Debris-¯ow Hazards and Related Phenomena
Matthias Jakob and Oldrich Hungr
Debris-flow Hazards and Related Phenomena ...
67 downloads
418 Views
27MB Size
Report
This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form
Debris-¯ow Hazards and Related Phenomena
Matthias Jakob and Oldrich Hungr
Debris-flow Hazards and Related Phenomena
Published in association with
Praxis Publishing Chichester, UK
Dr Matthias Jakob Senior Geoscientist BGC Engineering Inc. Vancouver British Columbia Canada Professor Oldrich Hungr Earth and Ocean Sciences Department University of British Columbia Vancouver British Columbia Canada
SPRINGER±PRAXIS BOOKS IN GEOPHYSICAL SCIENCES SUBJECT ADVISORY EDITOR: Dr Philippe Blondel, C.Geol., F.G.S., Ph.D., M.Sc., Senior Scientist, Department of Physics, University of Bath, Bath, UK
ISBN 3-540-20726-0 Springer-Verlag Berlin Heidelberg New York Springer is part of Springer-Science + Business Media (springeronline.com) Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliogra®e; detailed bibliographic data are available from the Internet at http://dnb.ddb.de Library of Congress Control Number: 2004117082 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. # Praxis Publishing Ltd, Chichester, UK, 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a speci®c statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Jim Wilkie Project Management: Originator Publishing Services, Gt Yarmouth, Norfolk, UK Printed on acid-free paper
(Matthias Jakob and Oldrich Hungr)
! "#"
$ % #
$ &
(Oldrich Hungr) (# # ) ) +# % #
' ' *
(Nigel A. Skermer and Douglas ,
"# - # # + /"
+ + ! " + # 0 1 + # 2 ! 3 $ # $ + # $ + 5 6"" 7389 : ; " !" ) +# % #
F.
VanDine)
$ $ & . ' * * & . ' ' 4 4
$ $ $$ * *$ & & &$ &&
# $ % & !
! (Kyoji Sassa and Gong hui Wang) $ ,
"# $ >
$ $ ! $ 3 " )@ J# "# # 7 ) @ > ) ; " @ '. 0 :@ C# " @ ;@ C* B@ ? 7 / !##@ ! 9 > )@ ;" )@ ; " @ C$+ !*@ ? . +? 8 .4$@ >!+
>! 7 # !" )@ ; $4 *@ 9@ :! '**@ @
? B & ," : " - /
@ +#) !##@ A8 ; &@ "@ !#" *44 @ A% ? ," : " - /
@ +#)
!##@ A8 ; &@ "@ !#" *44 @ A% ? $
4..* 5 ) 3@ " @ + '$4 '@ >!+
? : ) 9 @ 9 % @ 44 3 " % @ 1 @ ;@ C' */'@ ? 6 7 # !##@ > ) " )@ A ; .44@ #" #@ 1 B ? C D +" 9 ## ! #
+# M /
@ ; $&@ $4 ! " @ +"
#? D
; *@ ! ) :@ $ : @ 8L# /;$@ 7 @ 93 @ >!+ ? 7! )? C >! 7 # !" )@ ; $4 *@ 9@ :! '**@ @ 8 .4$@ >!+ ? 6 C 7 ) @ 9 #0> ) ; @ :# + **@ $$ ; @ 7 ) ? D # C !" 7 # + @ 9# N !# > N ! @ C A + @ @ .44 ; @ ,) ? E
+ ," : " - /
@ +#) !##@ A8 ; &@ "@ !#" *44 @ A% ? + + ," "6 + 1" @ ;"# 1" @ > 6 "6 ; "" @ A 5 ! .@ '4 0@ +" ? F + / 8# !##@ > ) ; " @ *' ! %@ C# " @ ; " @ C* B @ ? 1 #? >! 7 # !" )@ 44 !/ @ O44@ C# " @ 0+ '.*.@ >!+ ? # 7 9 C*B +'@
;7 / ,#@ $444 $ - ! @ C# " @ ;@
? $ 7 -) "# 8# / @ 1 2" > )@ -" % @ &44@ ? 1 9 + 0+ '.*.@ >!+
>! 7 # !" ) 44 !/ @ O44@ C# " @
? + >! 7 # !" )@ $ :( % @ : A @ + ' 4$@ >!+ #? G ," : " - /
@ +#)
!##@ A8 ; &@ "@ !#" *44 @ A% ? 7 &
7P 7P 7P P 3@
>! 7 # !" )@ 44 !/ @ O44@ C# " @
#? . # / 8# !##@ > ) ; " @ *' ! %@ C# " @ ;@ C* B @ ? # #. ," 7 # M 1"# !## 3@ A8 ; 4*. 3 -"@ 1 B #? 6 # : ) 9 @ 9 % @ 44 3 " % @ 1 @ ;@ C' */'@ ? 6 ? >! 7 # !" )@ # C # 8 )@ 44 !/ O44@ C# " @ 0+ '.*.'$.'@ >!+ ? 1 !" 7 # + @ 9# N !# > N ! @ C A + @ @ .44 ; @ ,) ? 1 9 ;82> > ) 1" % " # + 3 !##@ ! "#" / 1" - @ ,"
: " % / @ A 5 ! .@ +'4 C@ +" ! 9 % # ," 0!3@ 1" - @ 0 @ ! % # : @ -.'4 ; @ ! ? 1 6? 9 % # + # A
@ > ! > )@ 3 @ > . 4@ >!+ #? 6 1 C4% Q4@
7 + # 3@ * ;
% @ 7 @ ;@
? E88 . 2) > )@ A % # ,"@ % # 3@ 7 @ >I@ *44 2) @ 5 ? 2 . 44 *@ >!+ ? E #? . 0+ '.*.@ >!+
>! 7 # !" )@ A8 ; $4 *@ @ 8 .4$
>! 7 # !" )@ 44 !/ @ O44@ C# " @
? 1 . 2) > )@ A % # ,"@ 2) > )@ 7 @ >I *44@ 2) @ 5
; .9 ! "@ A8 ; .&@ . 3 % @ 2@ ;@ C4- 24@
0 C 7 # / 3@ *& 0
+"@ C# @ ;@ C.! 0@
? 7 0 >! 7 # !" )@ 44 !/ @ O44@ C# " @ 0+ '.*.@ >!+
? C? 2 2) > )@ A % # ,"@ % # 3@ 7 @ >I *44@ 2) @ 5
? G 2 ," : " - /
@ +#) !##@ A8 ; &@ "@ !#" *44 @ A%
? C D? 2 39 >! 7 # !" )@ $ :( %@ :! '4@ : A @ + ' 4$@ >!+
#? G !7! " ! 44 " 4@444
" ! !##
# #
# # +
# " : "@ ; " DE !## " ) @ # " " D E 9 # # # " DE #" # " # /
+ # " # ;J 1 A @ + ( #@ " "
#@
#@ ; " @ # # DK"#@ % @ " ,)E K" , ?
@4&
#@ # ( "# ( K" , ? ) 4 # (
# K" , ? ) & "# ( # K" , ? # ) " # RR# (==
# K" , ? # ) " #
RR"# (== # T " "# " # # C # #)
( ) # # /
" " # ) # # AA
% @ : " A" @ A
4& 4' ' 4
* & . '
' * & $ $ $
$
$$
* *. *'
*? *?" *?' *?( *?* *?*?/ *?
*? *?
*? *?"
*?'
-? -? -? -? -?"
-?' -?(
-?* -?-
D !" # ) # # #" )
"
" ( # # # 7 ) " "@ C # " " # # ) # # % # # D E " # #
" " ! # # # '. ) # # " %
: " ! - ! # # " '. ) # # " %
: " ! - -) # # !# % @ : " A" @ A@ * ! @ ''@
" +
)
" # # !# % D) # # E@ * ! @ ''@ : " A" DAE / ) # # J # " ) # # D E " '4 : #@ '. ) # # " % ;" " : " A" @ A@ "
"# "
: " A" @ A@ #" )
# ) ) # # +
" # # " ) # # ) ) # # "
) " # #" # " # ; " ) # " " ! + 9 # '$ # " # &* !# #
# # " #
D
?
# 3 @ , @ #
# # ) ; " ,% " # #
3 " I# 9" * A "
" # , # )
" ) +" : " "#
"
)
" ,!+% # )
? ?" ?' ?( ?* ??/
? ? ?
?
? ?
? ? ?"
? ? ?
?
? ?" ?' ?(
?*
# ) # # "# " 3
+9: # "@
" : " ! -= # 7 +9:
" # # # 4 #
" " # ," " +# @ " #@ ! " @ +" @ 0 +#@ ! " @ +" 1 :" # '&4 @ ! " @ +" 7 # 44 @ > +" @ +" +# " "#" @ 2 # # @ @ +" ;) " ! 5"@ 9 # ;) ;" #@ ! " @ +" 9
#
# 0 # #@ )
@ +" ! )
@ /# @ +" !
