQ`eb¤]

q

O8bo]u·XZO6YaOP¢`

i M

O8YaO

i

`cblbZOYWOPO8PQObZUW¥VO&[^X i

O

q_q

O8X

q

g#·VXZOYWOPQ`

i M

O8YWO i O

q

O.§

O

q

O8bm.O

°¦X¢dz`eUabo]

i

O#¥oXZO#boXZP

O q

Uh·VXZOV£&Yh[¥VO

q

gkUW`cb:~e° O©gk]$XlbZO#O8no]fO8b«gkUa`eb

i

X:PQ`

i M

OYaOcg

L

[^YWYa`&¡ ¡*[^]_O q

` M

X`cbXZ]fUWYaUhgO#Yh[]

q

[&bgÊ§¯`

q

P:[&]fUa`eb

i

U\[^e`cb[&YaUhg

O8O

i

O&g$PQ`

i

O&g$d

q

`ed

q

O©g¨¥VO

q

]fU\m8[^XZn6O8b[8rf`eXZ][&b¤]0YaO&g

O&·VX[©

]fUa`ebg

i

O]fOPQd

O q [^]fX

q

O#O8]

i L

XZPQU

i

Ua]

O

O©g¨d

q

O8PQUWO q g

q

O©gkXZYW][^]®g$d`cX

q

Yh[¥VO

q

gUa`eb:~c° gk`cbo]0d q

O&gO8bo]

O&g

OPQ`

i M

O8YWOO&g]#d[

q

[^YWY

O8YWUhg

OO8bXZ]_UaYaU\gf[&b¤]0Yh[:m`ebmO8dZ]_Ua`eb

i

OP

O8PQ`eU q O i

Uhg]

q

UaZX

OO[8¥VO&mY

[&U i O i

O6v p

vO&g_gf[^eO

p

[egfgkUWbZ

b¤]_O

q

§?[emO!

°0O8XZn¢gk]

q

[^]_O8cUWO&g

i

Oud[

q

[^YaY

O8YaUW¬&[^]_Ua`eb

i

O©g$m8[&YhmXZY\ggkO8PQUf[&

q

[^bZeUaO8bgO8]

YaO8X q+q

O&gXZYa]®[^]®g¦g`cbo]0m`cPQd«[

q

O©g

" ½Z&.»$#!¹

v`

i M

O8YWUhg_[^]fUW`cb

i

O:m.YaUaP[^]8£g_m L

OP:[:gkO8PQUf[&

q

[^bZeUaO8bN£

i

UO q

ObmO&gm`cPQd«[cm]_O&g¦bZUaO©g£

m8[^Y\mXZYhgd[

q

[^YWYaO8YWO&g

(6)

~

3 4

67:'9%$

¿

YaUaP[^]fO*P¢`

i

O8YaYWUabZU\g`cblO#`^§7]

L

OuPQ`Vg]$m.`cPQdZXl]fO

q

]fUWPQOÊm`cb«gkXZPQUWbZ#d

q

`cZYWO8P:g/Uab¢cO8`gfmUWO8bmO

65 L

UaYWO

gkO8PQUf[&

q

[^bZeUh[^b¢[^dld

q

`[cm

L

[^Yhg`27¤bZ`&¡*b¢[cg[cm'7¤¡3[

q i m L [ q

[em]fO

q

Uhg]fUhmgAPQO8]

L ` i

[^YaYW`&¡0g´]_`XgkO0

q

O&[©

]fO

q

]fUWPQOgk]fOdg]

L

[^b dzO

q

PQUW]f]fO

i

oj

¿ ª b¤XlPO

q

Ua]6Yh[em87lg ]

L

O§¯`

q

P:[^Yum`ebgkO

q

¥e[^]fUW`cbd

q

`cdO

q

]fUaO©g

K$L

Odz`e]fO8bo]fU\[^YN¥V`

q

]fU\mUa]jU\g$]

L

OcYW`c[&YAUWb¤¥e[

q

Uh[&b¤]+`^§]

L

O[^]_PQ`Vgd L O q

Uhm:9`&¡£g`¡

L

UWYaO

i

Uhgfm

q

O8]_Ua¬8UWbZUW]g

m`cbgO

q

¥e[&]fUa`ebYh[8¡£1`ebZO6m8[^b³[cm

L

UWO8¥VOzO]f]fO

q

m`cb«gkO

q

¥c[&]fUW`cbd

q

`cdO

q

]_UaO&g

K$L

Uhg¨§¯O&[&]fX

q

OUhg¦`&§*

q

O&[&]#UaP

dz`

q

]®[^bmO$§¯`

q

Ya`ebZ^?]fO

q

P=UWb¤]_O8

q

[^]_Ua`cb`&§]

L

O*PQ`

i

O8YVbZO8O i O i

§¯`

q d q O i

U\m][&ZUaYWUa]jugk]fX

i

UaO&g7[^b

i

gUaP6XZYh[&]fUa`eb

`^§+mYWUaP:[&]fO

TO8PQU_[^

q

[&bZcU\[^bP¢O8]

L ` i

Uhg*¡*U

i

OYaj6XgkO

i

bl`^¡ §¯`

q

b¤XZP¢O

q

U\m8[^Y¡$O&[&]

L O q d q O i

U\m]fUW`cb:ZXZ]

¡$OgO8O`cbZYWj§¯O8¡ [^]f]_O8PQdZ]®g$]f`XgOUW]$UabmYWUaP:[&]fO0PQ`

i

O8YWYaUWbZ<;~=?£6;&R=

K$L

O*[^dld

q

`[cm

L

[cgO

i

`cb6gO8PQU_[^

q

[&bZcU\[^b6[

i

¥VO&m]fUW`cb`^§d`c]fOb¤]_Uh[^Yo¥V`

q

]fU\mUa]j0¡*[cg7[^Y

q

O&[

i

j[&dZdZYWUaO

i

Uab>;R=§¯`

q

c°¶PQ`

i

O8Y+[^b i L

[cgg

L

`^¡*b³c`V`

i q

O&gkXlYa]g

bµ]

L

U\gm8[egkOV£]

L

O¢¡*Uab

i

«O8Y

i

UhgO8n¤d

q

O&g_gkO

i

Uab

]fO

q

P:g`&§[6gk]

q

O&[&P §¯Xlbm]fUW`cb[^b

i

¥VO8YW`omUa]jd`c]_O8b¤]_Uh[&Y

K$L

Uhg*[&Yhgk`¢[^YWYa`&¡0g*]f`6XgkO[^bXZbg][^ecO

q O i q Ui

¡*Ua]

L

[gkUablcYaOgkO8]`&§0]

q

[rfO&m]f`

q

UWO&g §¯`

q

[^YaY+¥e[

q

U\[^ZYWO&g]

L

X«g[©¥V`eU

i

UWbZP6XZYW]fUadlYaOgO8]`^§u]

q

[8rfO&m]_`

q

UaO&g#`

q

[

iZi

UW]fUW`cb[&YNUabo]fO

q

dzèYh[&]fUaèbg*[cg_gkòmU\[^]_O

i

¡*UW]

L

[g][&ccO

q O i q Ui ;R=

b]

L

OµgO8PQU_[^

q

[&bZcU\[^bPQ`

i

OYhg£]

L

Oµ[

i

¥VO&m.]fUa`eb d[

q

]QU\g

i

Uhgfm

q

O8]_Ua¬8O

i

¡*UW]

L ] L

O§¯`cX

q ] L ` q i O q

K$L

ObZUW]fO

i

U1O

q

O8bm.O

i

U\gfm

q

O8]fUW¬&[^]_Ua`ebg#Uab]

L

O:gkOPQU?UaP6dZYaU\mÕUW]¦d«[

q

]`&§0]

L

O¢PQ`

i

O8Y+[

q

OQXgX[^YWYajµ`^§u]

L O

gkO&m`eb

i ` q i O q K$L

Om`ePQd[em]$bZUW]fO

i

UO

q

O8bmO©g$XgkO

i

Uab:]

L

Uhg0gk]fX

i

j[^YaYW`&¡ ]_`

L

[8¥VO]

L

O§¯`cX q ] L

G`

q i O q

i

Uhg_m

q

O8]_Ua¬&[&]fUW`cbUWb]