@ 2 #@ )
@ +" !#
3
@ 1# #@ )
@ +"
(? (? (? (?" (?' (?( (?* (?-
* ' ' $4 $ $ $ $$ $$ $* $& $& $. $' *4 * * * * * **
D *? *? *? *?" *?' *?( *?* *?*?/ *? *? *? *? *?" *?' *?( *?* *?*? / *? *? *? *? *? " *? ' *? ( -? -? -? -? -?"
-?' -?( -?* -?-?/ -? -?
!
@ " #@ @ +" !
# @ B #@ ! " @ +" !
@ !# #@ )
@ +" !#
( @ : #@ )
@ +" !#
(@ ! #@ !) @ +" !#
@ 0 #@ !) @ +" ;
@ " #@ @ +" !#
@ 3 #@ ! " @ +" ;
@ , #@ )
@ +"
@ 3"" #@ ! " @ +"
444 @ 3"" #@ ! " @ +" !#
(@ 9 "@ 1 " ")@ 9
@ +) % @ 5 1
@ 7 #@ )
@ +" !#
(@ 3"" #@ ! " @ +" !#
( 444 @ 3"" #@ ! " @ +" !#
(@ % #@ ! " @ +" !#
(@ /" #@ ! " @ +" @ 9" % @ 5 @ # %@ ! # 3"" #@ ! " @ +" # 1 :" #@ ! " @ +" # ) " # 3 #@ )
@ +" # ) 3 DP#"
E % A )@ 9 # 3 : @ ! 3 : @ !
** *& *& *. *. *' *' &4 &4 & & & & & &
# # ! /# D E !## "#" @ # "# # % . 7 @ " ) % D. E ! # ) '$ DE C '$ D E ! " # '$ D#E !) J" D'$ E DE : ! )
# DE A DE A A ''. A =+ # " # ! K"#
#) I ! : #) 1
# A =+ + # #" # + DE + )# )
## +! 98%! /: 9A 8K A%, 3 /9A /1!8 /%3+0! /!A 9,% 7: 7,8 7,! 7A% 3; :+A
+# "# 9 :
+ # :
"# # # " # ""F9 1,% 1! 10! 89 A8 AB %/C %9 %A %> !+% !++ !9;+ !,A !%! !0; !0,% % 7%> !A C/, C1,% C!+
" "# 1
, 1 2" > ) 1 !## "# 1 0 ! #
# "# A#(# # 8#
"
## ) F ) "
Matthias Jakob and Oldrich Hungr
?
)>1. D F2. , C F> +);F#);F;
##" ## ) )@ # ## " #
) ##"
#@ "@
!# W
? 6 9
D ?? 9 ) # # " + " FFE
, # #@ #(# # ") "#) # : J# # " # ## -" # # # ) # # "# , !) 3@ 1 + # /"
7 )# > @ # # 7 ## / " # # % # # " I " " @ ## @
)@ )#@ ) "#@ )
)@ K" ) ##@ ) # # # D@ ''&S 0# 1 @ 444S %# @ 44E # # "@ 44* # " ,( - . D 0# @ '.&E@ " # # ##
V
D ?? + - " ,@ 5@ ) # @ #
) " 4
# " ) @
@ " # "
!# W
?
. 9 $
0 @ @ " J )# @ #) ) # # # (@ )
" " I#
"# "
I# ," # " @ #
#
# ## " # #) #" ##) # #!+@ ! D'.E # , - ( ( !) # " @ " # #
@ )
# D #
E # ) C " #(# #
" >! % # ; DC @ '$ @ '&.E@ " # ) 1 + # " D E , /@ -"# D'*.E # @ ) D-"# @ '..E@ #
#) # C + @ "
" D;# @ '.S ;"@ '* S @ '$&E@
" ) ) ( ##"
)
)
# # ;
# D'*'E
RR " ==@ # ) " # @ #)) / D! -"# @ '*'E@ " " # D # "@ 51 -"# @ 44E 3 !)@ # # # "
#@ # "" #
@ : 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
4
V
6 ?? 2) RR == # ) ## C D'&.E %
;
#
D.4X ( E
/ D.4X ( E
%
D$ F)E
% # D# @ E
#
0 % 3 ) /
3 D$ F)E
! "# ! # ; #
# "#
" ) ) # D# -"# @ ''E ; " D'* E
#@ # ' D .E 5 D'.E
" ) # #
D " ) E # # + # RR ' == " ) +" D'.4E +" @ " # )# # # @ # # ) # ) #@ ) (
" # # 9 # RR# "P "== RR
== D # "@ / 3
@ 444E : #
) " # ) # "# *4X ) " # D E ! D'& E # "# # #
A#(# 1 + # # RR ==
@ # " >!+ "#) ! 1 % # "#@ 0 @ @ %- D'.*E 3 ? + #
# " @ '@ *&. -" @ 8 D''&E ! ) D, E ,? % 9 : " DE@ * D $*E ++ ;@ % -" @ 8 D444E +) " " ) " )
- * @ "@ -" @ 8@ /@ !7@ ; @ :@ -"# @ 51 D44E % #(# ) -, - . @ 0@ . -"# @ 51 D'*.E : ,? %0 9 DE@ - . & D *..*'$E % @ 1 T -"# @ 51 D'..E 7 ? : # ## ) )
) ,? ; DE@ * = 0 DC @ *E ++ ;@ % -"# @ 51 D''E 2) ? 3 ,? - ; DE@ * > 0 3 13 #( ? DC @ .4$. E , @ %: D''&E )# ,( . @ "DE@ $'* 5 @ : D''*E : # ## #
) ; " @ C# " 5 @ : 5 @ A D44E
" ? #
# 1 1, -@ *DE@ $ ' 5 @ %A D'' E " : "@ ; " ? )# " )#
D$. E A @ 7 )@ > ) ; " @ C# " : @ 1% D'.$E 7 ## #
#
* 0 1 ! -3 ! DC @ $$.$E A @ D'.4E /
) : @ 1 " )@ 1 B - * @ "@ & & A @ D'.*E 9 " # @ : " ! -@ 0 ,? + + DE@ * D *''*E + M >@ ; !# @ 2:@ A @ A@ C#@ 50 D''E 3 , ) ! ( + 3 D89 % '4.$E >! 7 # !" )@ % @ C+
!# W
?
1
! @ 9! D'.E * " > ) A @ 1 T ! @ +0 -"# @ 51 D'*'E ! ) " " * @ 0 1 ! - D! "@ ' 4E !) @ 8 D'..E # "
@ @ $*&$& !)@ 5 D'4E C 0 =# > 6 "#"@ , "# V ! ( D/ ) : 5 1 ! @ ''&@ 4* E@ /;+ / "@ C# " @ W ! @ 1 D'& E * ( , & ( A D9 ! # 7 ## % A104E >! + #"" @ 0 @ @ D''E ! ( D,+-% : @ *$ E ++ ;@ % C@ 9 D'.$E
" 1 . @ @ *. C @ 5 D'$ E 3 )
# ,? /; /# DE@ -& * D!# % .@ 4 &E -) % # ; @ 1 +#) !##@ 0 @ C @ 5 D'&.E ! )
# ,? %5 !#" %5 2 DE@ 3 1 D!# % &*@ E % # ; @ 1 +#) !##@ 0 @ 0 @ 5@ !@ :/@ ,@ 53@ !@ %@ ; "@ 0+ D44 E %#
@
" # & @ @ ***
Nigel A. Skermer and Douglas F. VanDine
?
;61F@6F;
RR == #" )
" - ) 9 @ 9 " T@ #
# ( )
# # # ) ( 0 @ # " # ) #
" 9
@ : D'E / # " D'. E # /"
+ # % @ :" D'''E " 5 # #" ) , 1 + #@
# ) #" ) # D@ +# : " D @ '.&S 2 #@ '.&EE 0 " " @ # # " 9 @ 0 ! ( ! * @ ''@ ) #
# ) ) D ## " ( ) 5 @ ''E + # # #@ # @ # " ) ; -
D'.'E +
" ) " ) #)
# ; " @ @ ) C D''4E # " ; "
%" @ 0 @ :I 0 @
" .$.@ ,' ( ##"
) D @ .$.E # ( ) #
) D:
:@ '&.E ! 9@ " )
" A#(# %) .&@ J# ! % % #) : " 5 @ + ? RR0 @ ( : 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
*
V
D ?? "# )
. 8# @ '@ # ") ; ;#@ C# " @ ; " @ ) + #"
'' " " "
)@
# " # @ " # D! %" D''.ES C# " A" # 3 )@ !# # @ CA3 $.*E
( @ ( == D7 @ 444E
##"
- ! "@ ; " @ " ) #" ) D9" E # "# '&*@ " '& '&$ A +# # C# "
, D1 : # @ '&'E , #@ " " # )@ RR== " 44@ " ) @ ## ) / 1G , '.@ > " #
@ @ " @
# %# # " )@ # # $4 44X + "
@ # #) # ) " @ # . # " # " " # # @ " # >= 44)
) #" # ) ; D'.$E@ 2 3 D''.E # # # . & ) " #" )
/ 1G @ '&.'. A ") " "J
'*' D2)@ '*'E RR )== " )
# ) 0 0 ,, D' $E #" " # ) >! 7 # !" ) >! 1 % # "# +## ; -
D'.'E RR 1 == A " ) 3 + " .$@ .$@ .*.*@ .&..' @
.
V
' @ ' ' 1 T = ) ' @
3 +@ #" "
" " 4 ## # ) " ) (
" " ""@ @
" " ) ) : # " " ## ; "I" % @ # ) 3 + ") 9
# I" D/ @ '*E / #" #
3 + " ' @ #" D3# = #"
) ## #" ) E , # ) " " >!U4* ##) " ## 3 + ") " ' @ D- #(@ '*E :) ) ##
# "
# D9
@ '$'E : " ) "#" ##"
" " !!%
" # @ # 2= # " # #) ! : "@ #" # ) )
) , ! @ # #) 2 # & D9 +E@ " ) +) #) ) # I DC) )E " .$ " %" , 2 # @ " # %" #) " ) " ) @ " @ # + % @
7 D; )E 3 D:)E + #
!# $W
?" '
C ) ## " @ # @ # # "
) @ @ ) @ # " ##" ##" 9 @
)
## , # #"A#(# @ # @ # # " $4@444 ) , ) @ +
D " '.$E A" D A ''E ##"
) # ) ?"?
%# "# J# ) # ) + # 3 ;
+ " ! 7 # # "# " D:# ) -@ 444E ## ## + &' " : " C"" 1 ,) " # A - #""@ " " 4 ## )
"
) ) #) "# " ) L#" # ?"?
6
, + #@ # #"A#(#@ "# # #" ; ) #@ ) # # # )@ ( "
A #P # :# ) " ##"
" @444 )
I " " @444 ) ) @444 ) " " " # D! @ '''E ## # #
A #P@ # #"
) 1/A # # ;" 4 # 1
"# 7389@ " " # # D>1/A@ 44E ?(
#;) 2.6) D F2.
9 "
"
# D(
E "") #( T
# D# #) (E ) " @ ) " " : I " ) # ##"
&$ ) ) " # #
@ #" )
"# ) 1 @ % 3"#@ A@ "#@ 5:@ !@ -; D'.E 1 ! ( ! 0 D, #" 1 ..$&@ *$E >! , @ ;" " :@ 0 @ : )@ %+ D'E 1 I D4 E -) ;
@ 3 :"@ D'''E 6/ 12 0 , D& E ! A" #) @ ) :# )@ 90 -@ 9 D444E & ) -7 , - 9 :3 .2 -F D7!+ !# A 1 $E 7 # ! #) + #@ ; " @ 8 :#A@ 5+ D'.'E 1 # D& E 9
! " 7
"@ 1 T :) + #@ - D'$*E I , . - , D+ ! # 7 P# 1# / ! 1 E ! # 7 P# 1# / ! @ ! ! V !W :@ 3 D.'.E 8 T
* 0 . @ "@ ** 4 : @ 9 D'E
P " @ " P " =N P N I " B7 ! 7 # !" )@ % @ C+ !# @ 5; D''E " DRR ==E 7" 2 5 . )@ B0DQE@ ! @ @ + @ :@ :#@ 53@ 8 @ 5 D''*E % ## # A #@ :# ? A ) "" H . @ D$E@ '' 4 ! @ @ !#@ A@ >
"9"#"#@ 5 D'''E : A #
A # # @ #"@ # :# . @ D4E@ $$4$* ! @ 1+ D'.4E + ? + ; " H 1 * -@ *@ ' ! @ 1+ %"@ !8 D''.E . 8# 1 * -@ "@ ! @ 5/@ -@ 70@ !" @ 7@ ! @ 3 D''E -
) '.4 -, . @ *DE@ &. ! #@ A D'.&E A # @ '@ .4.$ ! @ 05@ A @ %3@ @ +9@ @ + D.'&E % # ) % ) " ! #) # 2
) 4 * @ *@ &$$4. !#"@ A D'&'E 0 # "" !"6
7 " -" D & )3 & (, D* E +" A
@ ; !"6
@ 7 ) V 7 W !)@ 5 D'4E C 0 # > @ ;"#"@ , "#@ +" D ) : 5 1+ ! @ ! (@ /;+ / "@ ' E !" @ + D.&4E - & DC E " @ A V 9 #W !" @ 0 D'E + "
)
) - #(& @ :) @ $*$* P )@ / D.'E 3 1 3 + 3 A )#T @ +! D'&'E
# " ; =) + % '&& . L - M@ *@ D , 2 *@ *DE@ $.*4E B@ : -"" @ D'*$E "" : 2" D/ 5 , E I 8@ *@ &*.
! ! William Savage and Rex Baum
?
;61F@6F;
, ) # ) " ##"
# 9" " ) " " # D@ E " # # "# )
# 9 ## ##@ "# @ @ ) # )
"" , 9" #" " # # #" " " # # ) @ @
" @ @ @ ) # " ,
" @ # #
# ) " 9@ )@
"
" " " #@ @
"
# " ) ) )
#@ " @ )@
# " # % @ " #
# ( ) " # 0 # ) # " ) + # ) # @ ( " # # : # )@ (
"# " ##"
@
@ " ) ,# # # #
" # " ) "# + " #) # #" @
"
@ # ##"
:) '. @ ") #" " #
# D5 @ 444E + " " " # #" @ @ @ @
# )@ # 9"
? .,
!!
!# W
$$
-)
" S
)
#
3
" S " #
% "" ! "
"
)
#
#
"
A
A
#
# # S ) ) ! #
D ?? !# " # "# " # "" + D'&$E
# ) I ) #
" ) )
# 9 # " "# D # 9" E ) " # 1@# #)6+F. FD . F) .6> 6G ; G..
, # ) ) #
# @ ( ) ) )
,)@ " "# # J# ,( ) )
%+ DC @ '. E # " "# " " # # # ) "# # "#) ;
>! 7 # !" ) " #
-T%>! *4 D!" @ ''.E # !7! 89 % 4 .@ & E >! 7 # !" )@ % @ C+ 8=3 "@ 3 D'& E J# ) 9#+?+:@ @
!# .W
?* 1
&'
A#@ %@ @ 7@ 7
@ 1 D''.E !,1:+A
#
) * Q 1 - . DC @ $&*$E + # ! #) / @ 1 T % @ :: D'' E 1 , 1 D>!7! ;" 4$'/E >! 7 # !" )@ % @ C+ %" @ 5 ! @ % D'*E ! " ( ? ) * @ (@ *$ !@ 0B@ 7 @ 50@ ;"@ %3 D44E + ) ) " ) ( * 5 0 1 ! ( ) + 3 * 3 3 /KR/63 6KK53 , 3 () D &'.&E : @ % !#@ 2:@ % @ 55@ ! #@ 5@ #@ 0/@ : )@ %@ !#" @ D44E )
# "# "# ) 8 % 1 . @ *@ ''$4 !"@ 5@ -"@ 2@ 7"#@ : D''.E $A 1 & /& , 3 I 3 I >+K D>! !) 3 ) % # % 1 E >! !) 3 )@ % @ !@ ; D''*E I ? 2 D & E 3@ ; # % @ 93 @ 2 D' E D$4 E 5 0) M ! @ 1 T C @ , D'. E !& & 3 ! & &
. &( ! ( ( - 1 &, & D>!7! 0 % " # , % . *'@ 4' E >! 7 # !" )@ % @ C+ 0
@ 35 D'&&E #
" ( @ @ . . ' 0 @ A3@ + @ :7@ 3 )@ : D44E + )
# "# # - * @ (@ .$'& 0 @ :@ -##@ 0 D'.'E %"# " ; ,? * /6 0 1 ! -3 3 /OQO D *'* E ++ ;@ %
" # $ % & !
! Kyoji Sassa and Gong hui Wang "?
;61F@6F;
" # RR == # " ) @ # ) #
" # " @ #"
# ) )
## D@ A @ ''4E@ ##"" D@ @ '&.@ ''E@ " #@ )
D@ 5 @ '. S !@ '.$S / 9@ '.&S , @ ''&E # " # @ #@
") , #@ ) #
" @ " D 0@ '. S !@ '.$@ 444S ! : @ '..S 5 @ '.'S 0# @ '.'@ 444S &E 0
@ "
# ) "
# D!@ 444E
# "
# ) -"# ; D'&E
" "
##"
: " >" !" I # @ "
"
" # )
##"
# D!@ '.$E
"# # "
# # " ) )
"
: 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
.