L

O0gO8PQUGUWPdZYWUhmUa]d[

q

]]

L

X«gAcUW¥¤UWbZ#`&¥VO

q

[&YaYV§¯`cX q ] L

?`

q i O q

[cmmX

q

[emj¡

L

UaYaO

q

O8][&UabZUWbZ

] L

OgUaPQdlYaUhm.Ua]j`^§7]

L

OgO&m`eb

i

?`

q i O q

g`cYW¥VO q g K$L

U\g$Uhg$[em

L

UaO8¥VO

i

ojQXgkUWbZ]

L O ª

`cX

q

UaO q+q

O8d

q

O&gkOb¤]®[^]fUW`cb

UabQ]

L

O#Ya`ebZcUW]fX

i

Uab[&Y i Uq

O&m]_Ua`eb

K$L

OY\[^]f]_O

q

[&Yhg`§?[cmUWYaUa]®[^]_O&g/]

L

O#UWPQdZYWO8POb¤]®[^]fUW`cb`&§/]

L

O¦§¯`cX q ] L

G`

q i O q

UaPQdZYWUhmU]

L ` q

Ua¬`cbo][^Y

i

UXgUa`eb

b:]

L

Uhg*d[^dO

q

£z¡+Od

q

O&gO8b¤]*]

L

OcYW`c[&Y blUa]fO.

i

UO

q

O8b«mO#PQ`

i

OYN¡

L

Uhm

L

Uhg$[egkO

i

`cb]

L

Od`e]fO8bo]fU\[^Y

¥V`

q

]_UhmUW]j#O&·VX[^]_Ua`cb6Uab]

L

O0c° m8[egkOu[^b

i

[^g`cYWXZ]fO0¥V`

q

]fUhm.Ua]j#O&·VX[^]_Ua`ebUWb]

L

O0~e° m8[egkO

K$L

O*b¤XZP¢O

q

U\m8[^Y

q

O&gXZYa]®g*[

q

OeUa¥VO8b§¯`

q

`c]

L

¥VO

q

gUa`ebg$`^§7]

L

OPQ`

i

O8Y

K$L

Od[

q

[^YaYWO8YNUaP¢dZYaO8P6O8bV]®[^]fUW`cb6`^§7]

L

O~e° PQ`

i

OY

`cb[

i

Uhgk]

q

UWZXZ]fO

i

P¢O8PQ`

q

jm`ePQdZXZ]_O

q

U\g

i

O&g_m

q

UWzO i1

? @

3 9 A ! /! &2B B¶/u ('

K$L

O[cgOg

L

[^YaYW`&¡ ¡3[^]fO

q

O&·X«[^]fUW`cbg$`eb]

L

Ogkd L O q

O[

q

Od`c]_O8b¤]_Uh[&Y1¥V`

q

]fU\mUa]j6O&·X«[^]fUW`cb

C

CD

EGFIHKJ

LNMOL0PRQTS

%U

P¢`cPQO8bo]fXlP=O&·VX[^]_Ua`ebg$¡

q

UW]f]fOb(UWb:]

L

O¥VO&m]_`

q

§¯`

q P `cb]

L

Ogkd L O q O

E

CV

CD

QXWYS

M[Z\L]M J_^a`

V

[&b

i

m.`cbo]fUaboXZUW]kjO©·X[&]fUW`cb

C

LKMOL0P

CD S M

LaMOL0P

b<c

x O q O F

Uhg]

L O q

O8Yh[&]fUa¥VO+¥V`

q

]fUhm.Ua]jV£

L

U\g/]

L O

d 80-!8efg'

£

L0P

Uhg/]

L O L

O8UW

L

]/`^§ ] L O0gX

q

§?[emOV£

J

0]

L O ¿ ` q

Ua`cYWUhg#d[

q

[^P¢O8]fO

q £ V L ` q

UW¬8`cbo][&Y¥VO8Ya`omUW]jV£hb-

i

UW¥VO

q

eO8bmO£

C%iRCD

#]

LZq

O8O.

i

UWPQO8bgUa`eb[^Y

[^

q

[^bZeUh[&b i O q

UW¥e[^]fUW¥VOV£

E

CV

CD QjW S L ` q

Ua¬8`eb¤]®[^YNd

q

`&rfO&m]_Ua`eb(`&§

E

CV

CD Q U

(7)

R

Z S

+m`Vg

H

Uhg#

q [ i

UWO8b¤]`cdO

q

[^]f`

q

`cb)]

L

O:gkd L O q

OV£

Ya`ebZcUW]fX

i

O£ uYh[&]fUa]_X

i

OV£

V

Uhg]

L

O6¥VO&m]f`

q

`&§

L ` q

Ua¬8`eb¤]®[^Y

¥VO8Ya`omUW]j¡*UW]

L ] L

Om`cP¢dz`ebZO8bo]g[&b i

Uab

[&b

i i Uq

O&m]_Ua`cb«g

q

O&gkdO&m]_Ua¥VO8YWjV£ *]

L

O²[

q ] Lq

[ i UaXg

[^b i ^

Uhg$]

L

OXlbZUa]*¥VO&m.]f`

q

UWb:]

L

O¥VO

q

]fUhm[^Y

v`ePQO8bo]fXZPO©·X[&]fUW`cbgN[

q

O$X«gkO

i

`cblYaj#]_`¦`eZ][&Uab]

L O q

Ua

L ] L

[&b

i

gU

i

O/§¯`

q ] L O i

Ua¥VO

q

cO8bm.OAO&·VX[&]fUa`eb

w4m.`cPQdZYWO8]fOYajQbZ`ebZYaUWbZO&[

q i

Uhgfm

q

O8]_Ua¬&[&]fUa`eb`^§3c`&¥VO

q

blUabZQO©·X[&]fUW`cbg#¡*[egXgO

i

UabT;Rf=

X q

§¯`

q

PX¤

Yh[^]_Ua`eb)m`cP6ZUWbZO&g¦]

L

[^]`&§ ;=+¡*Ua]

L

`cXZ]

i

Ua¥VO

q

cObmO

i

[^PQdlUabZ[^b i ] L

OQd`c]_O8bo]fUh[&Y$¥V`

q

]fU\mUa]jO&·X«[^]fUW`cb

i

Uhg_m

q

O8]_Ua¬8O

i

UWb[6gkUWPQdZYWO

q

¡*[8jQ]

L

[^bUab ;Rf=gk]_UaYaYYaO&[

i

Uabl]f`6gk]®[^ZYWOgfm

L

O8PQO

K$L

U\g¨P¢O&[^bg]

L

[&]¦¡+Om8[&b

XgkOYaUablO&[

q

g`cYa¥VO

q

Uabg]fO&[

i

`&§+bZ`cbZYWUabZO©[

q

P6XZYa]_Ua

q U i

gk`eYa¥VO q ] L

Xg$P:[$7¤UWbZ]

L

O}~c°±PQ`

i

O8Y

i

O¥VO8Ya`edZPQO8bo]

O&[cgUaO q

K$L

O]fO8PQd`

q

[^Y

i

Uhg_m

q

O8]_Ua¬&[&]fUW`cbUhg0[cgO

i

`eb"]

L

O6]k¡+`^?]fUWPQOYaO8¥VO8Y7gfm

L

O8P¢O¡*UW]

L ] L

OOn¤]

q

[^d`eYh[^]_Ua`eb

`^§*bl`cbZYWUabZO&[

q

]fO

q

P-UWb]

L

O¢m`eb¤]_UaboXZUa]j:O&·VX[^]_Ua`cb]_`:]

L

O6PQU

i

dz`eUabo]¦`&§*]

L

O]

q

[8rfO&m]_`

q j [^b

i

YaUWbZO&[

q

Ua¬O

i

] q

O©[^]fP¢O8b¤]*`&§§?[cgk]u

q

[8¥oUa]j¡3[8¥VO&g

gkO8P¢U?UaP6dZYaUWmUW]*gfm

L

O8P¢O! /YWO&[

i

UWbZQ]_`

x

O8YWP

L

`cYW]f¬?]j¤dO#O©·X[&]fUW`cb]f`

zO¢gk`eYa¥VO

i

[&]O&[em

L

]fUWPQOg]fO8d

5

OXgO]_O8PQd`

q

[^Y/XlbmO8bo]fO

q

UabZ¢Uabµ]