# $
"?
V $
@;1;) F;C FD 6+) 6F11);6 )F.6.
0 # #
@ ) 9" $&@ " ) " @
:)@ ''& 9" $.
D "?*? A 7
D
& + @ ''&E # ++ #
" )
7
De E
"?
6! $
'
Elevation (m)
!# $ W
Horizontal distance (m)
D "?-? ++ #
' 5")@ ''*@ & # @ ''*@ & + @ ''& r ##"
" 5")@ ''$ )
S s * # @ ''* S t
) + @ ''&
3 ++ # " ) # ++ 9" $'@ # " ' 5")@ ''* D * # @ ''* E@ & # @ ''* D ) E@ & + @ ''& D
E
( ' 5")@ ''* " # #
# " 5")@ ''$ ) ) D ) " E ) " * # @ ''*
)
) + @ ''& :
; 9" $. $'
7 ") + ) 9" $'@ " *
" " # ' 5")@ ''* & # @ ''* 3 D9" $'E ##"
" " 7 DE D E ! DD 4&'@ 4*&
!# $ W
"?
6! $
'$
0 "# @ # " " - % # #" # # 9" $4 )# D# #E # ) #" "
" " # # " 9" $4 " #
"
# ) # " # # # " " " " +
2) " # " ## # @ " ) " # " @ " # ) #
" "
1)D)1);).
@ 5/ 0@ 7 D'. E ! ( D>!7! 0 % " # @ 8( % . F*4*@ C E >! 7 # !" )@ % @ C+
4
# $
V $
#@ 0/@ %"@ !3@ 0 @ 5 D'.&E 8 ? B
)@ ) - *4 2 * 1 , 3 D,+-! A" # 1 *$@ &&E , + # -)
# !##@ #" #@ 1 B /@ ! 9@ %0 D'.&E :
@ ! 9 ## ;) ,? 5/ 79 0# DE@ ! (", 2 * 3 3 D7!+ % / 7 ) 1 &@ 4E 7 # ! #) + #@ ; " @ 8 -"# @ 5 ; @ % D'&E > @ " # " .B 8@ D E@ $$. , @ %:@ %@ :/@ 3-"@ %7 D''&E
,( - * @ "@ .$. 5 @ %0 D'.'E " A" %# ,? +A !#" %0 5 DE@ * - A * D7!+ !# A 1 *@ '$$E 7 # ! #) + #@ ; " @ 8 5 @ +: D'. E ,? ; " ; A DE@ 0 D $&*E 5 0) M ! @ 1 T 5!// D''E *, D5 ! #) /
/ ! ! 1 *@ **E ! @ ) V 5W 2) !)" 3 D''&E 7 D!# " 7 @ 4 E 1 L-M@ -D4E@ *4*&4 V 5W 2@ - D''&E , /OO> 3 # *3 ! ( D% 7 + !#(# % # ''*@ A
I# 1 4.444&@ E 2) > )@ ) : "@ -@ ! @ 8@ 0 @ 1 D''&E 7
* #
''*@ 5 #(@ /@ * A @ @ 5@ %5@ " @ 5@ ;
@ + D''4E A "
# ) 1 '.$ " 1 %"@ @ # 1. D F2
#
#) ( )
# #
@ " # ## )@ # ) ) " + " ) " @ ) J
"
# " #") ) " ## D@ # " @ " )#)@ " "#E , "#
# " ) # )#
+ @ " : 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
4*
$
V *
# # #
# #@ ) J
# # # #")
" # # D@ # @ @ # E@ ) " , "# # # ) # )# # , # @
# ! A#(# 1 ) " ) "@ " # (?'
)B# ). FD )#1 >16F; FD 6+) G) 16) F;)6
" ) # # " # 8" ,@ - ) D''E ! " # # @ " # # ) + # RR == "@ "
)@ D''E " # # # D # (E =
# L#" ) ) # #@ # " ) # "
$4
)
V &
@ " " # "") (#) #
) 9 0 D44E@ "
K" , ; " @ # )
# /
# @ #" # # " + # @ " # ## %" " # " 16.+ F @#> )>1.$D F2 6>.)
% : @ # ) ) :#: ; ) ; " @ ' #
K" ,@ ; " ) # "
) &44 @ # ## ) A # # # "" D9 % @ ''E , #
@ " #@ " # @444 @444 " #
"
# I" " + ' " " " )@ # ) # #@
(?( 6 > $ $
Number of reaches
!# &&W
Erosion depth (m)
(negative for deposition)
D (?/? K" , ?
@4&
#@ # ( "# ( # " ) : % @ 7 + # 3 : 0@ C# "
# @ # @ # # # (@ " " " ) @44 @
$44@444 "
44@444 @ &X @ # " ##"
#) ( 9" &4 "
#
&
" # # ? . . .
)
D E D
E@ # # # $ $
A "
@ " "
) 4$
# 4 # - @ # @ # (# "
" ) D# # 4 E
$
)
V &
6 (?? K" , ? ) # # ( # " ) : % @ 7 + # 3 : 0@ C# "
># (
(
!
+
!
+
!
+ 4$ *4 4 $4
4' $$ $$ 4
'$4 $.** 4&$ '*
4* 4.' 4& ..
* .'' $$& *$$
Number of reaches
!# #
@ #"" " #@ @ @ ) # , # #" D@ # (@ @ @ "@ "E (# )# "#
+) " " @
Yield rate (m 3 /m)
(negative for deposition)
D (?? K" , ? ) 4 # (
#
(?( 6 > $ $
Number of reaches
!# &&W
Yield rate (m 3 /m)
(negative for deposition)
D (?? K" , ? ) & "# (
#
" ) # ( "# ( # 9" & & #) , # "
) @ # ) " + " ) & , " " # & "@ " )# # ) # 9" & &
D" ) E D ) E " 6 (? ? K" , ?
D E # # ( ># (
(
!
+
!
+
!
+ 4$ *4 4 $4
44 4 4 4&
4' 4 4&
4 4' 4 4$ 4*
4. 4. 4&
$
)
V &
D (?? K" , ? # ) " # RR# (== #
# , # # ( #@ # " @ #
# ##" 4 @
) ") 8 @ " # J# "# ( # D9" & E , #@ @ 4 @ "
" " ,@ ##"
#
" )
#
(?*
F; @.F;.
) # "# # # " + # @ )# # ! 7 # !" )@ % @ C+ 9@ %5 % @ A D''E ? ! )# # # # " 1 . @ /@ &. 9@ %5 0@ :A D44E + ## # 1 . @ *@ '.'' 9 @ +: D'''E # # "# " @ 3" ,@ - 2 % - . @ @ &$' 7" @ 9:@ : @ !@ !# #: @ 7 D44E , "# #" ) )
## # D@ " ,)E? + " #
# -, . @ @ &. -" @ 8 D444E +) " " ) " )
- * @ "@ -" @ 8@ : @ 7@ 2 @ % D'. E K" )
" 1 . @ @ ***&& -"# @ 51 ; @ %2 D'&E > @ " # " .B 8@ @ $$. ,)@ - D'.E + - *4 D,+-! A" # 1 @ $&*$..E , + # -)
# !##@ 0 @ >2 , @ %: D''&E )# ,( . @ "DE@ $'* 5 @ :@ -" @ 8@ @ ; D''&E ") " ,? 3 DE@ * / 0 1 &' ( ) 2 3 * D .' E + # ! #) / @ 1 T
!# &'W
(?- 1
$&
5 @ :@ + @ @ 9" @ @ -" @ 8@ +) @ D444E + """) -" @ : 3@ ; " 1 . @ (@ 4'$ 5 :@ ; @ :@ 8@ : D44 E / " F@;1). FD +G)1F;);616) D F2
A
) ( ) # # , @ " ## ) # " " # # # "
" " # # , " @ ## # # )# # # D # " # #E #
## # # D " )
0 # ( #E@ )# # @
" ) # " D " A"@ '' S " @ ''$S , @ ''&S *E # " )#
#
" # ""@ @ # # )
) ; " D'* E ) ( ) # # " # # 4 X D 4 XE
*
+! , !
V .
*4 X D.4 XE 0 " # " # " " "# ) # # @ #) # #
" " #@ " DA !# @ '.$S @ '''E@
) " " D0 @ '.$S 2 @ '..E # ##" # " # . #) # " # # ) # ) " D0 0@ '' E
&
+! , !
V .
D *? ? !" # ) # # #" ) "
" ( # # # #" ) # " 9 3-$ 0" % D%"" # @ 1 BE@ & ! @ ''$@ 4' $ @
" # ! # # * X D
@ '''E A ) ! 5
D:) > )E
" #) # " # " ) @ # D:I @ 44E !"# " # " # " (
" #
) " # D
@ '''S :I @ 44E@ "
#" " # D9" . E
Bedload ; D # # E "
# ) # " " # # @ # # .)10) +G)1F;);616) D F2.
-) # # ) # ##
#) # ) " @ #"
##
, "#
) " # )#)
# # ) "
"# #@ ' @ "#
@ ) # # D .E@ ( "# ) )# " ( ! 7 # !" ) " '@ &@ .
" # (
) # # ) # / " # " '*4@ *$4@ $4 F@ #)
" $4X
# +
4 $ J (#)
# " ( ##"
) " #@ ) ' 3 RR ) "
# D E
# == D! 9 @ '.'S ! 3 @ ''E ) # ) # # @ ) # )
###
" " !7!E
! ( @ ) " # )@
" ) " "# )# # !(# ##" # # : #) !7! A
A
$.*@ &$E >! 7 # !" )@ % @ C+ @ 7 D''4E ! "#" " " . @ -"D;*E@ .*..*'* "@ - D''$E ! " # # # # # I . @ '"@ &' " @ % @ / D'$E ) "# # ,? * 1 8 3 ! V# ; )@ '.*W /"@ 9 0@ B D'. E , ) ) # # -@ /@ ' 9@ Q D'.E 7 #
) # # " ,? * 6 0 , D 4&4.E 0 % " # /# # A A @ 1I@ 7 @ :! D'*'E :" #
, 2 *@ @ 4 7 @ % D'&&E !
- * @ @ * 7#)@ A+ ;@ 50 D444E & ! 13 1 3 #, 3 5K3 /OQ5 D>!7! A
A *&@ ' E >! 7 # !" )@ % @ C+
'.
+! , !
V .
7#)@ A+ - @ 3 D'&$E /S3 /O@S3 ! - 1 3 #, D>!7! A
A '4@ . E >! 7 # !" )@ % @ C+ - @ :+ D'&$E # ( * @ "@ . . - @ :+ D'&'E ;" )#) * @ -@ &$&$. -@ : ; @ +5 D'.$E + " " ) . @ -/@ ' ''$. - @ D'*$E -) # # " D#" E , 3 ++1+-+@ -@ .$.. -" @ 8@ /@ !7@ ; @ :5@ -"# @ 51 D44E + #(# ) -, - . @ (@ . , @ %: D''&E )# ,( . @ "@ $'* , @ %: D44E ) ) ,? %#@ 3 DE@ &' ( ) 2 3 * 3 D 4 E : @ % , @ %: C#@ 50 D44E 1 " . @ -@ $. 5@ %5@ !# @ 2:@ 1 @ 2:@ : @ -+ D'.E 3 @ J#@ ,? A0 3@ % :"" DE@ /OQK - + 3 D>!7! A
A $4@ * &.E >! 7 # !" )@ % @ C+ 5
@ % @ 5/ D'.*E 3 . 3 & /=3 /OQ6 ( 1 ! 3 1 3 1 D>!7! A
A *'@ &. E >! 7 # !" )@ % @ C+ 5 @ +: D'&4E * * . D$$& E 0- 9 @ 1 T 5"@ AT 3@ T D''E % ) ) # # -@ (@ *$ 2@ B B@ ! D'.4E + ) ) # # # ,? * 0 , D $*E ! #) -) "# / @ ;I 2@ - 9"" @ ! D'*'E # # # ,? * & /5 1 3 0 DC @ 4E , + # -) "# % #@ /# A )#! 7 # !" )@ % @ C+ A@ 5@ @ %- D''E # . @ @ 44 A #@ % D'&E " ,? 1 A 3 /O/> D>!7! 0 !") A 44@ '$E >! 7 # !" )@ % @ C+
44
+! , !
V .
A @ D'.E # " # : @ 1 B@ # ) @ *@ '*4 A @ D'.*E 9 # @ : " ! -@ 0 ,? + + DE@ * D *''*E + M >@ ; A @ D'''E
" "
# : # '@ '. ,? A DE@ 1 8 & " ( 0 + I 3 3 /OQ6RQS D>!7! A
A $.*@ '*E >! 7 # !" )@ % @ C+ A @ @ 5/ D'.&E + # #(# "
. ,( - . @ (@ A @ !# @ 2: D'.$E " ?
) # # @ @ $$ A @ @ @ +!@ %)@ A5@ % @ ::@ ! "@ %@ " @ ;! D''*E 9 " : " A" @ 5")8# '' ,? 7 1 %! A"" ) DE@ ! 2 - * 3 * D ''$4E A ," C # ) ! )@ K" ) > ) 0 A @ ! A @ A
@ 2+ D'''E / " :) @ '. ,? A DE@ 1 8 & " ( 0 + I 3 3 /OQ6RQS D>!7! A
A $.*@ .4E >! 7 # !" )@ % @ C+ K@ T@ T@ 0@ B @ 0@ @ Q@ B@ 3@ Q"@ 0 D'.E ;# # # #
) # # ,? * 0 , D &$. E ! #) -) "# / @ ;I %# @ /C -)@ 9 D'*$E -) # # " D #" E , 3 ++1+-+@ -@ $4 %#@ D''E -) # # -@ (@ ' ' % @ 2!@ > @ 5C@ + @ %+@ % "@ @ A : @ :3@ ! @ 5-7@ /@ @ : @ T D''*E ) : " A" ? , @
#@ @ # ) "# # ,? 7 1 %! A"" ) DE@ ! 2 - * 3 * D '.'4E A ," C # ) ! )@ K" ) > ) 0 A @ ! !# @ 2: D'..E 3 , 3 & ! ( &1 ( ) , D>!7! A
A &+@ & E >! 7 # !" )@ % @ C+ !# @ 2: 7 @ 7 D'*.E ! ,3 1 2 3 3 D>!7! A
A :@ 4 E >! 7 # !" )@ % @ C+ !# @ 2:@ C#@ 50@ A @ A D''$E 3 , ) ! ( 3 D>!7! A
A $ &@ $* E >! 7 # !" )@ % @ C+ !# @ 2:@ 5@ %5@ "@ /7@ 7 @ /@ / @ ,@ ,@ :@ ! @ :@ -)@ 2 D''*E " '' ## : " A" ,? 7 1 %!
!# .4W
*?/ 1
4
A"" ) DE@ ! 2 - * 3 * D '&'..E A ," C # ) ! )@ K" ) > ) 0 A @ ! !
@ 2 D'$4E - *GB3 B3 7 D>!7! ;" '*$+@ * E >! 7 # !" )@ % @ C+ !"@ +@ @ 0@ 9@ Q D'''E # # # ,? +0 5) @ 5- 3@ BT 0 DE@ , & 2 D 44'E ++ ;@ % ! @ ; %# @ /C D'**E ! ( , 1 D>!7! A
A 5@ * E >! 7 # !" )@ % @ C+ ! @ ;@ %# @ /C@ -"@ 03 D'*E ! ( , 1 3 -F ! ! ( * D>!7! 0 !") A '.7@ * E >! 7 # !" )@ % @ C+ !@ 7+ 9 @ 05 D'.'E C ## "#
. @ (@ &$&* !@ 7+ 3 @ % D''E 3 ? C # )
# ) # # # "" ,? %C 9 7+ ! DE@ I D!/A: !# A" # $@ $'&4E ! #)
! ) 7 )@ "@ 8 ! @ T2 D''&E 8 # # @ '(@ $4$4' @ 85@ /@ / D' 4E T %
1, -@ /"@ * * @ !A D'.'E ! @ ) ) # # ? A 9 @ !0 , # # @ '@ $$4 %I@ 3 D'.E ! ) ,? * 6 0 , 3 //R/> 3 /OQ53 #C3 1 D . 'E 0 % " # /# # A A @ 1I@ C @ C+ D' *E " ) 1, - @ @ *&4 C @ C+ 1 # @ 71 D'*4E %#
1, - @ "@ 4&$ C @ 5 D'&.E ! )
# ,? %3 !#" @ %5 2 DE@ 2 1 D % # ; !# % &*@ E 1 +#) !##@ 0 @ 0
@ -- D'*&E ! ( - 1 * 1 - 0) I 3 1 D>!7! ;" ,@ & E >! 7 # !" )@ % @ C+ 0@ B D'.E , ! ( D! A 1 E ," -)
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
! @ ;I Q"@ 5 D'''E /
#" ) ) # # 3 A" 1@ '@ ' Q"@ 5 D44E " #
) # # - * @ (@ & '&$. Q"@ 5 D44 E ,# " @ # @ " # # @ T % @ 1@ -@ .'4& Q"@ 5 D44E -) # # T % "# ) # ? D . @ (@ ' 4 T@ 0 B @ 0 D'.E + ") # ) # #
" " ,? * 6 0 , 3 //R/> 3 /OQ53 #C3 1 D &$$E 0 % " # /# # A A @ 1I@ B@ - %@ B D'.E #" # ) # #
# 9 :@ "@ B " 0@ B@ K@ 9@ B@ A@ 7@ 9@ B D'.E # # "
# ) # # T % ,? * 6 0 , 3 //R/> 3 /OQ53 #C3 1 D *. *'E 0 % " # /# # A A @ 1I@
. & Jacques Locat and Homa J. Lee -?