L

O6PQ`cP¢O8b¤]_XZP [&b

i

m.`cbo]fUaboXZUW]kj

O&·X«[^]fUW`cbg¡

L

UWYaOQXgUabZ³mO8bo]fO q O i

Uab)]_UaPQO¢gfm

L

O8PQO6§¯`

q

dz`e]fO8bo]fU\[^Y*¥V`

q

]fU\mUa]jµO&·VX[^]_Ua`cb

K$L

O q O&[egk`eb

`^§0XZbm.O8b¤]_O

q

UWbZU\g]

L

O:gkXldZd

q

O©gfgkUW`cb)`^§u]

L

O:gkdZX

q

Ua`eXg`

q

`c

q

[^d

L

Uhm

q

O&g`cb[&bmOQUWb¤]

q

Uab«gkUhm]f`]

L

O:gO8PQU

[^

q

[^bZeUh[&bPQ`

i

O8Y\g ;=

K$L

O i Uhg_m

q

O8]_Ua¬&[&]fUW`cb`&§*]

L

Oe`^¥VO

q

bZUWbZQO&·VX[^]_Ua`ebg#Ya`V`7lg#[egu§¯`eYaYW`^¡0g

[cg]fO

q

Uhg7

i

O8bl`c]fO©g ] L

O¥e[^YWXZO&g

[^]*]

L O i

O8d[

q

]fX

q

Odz`eUabo]g*`^§]

q

[8rfO©m]f`

q

UaO©g

p

`c]fOb¤]_Uh[^Y¥V`

q

]fUhm.Ua]jO&·VX[^]_Ua`cb

EOF,HNJ

L MOL0P

Q

S E F

L MOL0PQ

H E

L

MKL0PQ

J U

¡ L O q O

L

S

L0P H

L MOL0P"!

M$#&%

' b

H

#%

' b

U

v`ePQO8bo]fXZP4O©·X[&]fUW`cbg(

E V

)

M V

* D

QXWYS M E

H,+

Z\L

HKJ_^a`

V !

H M +

Z\L

HNJ_^a`

V ! Q c

x O q O +

Uhg*gP:[^YWYz

q

gk]G`

q i O q i

O&mO8bo]fO

q

UabZd[

q

[^PQO]fO q

¿

`eb¤]_UaboXZUa]j6O&·VX[^]_Ua`cb

L.- )

MOL P M

L.-

MKL P

* D S

M0/L E H1+

b

H M +

b

Q M L -

MOL0P

*b

!

)2

'

3 U ~

¡ L O q O L - S L M /

L £ /

L

Uhg]

L O q

O.§¯O

q

O8b«mO

L

O8Ua

L

]£54

i

O8bZ`e]fO&g]

L

O:¥e[^YWXZO&gUWb¤]_O

q

d`cY\[^]_O

i

[^]6]

L O

PQU

i

d`eUabo]$`^§+]

q

[8rfO&m.]f`

q j K$L

O¥e[^YaXlO&g¦[&]#]

L

OUabo]fO

q

PQO

i

Uh[^]_O¦]_UaPQOuYaO8¥VO8Y6 H i

¢§¯`

q

g`cPQO#§¯XZb«m]fUW`cb87

[ q

O¢`cZ]®[^UablO i §q

`eP XgkX«[^Y$On¤]

q

[^d`eYh[^]_Ua`eb97 :2

' S ~ i

;7

M i

;7

=<>

TXm

L

O8no]

q

[^d`cY\[^]fUW`cbU\g[&Yhgk`

XgkO

i

]_``eZ][&Uab:]

L

O¥VO8YW`omUa]j¢m`cP¢dz`ebZO8bo]g+[^]0]fUaP¢O?6 H i

bZO&m.O&gfg_[

q

j¢]f`b ii

O8d[

q

]fX

q

Odz`eUabo]g

5

Om`cP6ZUWbZO¦P¢`cPQO8bo]fXlP=O&·VX[^]_Ua`ebg$]f`6`cZ]®[^UWb]

L O i

Ua¥VO

q

cO8bm.O¦O&·VX[&]fUa`eb&

b

)

S M

H,+

*

DA@

L -!

H

B U R

(8)

¡ L O q O]

L

O`cdO

q

[&]f`

q @

Uhg

@ S '

m`g

' '

' M

' m`Vg

H

' m`g

E

m.`Vg

Q

[^b

i

B S

+m`Vg

E

&

B

H

B !

H

m`Vg

B

M

B !

Q U

S H +

J * D U S H ' < U

B

S

H ' U

B S M ' H U

¡ L O q O

[&b

i [ q

OI7obZ`&¡*b:·X«[^bo]fUa]_UaO&g`^§NP¢`cPQO8bo]fXlP{O&·VX[^]_Ua`cb«g$[^]]

L

O?6ZG]

L

]fUWPQO*g]fO8d¢[^b

i

[&b

i ' i

O&gfm

q

UaO]

L

Om

L

[^bZeO`^§+`

q

UaO8bo][&]fUW`cb`^§3[¥VO©m]f`

q

[&]

i

O8d[

q

]fX

q

Od`cUWb¤] [cggkO8Ob[^][

qfq

UW¥e[^Y

dz`eUabo] ;=

tugkUabl

~ ]_`O8YWUaPQUWb[^]_O b

§ q

`eP

R ®£A¡$O¢`cZ]®[^Uab [gkUWbZcYWOO©·X[&]fUW`cb"§¯`

q L.-

]_`O:gk`eYa¥VO

i

[^]

O&[cm

L

]fUWPQO&g]fO8d

bZOm8[&bgkO8OQ]

L

[^]6`cX q i

Uhg_m

q

O8]_Ua¬8O

i

d`c]fOb¤]_Uh[^Y+¥V`

q

]fUhm.Ua]jO&·VX[^]_Ua`cb

i

UO

q

g§

q

`cP]

L

[^]`&§<;$=

b

d[

q

]fUhm.XZYh[

q

£¡$OXgkOXlbZPQ`

i

UO

i

d`c]fOb¤]_Uh[^Y¥V`

q

]fU\mUa]jQO&·VX[&]fUa`ebN£¡

L

UaYWOUWbK;=Ua]0¡*[cg*§¯`cXZb

i

blO&mO&g_gf[

q j

]f`XgO]

L

OYaUWbZO&[

q

Ua¬8O i ] q

O&[&]fPQOb¤]`^§]

L O ¿ ` q

UW`cYaU\g d«[

q

[&PQO8]_O

q

UWb ] L

UhgO©·X[&]fUW`cb

5

Oµg`cYa¥VO i ] L

Uhg

d q

`eZYaO8P ojQgO8d[

q

[^]_UabZ6]

L O ¿ ` q

UW`cYWUhg$d[

q

[^P¢O8]fO

q

]f`OO&gk]_UaP:[&]fO

i

[^]*]

L O i

Od[

q

]fX

q

Od`eUabo]$§

q

`cP ] L O

¥V`

q

]_UhmUW]j

K$L

O8b¡+Om8[&YhmXZY\[^]_OUW]#[&b[^YWj¤]_Uhm8[&YaYWj

q

[&]

L O q ] L

[^bUabo]fO

q

d`cY\[^]fOUa]

K$L

O`c]

L O q

d[

q

]fU\mXZYh[

q

UW]kj

m`cbgUhg]gUWbQXgUabZ]

L

O#PQ`

i

UO i L

O8Ua

L

]/O8Y

i

$ UabQ]

L

O#d`c]_O8bo]fUh[&Y1¥V`

q

]fU\mUa]jO&·X«[^]fUW`cb

K$L

Uhg*[^YWYa`&¡0g$[

zO]f]fO

q

[cm8m`eXZbo]*`^§7bZ`cbZYWUabZO©[

q

UW]j`&§]

L

Om`eb¤]_UaboXZUa]jO&·VX[&]fUa`eb

K$L

O#[cgUhm¦§¯`cX q ] L

G`

q i O q

m.`cPQd[em]/bZUW]fO

i

UO

q

O8bmO*§¯`

q

PXlYh[¦§¯`

q ] L

O¦

q

gk]

i O q

Ua¥e[^]_Ua¥VO

s¦XlPQO

q

`&¥

g

gfm

L

O8PQO! U\g$¡

q

Ua]_]fO8b[cg

E

Q

< H ~ E

Q

H

E

Q

S

M <

H

c

K$L

Uhggfm

L

O8PQO6m8[&b)zO[^Yhg``cZ]®[^UWbZO i § q

`eP ] L

ObZUW]fO?O8YWO8PQO8bo]#m.`cbgU i O q

[^]_Ua`cb«g`cb[XZbZU§¯`

q P PQO&g

L

¿

XZYWYaO8bN£&~$

5

O¢m8[&bgO8O]

L

[^]]

L

O¢s¦XZP¢O

q

`&¥

g0gfm

L

O8PQO

i

UO q g § q

`eP ] L

O6XgX[^Y3gfm

L

O8PQOUabµ]

L O

[©¥VO

q

[^eUabZ³`^§]

L O i O q

UW¥e[^]fUW¥VO¥e[^YWXZO&g.£¦¡

L

U\m

L

U\gQ[^gO8bo](UWbXgkX«[^Ygfm

L

O8PQO©g

beO8bZO

q

[^Y?£#m`ePQd[cm.]

gfm

L

O8PQO&g/d`Vg_gkO&g_g¦]

L O §¯`eYaYW`^¡*UWbZ[

i

¥e[^bo][&cO&g(

L

Ua

L

?`

q i O q

[em8mX

q

[cmju`cb]

L

O]

LZq

O8O?d`cUabo]gk]_O8bmUWY

s¦XlPQO

q

`&¥

ggfm

L

O8P¢OAU\g¨]_UaPQO&gPQ`

q

O[cmmX

q

[&]fO

] L

[&b:O8n¤dlYaUhm.Ua]/§¯`cX q ] L

?`

q i O q

m.O8b¤]

q

[&Y

i

U1O

q

O8bm.UabZ £

gkP:[&YaYd

L

[egkO}[^b

i

[^PQdZYWUa]_X

i

O0O qfq

` q g

K$L

O i U\gf[

i

¥c[&b¤]®[^eO`^§´gkX«m

L

gfm

L

O8P¢O&gAUhg$]

L

O#bZO©mO&gfgUa]j]f`¢gk`eYa¥VO#YWUabZO©[

q

gjZg]fO8Pg´¡*UW]

L

m`ebgk]®[^bo]*]

q Ui

Uh[8

c`cb«[^YP:[^]

q

Uhm.O&g

K$L

Od[

q

]0`^§]

L

Uhg$d

q

`omO&g_g¦m8[&b:zOdO

q

§¯`

q

P¢O

i

Uab[

i

¥e[^bmO

K$L

O §¯`eX q ] L

?`

q i O q

§¯`

q

P6XZYh[#§¯`

q ] L

OgkO&m`eb ii

O q UW¥c[&]fUW¥VO

q

O&[

i g

8

E '

'

Q

<>

H

E '

'

Q

H

8

E '

'

Q

S

M H <

'

H

c

(9)

§ m`cX

q

gkOV£VUW]U\g/O8n¤dO8b«gkUa¥VO*]_`UWPQdZYaOPO8bV]]

L

Uhg[^dZd

q

`V[em

L

Uab¢[gk]

q

[&Ua

L

]k§¯`

q

¡3[

q i

¡*[8jUab6]

L

O0P6XZYa]_U

i

UaPQObgkUW`cb[&Y1d

q

`cZYWO8P

X5

OXgO]

L O ª

`eX

q

UWO q*q

O8d

q

O&gO8b¤]®[^]_Ua`cb:UWbYa`ebZcUW]fX

i

Uab[&Y i Uq

O&m]fUW`cb:Uab]

L

OgO8PQU

UaPQdZYWUhmU]gk`eYa¥VO qNq

O8dZY\[cmUWbZ0m`cP¢d[cm]bZUW]fO

i

UO

q

O8bmO©g1Uab]

L

U\g i Uq

O&m]_Ua`cboj#]

L

O8U q ª

`cX

q

UaO

q

UaP:[&cO&g

K$L

Uhg

[^YaYW`&¡0gA]f`[^dldZYajO&[cgUaYaj§¯`cX q ] L

?`

q i O q

m`ePQd[cm.] blUa]fO

i

UO

q

ObmO&gN`cb¢[^b6XZbg][^ecO

q O i q Ui [&b

i

!

]f`

i

Uhgfm

q

O8]_Ua¬8O$

q

gk][&b

i

gkO©m`cb

i

G`

q i O q i O q

UW¥c[&]fUW¥VO&gAO8¥VO

q

j¤¡

L O q

O*O8nlmO8dl]A§¯`

q ] L

O#d`eYaO&g

q

O&gXZYa]_UabZUab¢]

L O

gf[^P¢O]kjodO`&§0]

q U i

U\[^c`eb[^YYWUabZO&[

q

gkjlgk]fOP-§¯`

q

O©[cm

L

YW`cbZeUa]fX

i

Uab[&Y¡*[8¥VO8boXZPO

q

[eg §¯`

q

gkO©m`cb

i

G`

q i O q

mO8bo]

q

[&Y

i

U1O

q

O8bm.O&g

K$L

UhgPQO&[^b«g´]

L

[^]+]

L

Oum`ePQdZXZ]®[^]fUW`cb[&Y`^¥VO qfL

O&[

ii

XZO#]f`

L

Ua

L

?`

q i O q

[&dZd

q

`&noUaP:[8

]fUa`eb:Uhg

q

O8Yh[&]fUW¥VO8Yaj}gkP:[&YaY

K$L

O ª

`cX

q

UaO q+q

O8d

q

O&gkOb¤]®[^]fUW`cbQUWb:Ya`cblcUa]_X

i

O[&Yhg` §?[emUaYWUa][&]fO&g]

L

OuUabmYWXgkUW`cbQ`&§

] L

O*UWPQdZYaU\mUa]§¯`cX q ] L

?`

q i O q i

U1X«gkUa`ebUWPQdZYWO8POb¤]_O

i

[cg/UWb ;8=lXgkUWbZ

`

#ZYW`om87V?]

q Ui

Uh[&c`eb[^YUabo¥VO

q

gkUa`eb

Uab:Yh[&]fUa]_X i O

O]X«g$m`ebgkU

i O q ] L O i

U\gfm

q

O8]fUW¬&[^]_Ua`cb`&§]

L

O0`cdO

q

[^]_`

q @

Uab¢²·

R

ª

Uq g]¡$O

q

O¡

q

Ua]_O¦]

L

O*§¯`

q

P6XZY\[

! /§¯`

q ] L

OgkO&m.`cb i:i

O q

Ua¥e[^]_Ua¥VO#`&§g`cPQO#§¯XZb«m]fUW`cb

J

¡*Ua]

L(q

O&gkdO&m.]*]f`

[cg

4 E ' J

& '

QKS

* ' J U

!

4 O8UWbZ6]

q Ui

Uh[&c`eb[^YNP:[&]

q

Uan6¡*Ua]

L ] L

OO8YaO8P¢O8b¤]®g i

%U/

i

%U/

i

²/nod[^b

i

UabZ

J

Uab

ª

`cX

q

UaO

q

gkO

q

UaO&g$UWb(YW`cbZeUa]_X

i

Uab«[^Y i Uq

O&m]_Ua`ebN£¤¡+Om8[^b

q

O8¡

q

Ua]_O §¯`

q

O&[cm L ª

`eX

q

UWO

q

L [ q

PQ`cbZU\m

J

[cg

'

J

>' M

'

J

U

¡ L O q O

'

[^dZd

q

`&n¤UWP:[^]_O&g '

[&b

i

U\g$]

L O ª

`cX

q

UaO

q

UWP:[^eO#`^§7]

L

O`edO

q

[&]f`

q 4 < * ' £

'

S

gkUWb '

*

' M i

~/gkUWb '

*

i U

*

Uhg$]

L

OPQO&g

L

gkUW¬8O#Uab:YW`cbZeUa]fX

i

Uab[&Y i Uq

O&m]_Ua`cb

TVUWPQUaY\[

q

YWjV£

i

Uhg*[&dZd

q

`&noUaP:[&]fO

i

¤j

J

M

J

U

S

gUab

*

* M i

~7gkUab '

* i

[^b

i

S M

ª

Uab[&YaYaj¢]

L O i

Uhg_m

q

O8]_Ua¬&[&]fUW`cb:`^§]

L

O`edO

q

[&]f`

q

UWb

R $§¯`

q

O&[cm L:L

[ q PQ`cbZU\m

J

¡*UW]

L

O8nZm.O8dZ]fUW`cbQ§¯`

q

] L

Od`cYWOd`eUabo]g*Uhg$`cl][^UWbZO

i

oj

i

Uhg_m

q

O]fUa¬UabZ

' m`Vg

E

m`Vg

Q

[cg

2

'

m.`Vg

2

'

J

M

J

M

<>:2

'

m`g

< 2

'

J

M

J

<>

' m`Vg

* '

[&b

i

P6XZYW]fUadlYajoUbl[&YaYN`e]

L O q

]_O

q

Pg`^§7]

L

O`edO

q

[&]f`

q

¤j 4 '

m.`Vg

K$L

O q

O©gkXZYW]*Uhg

' m`Vg

@

J

!