;61F@6F;
!" 1. D F2.
, # "# )@ @ @ # ##" " # ) " #
# 9" '* # " # A C # D3 # @ 44 E # !# '* # ( ) @ ) # " ) "@ @ : " " # ) ) " #E !" " D( E
#"
"
A
!)
>
>
%
" %8 "
! D E ! DE 7 ## ) !
) 0 # DXE A# DXE 3 DAE % " DAE !) 0 J# DAE A # " DAE 8 # !) 9 # D E DAE A " DAE /# " DAE 7 " D) E DAE A " / # D E " " ) "
) 5 D'. E A C #
%" " #@ DE
9
3 # D44 E
! @ DFE DE
% DE D E
D -?'? A # ) " D E
@ " " " # # A C # 9
3 # D44 E
) # " " " " # D9" '*D EE , " )@ )@ " " 4 " @444 ; # ( # @ " # ) ) J# # ) @ # " " " " # %" 9" '&DE )
" 9
" 9" '&DE@ @
. &
V '
%" " #@ DE
%" " #@ DE
, #@ DE DE
, @ DE D E
D -?(? /J# # D E D E " " # D E A C # 9
3 # D44 E
" @ # ) (# J# # " " " " # 8 @ " ) @ " "# " " # 9)@ " "@ 9" '&DE@ J# # " "
" # D9" '&D EE %" # " " # # " # @444 @$44 9
) 9" '&@ ?
# " " #@ @ %@ @ :@ "#@ : D44E !" >
!") 9I @ DK"P #@ E@ ) ** ! 7 # !" )@ % @ C+ 1 @ 0%@ :#7@ :@ ! @ % D44 E + A C " #@ " . @ /@ &$' 8=; @ 5! 5"@ AT D'..E 3 ) ) "
1 -@ @ .&&..& 8 @ 3 ; @ 1+ D''E J# " # ## ) ,,? #@ " @ " ) ; ) !@ +5@ ; @ A@ 3% @ A@ ; )@ 0% D44 E , # . @ /@ $$** !")@ 51 A @ ; D'&.E / " 1/!8@ A 0 @ 5% :@ 5C D'&4E !" " : 9@ 1 7" :# . @ *@ 44. 0 @ A@ 3 :- D''E ! * ! D & E ! C @ 1 T T "@ +7@ ; )@ 0%@ ! )@ 1@ ; @ 5%@ 7 @ ! D44E + " ! /# + : * F 1 D%8:E
/ 0 James W. Vallance
/?
;61F@6F;
C ## @ # ) @ ) @ " # ) J 0 # )
" 4 4 & @ ##
4 4 ' J # # ) "#
# S # )
)
# ## (#S "# # @ #
@ )
)S "
" S " ) " 8 # #" # # J# " @ )#
C ## " # #
# D)
## E #
# # @ @ C ## "
" #
" !+@ &44 ;A % @ >!+@ $*44 ;A
A)
##
+#
-) "
2"@ , @ .&$
"
!" I@ 5@ '$$ , "@ %#@ '* ! "@ , @ '4' ! "@ , @ '. :) @ , @ .&$ >@ 5@ ''4''$ A" @ A@ ''
%""@ 1 B@ '$ A @ A@ ''$
2"@ , @ ''4
+"@ , @ '* A" @ A@ ''
% " "
% @ >!+@ $44 ;A % @ >!+@ 44 ;A % @ >!+@ $44 ;A ! -@ >!+@ '.4
C #@ @ ' ' C #@ @ '*F'* C #@ @ '&
3 # "
% @ >!+@ 44 ;A ! -@ >!+@ '.4 ! -@ >!+@ '. % " @ >!+@ '.'
*
H $
& @$44
$ 4
* , 9 : )
44 44
)
@444
* $
$
4 *
4 . 4 & N4 . $ 4 . 4 .
4 . 4 '
4 . 4 & 4 &
3 $ $$
)
##
9" # @
) 4 !# ) "
" % .$4 F " ) #)H
% " " )
T") # ### " $ 5"
/ " # !+@ A @ $44 ;A
3 " D # E
@$44
+"@ 7"@ $ : # @ 1# "@ $&4 :) @ A@ '.
@ 1# "@ ''.
-) "# "
C/, # ) S
% @ >!+@ ' & % @ >!+@ '*4=
44 44 44
0 ,@ 1 B@ ' 8@ 5@ '.
7# " "
C/,
F F
F
F F F
A F F
9
/ )+0F1
+ # ) ) " D )E@ " D# )E@
" " D 4E 7 )+0F1
3
@ # # # # ) S @ #"
) # @ # "#
"# # # ! D 4 * E@ ) ## @ # ) # # #" @ "
# # @ #
) ) #
# > #" # " ) # # 3 # # " # D4 E "# @
#@ ) " ## # ) ) ") " " A
" # # # ;"
) # #
# D9" 4E ,
# # "@
") # 0 # " @ # # # @ ""@ # ""@ # ;#"
@ ) # # #
# ) #)
( )#) )@
@ " " " # # 9 # ") # /? ?
$ 3 ! $ !
A # # J#) ) ) @ "
# ) # @
# #@ " )@ )
( # " DC#@ 444E : " " #
" ) #" #
# D @ 44 E 7 #
# ) " # @
# # " # # DC#@ '' E A # ##" #@ " "# ) #@ D! 3"@ '..E
# ##" # ) " # "# ) ) # ) " # " D! 3"@ '..E " # # # @ ") " # #" # " # D9" 4E !"# #
# # ) #" # # @ " # #" ## # D9" 4E 3 ) # # ) # # " # D @ 44 E A # @ "#@ " )) , @ # ) " # " " "L#
/?
!# 4 W A SIDE VIEW (cross section moving with flow)
! $'
Path of largest particles
Largest particles collect at front and are pushed to sides
Velocity profile B TOP VIEW (Moving with front of flow) Paths of largest particles at surface
Largest particles lag behind as levees form
D /?? !## # # " # " # #
DE D E 1 #
")@ " ) " ##
# , ) # " @ #
)
##
# #" ) # #
# , ) #@ #" ) + # @ # ) ) " ) " 9" @ " " # " 9 ")@ # # ) # )
" ) #" , $ ) @ " "##") #"
## D! ! @ '' E C ##
) #" " # ") # # #" ) " # ) # "
"# " # ##" ") # "# ##"
C ## #) " " # ##" # ) ) ## !"# # ) # ##" " )
!# 4&W
/?( 1
&
I ## " # + " " @ :"@ 1# " ;"@ ; D''*E : " A" # 3" ,? 7 1 %! A" ) DE@ ! 2 - * 3 * D $* E > ) 0 A @ ! ; " @ 53@ A @ ,@ " @ 5@ ; " @ 7@ C#@ A: D''&E 8 @ ) "
# ''4 " 2" # @ , I . @ (-@ .4
# 1"PG@ 7@ C#@ 50@ % @ 0, D'' E + " " #"#
P # @ :# ? ,# I . @ "-@ $ * @ % D'&E * I 3 D>!7! A
A *&&@ &$ E >! 7 # !" )@ % @ C+ @ % :""@ % D'&$E #!7! 8( % '. .@ @ E >! 7 # !" )@ % @ C+ - @ 2+ :@ C% D'''E ! ) @ : " ! @ %"" # @ 1 B . @ D$E@ & &$ , @ %: D''&E )# ,( . @ "@ $'* , @ %:@ !#@ !@ C#@ 50 D''.E 8 I# " . @ /@ '&'. 5@ %5@ !# @ 2:@ 1 @ 2:@ : @ -+ D'.E , 3 -F D>!7! A
A $4@ * &.E >! 7 # !" )@ % @ C+ 3@ 9@ " @ 5@ C @ ;@ !"@ -@ !" ) @ + D444E 3 : # @ 5? + I . @ //@ $* 3@ 9 " @ 5 D44E ! ) : C # @ 5@ , . @ -DFE@ $*' :I @ 55 1@ 7 D'.'E ! # " " # ## "
? + I & @ "@ & : )@ %@ A(@ :!@ -)@ !2 D'''E ) : " A" . @ (@ && : @ A+ D''E 3 # @ /#" ? - " . ) 3 # & D $*E M -@ 3 : @ A+@ -@ :3@ 5@ %5 D''.E " C) 3 ? +
# @ /#" I @ "-@ 1@ C/ D'&*E 3 I # 0 - . @ @ 4 1@ 7 !@ ! D'.E ## ) DC/,E? + " # # . @ *(@ . A @ D'''E
" "