S

M ' `

` E

< 2

'

&Rm`Vg

< 2 '

J

< H

e

R

<>:2 ' H

2

'

m`g

J

H

2

'

&Rm`Vg

2 '

J

Q M

Þhâ/çNÞhè

(10)

M

E

8

<

J

<>

H

8

J

H

J

Q H

H

2

'

m`Vg

2

'

J

M

J

M < 2

'

m`Vg>

<>:2

'

J

M

J

<

* ' c

x O q

OQ¡+O

L

[8¥VO(]_`[&dZd

q

`^noUaP[^]fO

i

m`Vg {Uab)]

L

O:

q

g]]fO

q

P`^§ ] L

O:`cdO

q

[^]_`

q

[eg[&b[8¥VO

q

[&cO

zO]k¡+O8O8b:[

i

r[cm.O8b¤]*

q U i

d`eUabo]g*]f`6d

q

O&gO

q

¥VOu]

L

OgkjoPQPQO.]

q

j`&§]

L O i

U\gfm

q

O8]fUW¬8O

i

[^dZY\[cmU\[^b

] L O q

]_O

q

P:g0Uabµ]

L O i

U\gfm

q

O8]fUW¬8O

i

§¯`

q P `&§

R #[

q

O¢[^Y\gk`P6XZYW]fUadlYaUO

i

¤j 4 '

m.`Vg ]_`:`cZ]®[^Uab³]

L O

§¯`cX q ] L

?`

q i O q i

Uhg_m

q

O8]_Ua¬&[&]fUW`cb

w*]6]

L

Od`cYWO&g£0]

L

OUWb¤]_O8

q

[^Y[&dZd

q

`V[cm

L i

O&gfm

q

UaO

i

Uab ;=#U\gXgkO

i

]_``cZ]®[^UWb ] L

OµgkO&m.`cb

i ` q i O q

i

Uhg_m

q

O8]_Ua¬&[&]fUW`cb ¥e[&YaU

i

[^]:]

L

O&gkOµd`cUWb¤]®g

5

OµP:[$7VOXgO"`&§]

L

O§?[cm]:]

L

[^]]

L

Oµgfm[^Yh[

q

O8Y

i L -

m8[&b

L

[8¥VO`cbZYWj¬8O

q

`e]

L ª

`cX

q

UaO

q

m`VO

mUWO8b¤]0bZ`e]O&·VX[^Y]_`(¬O

q

`[^]]

L

O6d`cYWO&g

K$L

O q

O&gkXlYa]fUWbZ:]

q U i

U\[^c`eb[^Y

P:[^]

q

Uan:O&·VX[&]fUa`eb"¡*UW]

L

m`cP¢dZYaO8n:XZb-7¤bZ`&¡*bgUhggk`eYa¥VO

i

§¯`

q

O&[em L L -

XgUabZ:XgX[^Y+]

q U i

Uh[&c`eb[^Yu[^Xg_g

O8YaUWPQUab[&]fUW`cb

bm.O L -

Uhg,7obZ`&¡*bN£N]

L O i

UW¥VO

q

eO8bmOb5Uhg#m8[&YhmXlYh[^]_O i § q

`eP R

K$L

U\g¦¡*[eg¦§¯`cXZb

i

]f`:eUa¥VOP6Xm

L

YaO&g_g¨bZ`eUhgj(O8Y i ] L

[^bµg]

q

[&Ua

L

]§¯`

q

¡3[

q i

XgO`&§

~

s¦O8no]#g]fO8dUhg¦]_`Q`cZ]®[^UWb

L

[^b i ] L

O8b

q

O8Y\[^]fUW¥VO

¥V`

q

]_UhmUW]j

F

)

§ q

`eP

$ 0[^b

i q

O&gdzO©m]fUW¥VO8Yaj

s¦`&¡±]

L

Od[^U

q

`^§

p

`cU\gfgk`eb"O©·X[&]fUW`cbg*`cb]

L

O6gkd L O q O

Uhg*gk`eYa¥VO

i

]f`b i ] L

Og]

q

O©[^P§¯XZb«m]fUW`cb[&b

i

¥VO8YW`omUa]jd`c]_O8bo]fUh[&Y

Z ' S F U

Z ' S

b+c

8

K$L

O i Uhg_m

q

O]fUa¬©[^]fUW`cb6`^§7]

L

O©gkO#O&·VX[&]fUa`ebgU\g[egkO

i

`eb(]

L

Og_[^PQOu[^dZd

q

`V[em

L

[eg§¯`

q

g`cYW¥¤UWbZ

R

K$L

O

`cbZYWj

i

UO

q

O8bmOU\g¨]

L

[^]*§¯`

q ] L

OO8noUhgk]_O8bmOu`^§]

L

Ogk`cYWXZ]fUW`cb¡+O

L

[©¥VO]_` §¯XZYYN]

L

Om`eb

i

Ua]_Ua`eb]

L

[^]0]

L O

cYa`e[^YlPQO&[^b`^§ ] L O q Ua

L ] L

[&b

i

gkU

i

O&gAO*¬8O q ` K$L

UhgAU\g

q

O&[

i

UaYWj[cm

L

UaO8¥VO

i

ojgkXlZ]

q

[cm]_UabZ#]

L

O&gO*cYa`e[^Y

PQO&[^b¢¥c[&YaXZO©g§

q

`cP ] L O q

O©gkdO&m]_Ua¥VO

q

Ua

L ] L

[&b

i

gkU

i

O&g

gkO8O ;.=1§¯`

q i

O8][&UaYhg

ª

Uab[&YaYaj6]

L O L ` q

UW¬8`cbo][&YN¥VO8Ya`om.Ua]j6m`cP¢dz`ebZO8bo]g [^b

i [ q O q

O&g]f`

q O i

XgkUWbZ

x

O8YWP

L

`cYW]f¬0]

L

O`

q

OP

S M

H

$m`g

&

U

c

S

$m.`Vg

&

H

c

8

5

OXgOs0XZPQO

q

`^¥

gg_m

L

OPQO¦]_`

i

Uhg_m

q

O]fUa¬O#]

L

O©gkO i O q

Ua¥e[&]fUa¥VO©g

]P:[8jgkO8OP ] L

[&]]

L

Od

q

`cd`VgO

i

§¯`eX q ] L

G`

q i O q

[^Yae`

q

Ua]

L

P-§¯`

q

O8YaYWUadZ]_UhmÕ?]j¤dOO&·X«[^]fUW`cbgUhg#P6Xm

L

PQ`

q

O#m`ePQdZYWUhm8[&]fO i ] L

[^b:]

L

O`ebZO#[egkO

i

`ebgO&m`eb

i

?`

q i O q i

UO

q

O8bmO©g

x

`&¡$O¥VO

q

£V[eg$¡$O#d

q

O&m`ePQdZXZ]_O

[^YaYu·VX[^bo]fUW]fUaO©g ]

L

[^]

i

`)bZ`e]:m

L

[^bZeO"UWb ]fUWPQO:]f`gk`eYa¥VO

R ¢[&b

i 8$ £0`cX

q

[^dld

q

`[cm

L q

O&·XlU

q

O©g

`cbZYWj ~³[

iZi

UW]fUW`cb[&Y[

q

Ua]

L

PQO8]fU\mQ`cdO

q

[&]fUW`cbgdO

q

O&·X«[^]fUW`cb [&b i q Ui

d`cUWb¤]Q]_`)[^dldZYaj 4 '

m`g =]f`

] L O q

O&gdzO©m]fUW¥VO

q

UW

L ] L

[&b

i

gkU

i

O]_O

q

Pg

x

`&¡+O8¥VO

q

£]

L O q

OUhg6[^b [

ili

Ua]_Ua`cb«[^Yum`Vg]QUab [^dZdZYWj¤UWbZµ]

L O

§¯`cX q ] L

?`

q i O q

m`cPQd«[cm]

i

UO

q

O8bmUWbZ]_`

cÕ®8$

b:gO8PQUf[&

q

[&bZcU\[^b[

i

¥VO&m]fUW`cb6d[

q ] x O q

PQUa]_O$Uabo]fO

q

d`cY\[^]fUW`cbQ¡*UW]

L

l§¯]

L

?`

q i O q

m`ePQd[cm.]

i

UO

q

Ob¤

mUabZ

¿

t#°¨Ê

i O q

UW¥c[&]fUW¥VO&gO&g]fUWP:[^]_O&g ;¤.=Uhg$X«gkO

i

]f`¢m8[^Y\mXZYh[&]fO]

L

i

O8d«[

q

]_X

q

Od`cUabo]g

`^§*]

q

[8rfO©m]f`

q

UaO©g

K$L

O:[^YWc`

q

Ua]

L

P-§¯`

q

b

i

UWbZ:]

L O i

O8d[

q

]fX

q

Od`eUabo]g`&§*]

q

[8rfO&m.]f`

q

UaO&g#U\g

i

O&gfm

q

UaO

i

Uab

; $=

65

O#X«gkO#YWUabZO&[

q

UWb¤]_O

q

d`cY\[^]_Ua`cb«g]f`O&gk]_UaP:[&]fO*O8no]

q

[^d`cY\[^]_O

i

¥VO8YW`omUa]_UaO&g[^b

i

bZ`cblYaUablO&[

q

]fO

q

P4`^§7]

L O

m`cbo]fUWb¤XZUW]jO&·X«[^]fUW`cb[^]0]

L

OP¢U

i

d`cUWb¤]®g`&§/]

q

[8rfO&m.]f`

q

UaO&g

(11)

K

[&ZYaO6

'

[^b

i

{O qfq

` q bZ`

q

P:g

'

!#"%$'& () * * *

+ ,

9 #$&%3 ³/9. AV /!&82B B 7#.-6#$/

ª Uq

gk]Q]

L

O"P¢`

i

O8Y0d

q

`eZYaO8P `&§

q

O&gk]_`

q

UWbZ)¥VO8Ya`om.Ua]fUWO&g§

q

`cP 7obZ`&¡*b ¥V`

q

]_UhmUW]j [&b i i

Ua¥VO

q

cO8b«mOXgUabZ

x

O8YaP

L

`cYW]f¬]

L

O8`

q

O8P ¡3[cgm`ebgkU

i O q O i

²·¤g

6

K$L

O:¥VO8YW`omUa]j(«O8Y

i

]f`O

q

O©gk]f`

q O i

U\g]

L O

UabZUW]fUh[&Y1¥VO8YW`omUa]j`&§/]

L O y

`gfgkojV

x

[&X

q

¡*UW]f¬¡*[8¥VO#boXZPO

q R ;e=:

S

0/¢m.`Vg H

m.`Vg

'

R´gkUab

' M

m`g

'

om.`VgZR ! U

S M R /¢m`Vg21 gkUab gkUWb*R

[^b i ] L

O[cg_gk`omU\[^]_O

i

¥V`

q

]fU\mUa]j6[&b ii

UW¥VO

q

eO8bmOu[

q O

F S

/¢gUab M

~c/m.`Vg

m`VgZR ! U

b S U

¡ L O q O3/

S

cÚ^RV

`

<4

ª

UaeX

q

O6

çNÛ.ßÒß658ê87:9/Óà&ÐÒìNÙÜÖ6;/ì Ó=<Ï/ÙÚÔ^ÙÚÖÒÙÓØcß¯Ö?ÓÕÖ¯Ï.ñ

K

[^lYaO6d

q

O&gO8bo]g]

L

O>

'

[^b

i

O

qfq

` q bl`

q

Pg `&§ )[^b

i

§¯`

q ] L

Om`cbo¥VO8bo]fUa`eb[^Y´gkO&m`eb

i ` q i O q

[^b

i

§¯`cX q ] L

?`

q i O q

m`cPQd«[cm]bZUa]_O

i

UO

q

O8bmO:g`cYW¥VO

q

g¡*Ua]

L ] L O q

O&gk`eYaXZ]_Ua`cb

i

O8

q

O8O&gUWb)Ya`cblcUa]_X i O

[^b

i

Yh[&]fUa]_X i O

i

£c]

L

O*§¯`cX q ] L

G`

q i O q

m`cP¢d[cm]bZUa]_O

i

UO

q

O8bmO0[&dZd

q

`[cm

L

¡*[egA§¯`cXZb

i

]f`O

PQ`

q

O[cm8m.X

q

[&]fO]

L

[&bgO&m`cb

i

G`

q i O q

bZUa]_O

i

UO

q

O8bmO&g

(12)

ª

UWcX

q

O

<.Û.ØÜà&ÖÒÙÜÛ.Ô*Ûáç Û.ß¯ß 58ê797ÓÕà&Ð¯ìNÙÜÖ;ìNÓ=<.ÏÓfáWÖÒÏÐ=7héeÓfê*ÙÜÔ8Ö¯ÏÐ?ÓÕÖ¯ÙÜÛ.Ôoñ

ª X q ] L O q

]fO&g]g/¡$O

q

O*m.`cb

i

X«m]fO

i

¡*Ua]

L ] L

O0e° ¥VO

q

gkUW`cb`&§N]

L

O*PQ`

i

O8YZ¡*UW]

L ] L O q

O&g`cYWXZ]fUW`cb¢

i

O8

q

O8O&g

Uab6Ya`cblcUa]_X

i

Ou[^b

i

Yh[^]_Ua]_X

i

O0[^b i ] L

O0]fUWPQO*g]fO8d L

`cX q K$L

O i

UWcUa]®[^Y¤«Ya]fO

q

L ] L O

mXZ]f`&dO

q

Ua`

i L

`cX

q g ¡3[cg#[&dZdZYWUaO

i

Uab[&YaY7m8[cgO&g

K$L

O6gk][&b i [ q i

dz`eYh[

q

b¤XlPQO

q

U\m8g]_O&gk] [^b i y

`Vg_gkoj

x

[^X

q

¡*Ua]_¬$¡*[8¥VO+b¤XZP6O

q

R]_O&gk]

i

O&g_m

q

UWzO

i

Uab ;R=o¡$O

q

O*gXm8mO&g_gÊ§¯XZYWYaj#d«[cgfgO

i

¤j]

L

O$PQ`

i

OY

K$L

O*PQ`

i

OY

¡*[cg$§¯`cXlb

i

]_`P:[^UWb¤]®[^Uab¢]

L

OUablUa]fU\[^Yg

L

[^dO`&§

y

`Vgfg¤jV

x

[^X

q

¡*Ua]_¬¡3[8¥VO¦§¯`

q

[^]0YaO&[egk]*`ebZOPQ`eb¤]

L K$L

O

i

UW]g*g

L

[^dO6[©§¯]_O

q

gkO8¥VOb[&b

i

.R

i

[8jlg$`^§PQ`

i

O8YNUabo]fO8

q

[&]fUa`eb[

q

O}g

L

`&¡*bUab

ª

Uag

~

q

TVO8O ;=z§¯`

q [ i

U\gfmX«gfgkUW`cb:[&`cXZ]ug

L

[&dO`&§

y

`gfg¤jV

x

[^X

q

i

UO

q

O8b¤]PQ`

i

O8Yhg

ª

UWcX

q

O~

<Û.ØÜà&Ö¯ÙÜÛÔ0ÛáçNÛß¯ß658ê8797Óà^Ð¯ìNÙÜÖ6;/ìNÓ=<.ÏÓfáWÖÒÏÐ 7\écÓfê+ÙÜÔ8Ö¯ÏÐ?ÓÕÖ¯ÙÜÛ.Ôoñ