# : # '@ '. ,? A DE@ 1 8 & " ( 0 + I 3 /OQ6RQS D '*E >! 7 # !" )@ % @ C+ A @ !# @ 2: D'.$E " ?
) # # @ @ $$ A @ @ 5@ %5@ " @ 5@ ;
@ + D''4E A "
# ) 1 '.$ " 1 %"@ @
!# 4&W
/?( 1
&
# !7! 8( % 4 @ ' @ E >! 7 # !" )@ % @ C+ !#@ 27 D' E !#"
6 : " 5 # +" "# '4 0 # &0 D@ D&E@ '4 !# @ 2: D'..E 3 , 3 & ! ( &1 ( ) , D>!7! A
A &+@ &$ E >! 7 # !" )@ % @ C+ !# @ 2: C#@ 5: D''$E ! (3 , 3 ! ) ( 3 D>!7! -)
# , + -+&'@ ' @ E >! 7 # !" )@ % @ C+ !# @ 2:@ C#@ 50@ A @ A D''$E 3 , 3 ) ! ( 3 D>!7! A
A $ &@ 4* @ E >! 7 # !" )@ % @ C+ !# @ 2:@ 5@ %5@ "@ /7@ 7 @ /@ / @ ,@ ,@ :@ ! :@ -)@ 2 D''*E " '' ## : " A" ,? 7 1 %! A" ) DE@ ! 2 - * 3 * D '&'..E > ) 0 A @ ! !# @ 0/@ - @ %A@
@ %@ !@ 3@ : @ :@ 1 @ 5 D''* E A)
## 5" $@ ''@ ### " : " A" ,? 7 1 %! A" ) DE@ ! 2 - * 3 * D $* E > ) 0 A @ ! !# @ 2:@ :#ZP @ 53@ 1 I @ 5+@ % ZP "@ !@ :#7@ 5A D44E 1& ! ( I 2 3 ) 3 D>!7! A
A *4@ $' E >! 7 # !" )@ % @ C+ !# @ 2:@ C#@ 50@ 2 @ 1@ :#ZP @ 53@ ! "#@ 0@ @ 7 D, E
# # # @ 1# "? 8##"
#@ "@ - * !# @ 5; D''E " D E 7" " 2 5 . )@ ''@
&
0
V 4
!@ ! @ 3 D'' E I D ' E 7 ## A @ "# @ +B !@ 7+ D'.*E ### ? )
# . @ -(@ 4 !@ 7+ 9 @ 05 D'.'E C ## "#
. @ (@ &$&* " @ 5 D''4E /J# 1 @ '.$ " # # # 1 %"@ I . @ @ &&4 " @ 5@ @ 5:@ !@ %@ :" #@ + D''4E K" ) " )
1 %"@ I . @ @ $$ C#@ 50 D'' E / ( " " # # # D'& E A @ :# # # > )@ - " @ :# C#@ 50 D444E 3 ,? - !" @ ;9 - " @ !% :#1"@ - %) @ 5 ! DE@ - I D *4**E +## A @ 3 C#@ 50 !# @ 2: D''&E 8# :"
: " % ? ! ) # " #) # . @ /-DE@ * C#@ 50@ "# @ :3@ !#@ !A D44E &' ( ) 1 -, 3 D>!7! 8( % 4*.@ @ E >! 7 # !" )@ % @ C+ C#@ 50@ !#@ !A@ @ 7@ %@ :/@ - @ ::@ ; @ 3 D44 E ) 1 1 B , 3 # D>!7! 8( % 4 *&@ @ E >! 7 # !" )@ % @ C+ ;@ %0 D' 'E . 0 DC +@ & E 7 A 8L#@ -" > @ 5C D''&E 9 ) A" # ? # " ) . * @ "DE@ ' 0@ % D'.'E !
D E #" ) )
## " : " ! - # @ 0 @ . :) '.4 I @ "@ .$& 0 @ D.&.E - 1 7 A - 6> /Q@@ 9 1 7 ! - 6> 3 /Q@@: , # @ 7")!+ 1
" " ) @ ) # # " "
) # #
" L#" ) ) 9"
" " 1 # # + " @ " #
( )
" #
)
&.
!!
!
V
D ?? # 3 @ , @ #
# " 1 8K "
)
" I" #
>! 7 # !" )
D ? ? # ) ; " 1 "
" #
9 A
"#
, "@ # " " #
# D # E # @ 4$ "
) # #) # " ) #( )
!# W
? 1
&'
, ( " " #" # ,% ,% ( @ @ 1,% ,% ,% #) "" J # " # "" ) 0 ,%@ ) #
# + @ ) " #" "
# ) # ) #
" ! ) ,%@
" #) # )
" #
" #
# # 9" $ D # # E ,% # ) " # # # # ! > )@ 3 @ > 2@ -@ 2"
@ :@ 8 )@ !@ 2 I@ - D''E 8 # ) # @ DE@ $ 2" @ - T"#@ T D444E # "
) * - @ ''DE@ & 2 @ 8@ ;@ :A@ @ +@ "@ 50@ :) @ 0@ A @ %-@ !@ A@ 0 @ - D''*E !# # ,? * 3
* + # ! #) A ) % !@ ;@ : 3@ @ 1# @ 7@ #@ @ 9 ")7"#@ 5@ ! @ +5 D44E )
)
" !+% ,
0--- . @ D E@ & $&$ 3 @ 90 D''.E % ) ,? 9: - +5 3 DE@ * 0 + # ! #) A ) % ! 5 0) M ! @ 1 T 3@ :@ 2 %0@ @ 50 D44 E 0 0& D$ @ &* E 5 0) M ! @ 1 T A @ 7@ 1"#@ ;@ > #@ + D444E 3 # ? ## # #@ # ) 3 0 3 3 =R@ + A#@ % D44E / # " # ) 5@ - . . -3 3 0 + A#@ % D44E
#
I# RRK") / " ! ! ,"
: 9 @ + %; +
#== # "# > ! > )@ " ) >! + #"" # # ''44.$@ ''' 44 A @ 5@ :"@ ;@ ; @ +@ " # @ 3 D''&E !# # " ) # ! 7 # !" )@ % @ C+ 3@ 9@ " @ 5@ C @ ;@ T "@ 2@ 3-"@ %@ : @ 5@ !" ) @ +@ I@ :@ !)"@ ! D444E , " : # @ 5@ , I . @ //@ $& &. %@ :/@ ; @ 3@ 3-"@ %7@ % @ 55@ 9"@ 5@ /@ ! D44E
@ ,? %# 3 DE@ &' ( ) 2 3 * + %# @ !5 D'*$E ! "# " ,? + ;# DE@ DA @ $*E + # ! #) +
)@ : @ 0, !@ 5 2@ 3 D'.E : "
# > # ) @ -D*E@ # @ $&$. !"@ - 8"@ ! D'.$E :" 5 * 0I 0& 1 ! 3 D ' 44E @ 7@ T"@ :@ B #"@ 0@ B@ ! D'..E # # # "#) " # )? ! # @ D&E@ 5")@ ' $'$ B@ ! D''E + #
# # ) @ (@
1 ! Dieter Rickenmann
?
;61F@6F;
%" " # " J# ) @ #
"# DA ## 2 @ 44E + #" " " @ @ -" D'. E@ D'.'E@ ;" D''&E@ 9 0 D44E@ :# " -" D44E " " ) # @ #) # # # ( " " D@ -" @ '. S
@ ''*E 9 @ 5 " " #
4 @ ##" "# ) # " D,)@ '&'E 8 "# " " # #" " D; ")@ ''4S 9 0@ 44S 3# @ 44E@ # #
D3# @ 44E@ #
# " " D
@ ''*E 9 #(# )@ )# # (
@ @ D@ C@ ''*S 9 0@ 44E ) # # @ ) J # ) C ) # @ )#) @ ) & D%# B @ ''E@ ) @
) DA @ ''$E A # " " # ) ## )# " ##
# ) "@ ) " ) # # )# )#) # "
: 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
4*
1 !