K$L

O]

LZq

OO

q

O&[^Y

i

[^]®[g

L

[^YWYa`&¡$?¡*[^]_O

q

]fO&g]g$¡*Ua]

L

`cXl]¦`

q

`c

q

[&d

L

jQ§

q

`cP ;c=N¡+O q O m8[

q_q

UaO

i

`eXZ]

K$L

O

cYa`e[^YbZ`

q

P:[&YaUW¬8O i y

v"TO q_q

` q g¦§¯`

q ] L O L

O8UW

L

]¦O8Y

i

¡*UW]

Lµq

O&gdzO©m]]f`]

L O L

Ua

L q

O&gk`eYaXZ]_Ua`eb K

¤8~$

gkdO&m]

q

[^Yl²/XZYaO

q

Uh[&bPQ`

i

O8Yog`cYaXl]fUa`eb ;c~=o[

q

O*cUW¥VO8bUab

ª

Ua

R[

X5

O$gO8O$]

L

[^]7]

L

O&gOO qfq

` q g7[

q

O+bZ`c]¡$`

q

gO

(13)

8

] L [&b]

L

O&gkO*`&§7gk`eYaXZ]_Ua`cb«g´`eZ][&UabZO

i

¡*UW]

L

gkdO&m]

q

[^Y«²´XlYaO

q

Uh[^b6PQ`

i

OY¤¡*UW]

L [ YWUa]_]fYaO+ZUa]

L

UW

L O q

O&·VXZUa¥e[^YWO8bo]

q

O&g`cYaXl]fUa`eb K

c~o£A

V&

i

O8

q

O8O&g +[^b i ] L

O]fUWPQOugk]fOd§¯`eX

q

]fUaP¢O&ggkP:[&YaYaO

q ;e~=G£

ª

Ua

e

Normalized RMS height errors

21 December 1978 9 January 1979 16 January 1979 x 10-3

Hours 0.00

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80

0.00 20.00 40.00 60.00 80.00 100.00 120.00

21 December 1978 9 January 1979 16 January 1979 x 10-3

Hours 0.00

0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 3.20 3.40 3.60

0.00 20.00 40.00 60.00 80.00 100.00 120.00

ª

UaeX

q

OR

å&Ï .ØÜÛ5eÓÕØ.Ô&ÛÐ¯Ñ#ÓØÜÙ;Ïé7çAäë/ÏÐÒÐ¯ÛÐ¯ßZÛáeÖÒå&Ï1å&ÏÙ.å8ÖcÏØÜé+ÓßáWà&Ô&ãÖÒÙÜÛ.Ô&ß¤ÛáeÖÒå&ÏáaÛ.Ð¯Ïkã_ÓßÒÖlÖÒÙÜÑ0Ï.ñ9ÏkÐ¯Ñ0ÙÜÖÒÏ1í 7

ÙÜÔ8Ö¯ÏÐ eÛØÓÕÖ¯ÙÜÛ.ÔeÐÒß¯Ö 7\ÛÐ¯é&ÏÐAé&ÏãÏkÔÖÒÏÐ¯ÙÜÔ eÓÕÐ?ÓÕÑ0ÏÖÒÏÐ oo .æå&Û.ÐÒÙ;Û.Ô8Ö?ÓÕØVé&Ùà^ß¯ÙÜÛ.Ô#ãÛ8ÏG×0ãÙÜÏÔ8Ö *o! Ñ#"%$ßfæ

&

'( o%"/Ñ*)+ØÜÏGáaÖ,).-8ÖÒå&Ï/ß?ÓÕÑ0Ï 5&à&Ö1áWÛÐãkà5&ÙÜã#/oÓ .ÐGÓÔ ÙÓÕÔ*ÙÜÔÖÒÏÐ0 cÛ.ØÓÕÖ¯ÙÜÛ.ÔÐ¯ÙåÖ1)ñ

ª ` q

m`cPQd«[

q

U\gk`ebN£/¡$O [^Y\gk` d q

O&gO8b¤]

y

v"TµO q_q

` q g§¯`

q ] L

O&gO:m8[cgO&g`cl][^UWbZO

i

¡*Ua]

L

`cX

q

gO8PQU

[^

q

[^bZeUh[&b(P¢`

i

O8YoZXZ]XgkUWbZm`cbo¥VO8bo]fUW`cb[&YZmXlZUhm¦[&

q

[&bZcU\[^b:Uabo]fO

q

d`cY\[^]fUW`cb6]f`O&g]fUaP[^]fO

i

O8d[

q

]_X q O

dz`eUabo]Q·VX[&b¤]_Ua]fUWO&g ª

UW

Re

bZO m8[^b gO8O]

L

[^]:]

L

O&gkOO qfq

` q gQ[

q

O

q

O&[^]_O

q

UWb ] L

Oµm8[cgO`^§}mXlZUhm

[^

q

[^bZeUh[&bUabo]fO

q

dz`eYh[&]fUa`eb

ª

X q ] L O q

[&b[^YWjZgUhg

L

[cg6g

L

`&¡*b]

L

[&]]

L

O:PQ`Vg]6gkUaebZUzm8[^bo]

q

O&gd`cbgO]f`

] L Om

L

[^bZeO`&§Uabo]fO

q

d`cYh[&]fUW`cbU\g¨`egkO

q

¥VO

i

Uab]

L O i

U\gfm

q

O8]fOd`c]_O8bo]fUh[&YA¥V`

q

]_UhmUW]kj6O&·VX[^]_Ua`eb(¡

L

UaYaO`e]

L O q

O&·X«[^]fUW`cbg*[

q

OgkObgkUW]fUa¥VOu]f`6]

L

O]j¤dO#`&§Uabo]fO

q

d`cY\[^]fUW`cb:]f`6[6gkP[^YaYWO

q

O8no]fO8bo]

]+UhgUWb¤]_O

q

L

Og]

q

[&Ua

L

]§¯`

q

¡3[

q i

X«gkO#`&§

L

)

Uabg]fO&[

i

`&§

L

Uab¢]

L

O#d`e]fO8bo]fU\[^Y

¥V`

q

]_UhmUW]jO&·X«[^]fUW`cb

q

O&gkXlYa]g$UWb:[

q

`&¡*]

L

`^§´O qfq

` q g$¡

L

Uhm

L

U\g*(24`cb [8¥VO

q

[&cO`cb:]

L O l§¯]

L i

[©j

ª ` q

`ebZO`&§]

L

q ] L

OUablUa]fU\[^Y

i

[^]®[`^§+eceQt K¦¿

o°¦O&mOPO

q

8V&Q¡$O[&Yhgk`

d q

O&gO8bo]*]

L

OUablUa]fU\[^Y

L

O8Ua

L

]$«O8Y

i

£Z]

L O q

O§¯O

q

O8bmOg`cYWXZ]fUW`cb:`^§

K

o8~P¢`

i

O8Y[^b i ] L

Og`cYWXZ]fUW`cbeUa¥VO8b:oj

`cX

q

PQ`

i

O8Y ª

Ua

ª

Ua

#g

L

`^¡0g/]

L

O$eO8`cd`c]_O8bo]fUh[&Y¤O8Y

i

`cb]

L

O0gkO&m.`cb ii

[8j§¯`

q ] L

O$UWbZUa]_Uh[^Y

i

[&][#`^§78

ª

O

q

X[

q

j¢8©

§¯`

q ] L

O6¥VO

q

gUa`cbµ¡*Ua]

L ] L

O6`

q

`e

q

[^d

L j K$L

O q

i

O8

q

O8O&g[&b

i

]fUWPQO6gk]_O8d

L

`cX

q

g£

] L O:`

q

`c

q

[^d

L

j¡*[cg][$7VO8b§

q

`eP ;=0[^b i ] L

O:¥e[^YWXZO`&§

i

O&mOb¤]_O

q

UWbZd[

q

[&PQO8]fO q +

Uab P¢`cPQO8bo]fXlP

[^b

i

co£Z]

L

O#d`e]fO8bo]fU\[^Y1¥V`

q

]_UhmUW]kjO&·VX[^]_Ua`cb¢zOUabZ6mOb¤]_O q O i

Uab¢]fUaP¢O

5

O

`cgO

q

¥VO]

L

[^]ugkdZX

q

Ua`eXg¨`

q

`e

q

[&d

L

U\m

q

O&gfgO

i

¡*UW]

L

`eXZ]

i

O8

q [ i

UabZQ]

L

O[cm8m.X

q

[emj

`^§7]

L

Ogk`eYaXZ]_Ua`eb

gO8O<;=1§¯`

q i

Uhgfm.XgfgUa`cb [^b i q

O§¯O

q

ObmOg`cYaXl]fUa`eb

K$L

O¦O

L

[8¥oUa`eX

q

`^§cYW`c[&YUabo¥c[

q

U\[^bo]g/¡*[eg$gk]_X

i

UWO

i

UWb]

L

O0]k¡+`PQ`cbo]

L

g7gkUaP6XZY\[^]fUW`cb¡*Ua]

L i

O8

q

O8O&g

q

O&g`cYaXl]fUa`ebµgk]®[

q

]_UabZQ§

q

`cP o6°¦O&mO8P6O

q

8V&

q

O&[&Y

i

[^]®[Q¡*Ua]

L

`cXZ]#`

q

`e

q

[&d

L j K$L

O q

O8Y\[^]_Ua¥VOm

L

[&bZcO

`^§+P:[cg_g i X q

UWbZQ]

L

OdO

q

UW`

i

`^§+Uabo]fO

q

[&]fUW`cb¡3[cg#

&R32

K$L

O]f`e][&Y/O8bZO

q

cj[©§¯]_O

q

¡+O&[7:`Vg_mUaYWYh[&]fUa`ebg

i X q

UWbZ#

q

g]08

i

[8jZg

i

O©m

q

O&[egkO&g/¡*UW]

L

[gP:[^YWY

q

[^]_O¦¡

L

UWYaO*]

L

O¦d`e]fO8bo]fU\[^YZO8b«gk]

q

`cd

L

j6gk]_O&[

i

UaYaj

i

O&m

q

O&[cgO&g

gk][

q

]_UabZ§

q

`cP ] L

O¦O8eUabZbZUWbZ`&§/]

L O q

XZbN£o]

L

q

ej6[^b

i

dz`e]fO8bo]fU\[^YO8bgk]

q

`ed

L

j¢[©§¯]_O

q

]k¡+`PQ`cbo]

L

[^bUWbZUa]_Uh[&Y1¥e[^YWXZO&g

b:]

L

O[^«gkO8bm.O`&§`

q

`c

q

[^d

L

Uhm#§¯`

q

m.UabZl£Z]

L O

i

Uhg_gkUad«[^]fUW`cbUabmYWX i O i

UWb(]

L

OP¢`

i

O8Y i

XZO]f`QUWb¤]_O

q

d`cY\[^]_Ua`cb[&b

i

d[

q

[^PQO]

q

UW¬8O iQi

UXgkUW`cb +P6Xgk]*YWO&[

i

]f`6[

i

O&m8[8j6`^§]_`c][&YNO8bZO

q

cj:[&b

i

d`e]fO8bo]fU\[^YN¥V`

q

]fU\mUa]j

(14)

c

ª

UaeX

q

O¢

çNÏÊáWÏÐ¯ÏkÔ&ãÏ#å&Ù.å7hÐ¯Ïkß¯Û.ØÜà&ÖÒÙÜÛ.Ôß¯Û.ØÜà&ÖÒÙÜÛ.Ô6ÓÖÖ¯å&Ï&áaÖ¯åéeÓfê ØÜÏGáWÖ1)*æ¤ß¯Û.ØÜà&ÖÒÙÜÛ.ÔÛáNÖ¯å^Ï0Ñ0Û8é&ÏkØlÛÔÖ¯å&Ï &áWÖÒåéeÓfê

Ð¯Ù.å8Ö1)+ÓÕÔ&éQÖ¯å&ÏÙÜÔ&ÙÜÖÒÙÓÕØ eÏØÜé 5cÏØÜÛì)áWÛÐ ÏkãÏÑ5cÏÐ pã_ÓßÒÏ.ñ AÏãÏkÔÖÒÏÐ¯ÙÜÔ ( eÓÐGÓÑ¦ÏÖ¯ÏÐ o o .æZé&ÙVà&ß¯ÙÜÛ.Ô

ãkÛÏÊ×0ãÙÜÏÔ8Ö *o GÑ " $Õß_ñ

(15)

8

ª

UaeX

q O

å&Ï eÓÐÒÖlÛÕá&Ö¯å&Ï .ØÜÛ5cÓØ pNå&Ûà&Ð¯ßáWÛ.ÐÒÏã_ÓÕß¯ÖZå&ÏÙ.å8Ö eÏØÜéáaÐ¯Û.ÑÖ¯å^ÏÙÜÔ&ÙÜÖ¯ÙÓÕØéeÓÖGÓ&Ï 5&Ð¯àeÓÕÐ¯ê &æÛÐ¯Û .Ð?Ó &å8ê

ÙÜÔ&ãkØÚà^é&Ïé eÐÒß¯Ö 7\ÛÐ¯é&ÏÐAé&ÏãÏkÔÖÒÏÐ¯ÙÜÔ eÓÕÐ?ÓÕÑ0ÏÖÒÏÐ o^æ8å&Û.ÐÒÙ;Û.Ô8Ö?ÓÕØVé&Ùà^ß¯ÙÜÛ.Ô¦ãÛ8ÏG×0ãÙÜÏÔ8Ö *oGÑ#"%$ß1)ñ

!#¦1'& 78 ('

K$L

Oc`&¥VO

q

bZUabZµO&·VX[^]_Ua`ebg §¯`

q ] L

OPQ`eUhg]Q[&]fPQ`gkd L O q

O[

q

O¡

q

Ua]f]_O8bUab]

L

O¥VO

q

]fU\m8[^YzÊm`V`

q i

UWb[^]_O

S 7 i 7 P

£/¡

L O q O 7 P

Uhg]

L

O:gX

q

§?[emOQd

q

O&gfgX

q O K$L

O[^g`cYaXl]fO:¥V`

q

]fUhm.Ua]jU\gXgO

i

[cg[d

q

`cebZ`Vg]fU\m

¥c[

q

U\[^ZYWO

q

[^]

L O q ] L

[&bdz`e]fO8bo]fU\[^Y¥V`

q

]fUhm.Ua]jV£7VO8O8dZUWbZUabPQUab i ] L

[&]#]

L

OY\[^]_]fO

q

Uhg*¥VO q j i U

mXZYW]$]f`¢XgkO

¡*Ua]

L

:¥VO

q

]_Uhm8[&YZm.`V`

q i

Uab[&]fO

[&]fO

q

£¡*UW]

L ] L

O*UWb¤]

q ` i

X«m]fUW`cb6`^§N]

L O L

j¤

q Ui M

m`V`

q i

Uab[&]fOV£V¡+O*dZYh[&b

]f`6gk¡*UW]m

L

]f`6]

L

Od`c]_O8b¤]_Uh[&Y1¥V`

q

]fU\mUa]j6O&·X«[^]fUW`cb

K$L

q

]_UhmUW]j

gkO8OV£V§¯`

q

O8nl[^P¢dZYaOV£ ;8=

C

CD

E

F,HNJ

QOS M

FIHKJ

b

M

' m`Vg

E

YWb.7

P

M

Yab.7

P

Q M

M

+m`Vg

&

M

m`Vg>

! H

c

8~

x ` q

UW¬8`cbo][&Y1PQ`ePQO8bo]fXZP O&·VX[^]_Ua`cb«g

XgkO

i

]_`d q ` i

XmO

i

U\gfm

q

O8]fO

i

Ua¥VO

q

cO8b«mO#O&·VX[^]_Ua`eb

E

CV

CD QlWYS

M Z\L]M

Z

Yab.7 PXM

J_^a`

V

H

U

R

x j i q

`Vg][^]_Uhm#O&·VX[^]_Ua`eb

L

YWb

S M

c

8

¿

`eb¤]_UaboXZUa]j6O&·VX[^]_Ua`cb

C

Yab 7 P

CD

H b H

S

%U

K$L

O q PQ`

i

j¤b[&PQUhm*O&·VX[^]_Ua`eb

C

CD

M

;

H

M ! $=

E

H C

YWb.7

P

CD

QTS

#"

U

^!