V
6 ?? 8 " " # #" 7
#
2) # #
, 9 : # " C " # C " # 0 " 0 : C )
# ,
# 3 # # I"# 9 ' (: # ! #
C " # #
# +)#
# : # 9 : "" " C " # " "# # " # " # "
# # 9 " 4 @
##"
# ) #
" "# + ) " )
! +
"# !+ ,? %# 3 DE@ &' ( ) 2 3 * 3 2 * 5 0 ! 1 3 , 3 () D ' : @ % -" @ 8 D''E %" " # #? +)# ,? * . # ) 3 I ,3 1 D ' E C# " 7 ## ! #)F 7 ## ! #) ;# A" @ %# @ -" @ 8 D''$E + " " ) @ @ # 1 . @ @ *4* -" @ 8@ : @ 7 2 @ % D'. E K" )
" 1 . @ @ ***&& -" @ 8@ : @ 7@ C@ 9@ 3 @ % D'.&E # ; " ,? 5/ 79 0# DE@ ! (2 * 3 D7!+ % / 7 )@ C &@ 4E 7 # ! #) + #@ ; " @ 8 ,)@ - D'&'E 0 2 *, D( / @ *. E 5 ! + # @ ) ,)@ - D'.E + - *4 D,+-! A" 1 E , + # -)
# !##@ #" #@ 1 B ,)@ - D'.'E # " " 5 0 & - . @ /@ $ , @ 5@ A @ 7@ 3 #@ 5@ 3@ - D44E 1" # ") " / @ * 5@ : 9 @ 3 D'''E "F ") -@ "D.E@ .&. 5 @ %A D'' E " : "@ ; " ? )# " )#
A @ > ) ; " @ C# " 2 6 @ -5 D'.4E : " ; #" ; " " 3 #" 0& ;;0,6 B 6 " 3 () )@ (DE@ $'*@ D$E@ &@ D&E@ * '@ D'E@ .4.$ V 7 W C @ ; ! "@ 5 D'' E 3
8? + # ) # )# - . @ *@ *'& 0@ :A D''&E A
# # " # " # :!# @ > ) ; " @ C# " B @ :@ :@ A@ 7@ A@ 7 @ A@ - @ 8@ -" @ 7 D''&E N D 2 .0& ) D!#" # 19A @ * E /-@ B" # V 7 W
Gerald F. Wieczorek and Thomas Glade ?
;61F@6F;
+ ) ## # "# ##"
# @ # #" " D E # # " I# " )
# # # # "# #) , @ ## # ) # # ) % (
@ #" " ) #
" @ ) # ) # @ #(#) @ " D, @ 444E # #" ) # ) ## # "# ##"
# A ) ## "# #) @ "# !# ) ## "# @ "# # # @ "# " !+ D9" $E " "##")
V
) " ##"
# #) +@ D @ ''&E " " ; " #
@ ) ) @ )
)
@
" D" # :@ '.&E ? ??
.)F;1G #6 D6F1.
D'&$E ( # *& # )
"# ) ! : # : " " " # #
" ( " ##) !+@ ) @ #" ! 9 ## ;) D /@ '.$E@ - ""@ - D0 @ ''E@ A" %# D5 @ '.'S 3 ! @ ''E@ !@ 0 D @ 444@ 44E@ +# ;" % : " >!+ D1 ) !@ '.&S 0# @ 444E D9" *E % ) # " D E ! " # ) )@
D2 @ '.&S 0 @ 44$E@ ,) D, @ ''.E@ ; D8 @ 44E@ - 2 D; '.$S - @ ''$E ## # % " # @ #" ) @ # #) !"# # ## D : # @ 44E # D /@ '.$S 7@ ''.S 5 0 )@
V
Rainfall intensity (mm/h)
Rainfall (in/h)
*
Duration (h)
D ?'? - D-@ -E@ A" %# DA%E@ ;" % : " # C D;%E@ ! 9 ## ;) D!9;%E 0# D444E
44E + ) 0 D444E@ "##"
# # )@ )@ # # # ) # ) "
##"
# 9 @ 7 D''.E # ) " ##"
# D9" &E 8 # #" D
: )@ '''E@ D9 @ '''E@ D56
"@ '' E@ ) D! 3 @ ''$S " @ '''E % ) "# " 9 ,)@
9 D444E #
) " J " ) D9" .E " # " ) ) D9" 'E % " ) # @ "# )@ )@ )
)@ : ) @ J ) # D ## @ 444E
!# W
?
@ &
, J# ## A#(# >!+@ 0 D444E # D%>E 7 @ # # ) ## @ 4$ " ) 4$ " " @ #" + ##@ " '*''4 # # # ?
D9AE # ) " # 44X ##" S D:9AE 9A ## " '4X S D/9AE ## " $4X D9" E " " #
) # @
9A :9A /9A # ) 9A@ :9A@ /9A " ) 9A ) # ? ?
D
9 ## # @ #@ ) # " ) )@ I #
V
LB model
Fitted interval
I(t) (mm/hr)
Piezometric response (cm of H2 O)
PZ
Time (hours, from 12:00 a.m., 12 February, 1986
D ?? A # DABE D E RR == D3;E D ) E ) ?44 @ 9 " )@ '.* 3 - @ 0 0# D''$E
"
# #" # # ) +
# " "# RR ( ( =KV ' ( ( T$ == 1 #(# # # ( , # @ # #(#
" # " )@ @
# , >!+@ # ! 7 # !" ) 1 0 ! # D10!E
'.* ''$ ! 9 ## ;) " " # # # )
"# D0 @ 44$E ) (# #) ) / D'.$E@ # ) 10!@ ) # ( " # " " !7! 89 % '.4 E >! 7 # !" )@ % @ C+ + 2"" ++ ," "/OOQ" &OQ&K/6S" @ +9 D444E * * & 3 D>!7! 89 % 444 *'E >! 7 # !" )@ % @ C+ + 2"" ++ ," "6KKK" &KK&KS>O" @ +9 D44E * -, * 3 3 D>!7! 89 % 4 *E >! 7 # !" )@ % @ C+ + 2"" ++ ," "6KK5" & K5&S>5" @ +9@ /@ 03@ 2 @ D''&E 0, 0& N . " &' ( 3 3 1 D>!7! 89 % '&&&@ & E >! 7 # !" )@ % @ C+ " )@ % 9I@ A D44E ># "# % - . @ "@ **' " #@ :@ :@ :5 D'.&E :
# # " ; " ? ! # " ,? 5/ 79 0# DE@ ! (", 2 * 3 D% / 7 )@ C &@ *.4E 7 # ! #) + #@ ; " @ 8
@ 5 : )@ 5 D'''E %# "# # #)
3 % @ / A) @ ! . @ /DFE@ &''
@ +7 D'.E !18/3 #R/Q D * .&E ( 7 @ A "@ ,)
@ 7; 9 @ A D44E " ) # ) - @ DFE@ .'
@ :5 D'.'E 2 13 1 8 -, % "@ 3
@ :5 D''&E # # "? + " # ,? 5+ :@ ; "@ ; 9 @ ; 76 @ :: 0_ DE@ , 1 -, 2 * DC '@ $ E 7" 9# C @ !"
@ :5 D'''E A # ? + #
" - * @ D'E@ .$.
@ :5 /)@ %5 D'.4E +
) ,? ## 7
" DE@ * 5 R#( ? 1 . & 3 DC *@ &$E 1 B ," / @ 0
@ :5 7@ D'''E 9 R/Q D *&&E ++ ;@ % @ : ;"@ 5 D'''E : "" #) # #" . @ /DFE@ &$.& "@ % 56 @ ! D''$E 3 1 :# 7 ) ,? 9: :#7 + DE@ . 1 -, D $*.E 5 0) M ! @ # @ >2 /@ ! 0# @ 79 DE D'..E 3 ! 3 -F 5R=3 /OQ63 ! 3 1 D>!7! A
A @ 4 E >! 7 # !" )@ % @ C+ /@ !7 "@ 55 D'' E %# ## # #
# #
# "
. @ /@ 4&. /)@ %5 D'&'E ! 0 )@ 1 B #( ? @ DE@ & /)@ %5 /)@ 78 D'.E %# * // #( ? . 1 3 D .E 1 B 7 # ! #)@ 0 /)@ %5@
@ :5@ 0 @ %- D'&.E 3 0 ) #( ? . @ DE@ $.& 9@ 5@ 3"@ -@ 0"@ :5@ T"@ !2 D44E # #
##"
# # '''
$*
V
7 " @ 5 D44E ##"
# ; ? D . 3 @ "@ - @ %/ D'.E A # #
" " # ) 0 @ 2 D44E ! "
,? 22! - 2! 3 DE@ . - R !7! A
A $$@ @ &&E >! 7 # !" )@ % @ C+ 2 @ 2@ 0 @ %@ : @ %2@ ; @ //@ ;
@ 0: ,,,@ /@ !@ - @ /3@ 0# @ 79@ + @ !@ B@ %! D'.&E % " ) @ *@ ''$ 2 @ 2@ : )@ :/@ 9 #@ ! D44E + .444) #
, " A " / 1G 3 /OOO D ' $'E / ; @ @ ,) A "##@ 8 A @ : D44E -)
# " ? + # # " # ,? 5 %) P @ 5 ! A 0 DE@ 2 * / - 1 3 *3 6SR6>3 6KK6 D *'& E ++ ;@ % A @ D'''E % : A" @ A@ 5" '' " ,? 2 ! DE@ D . .'E 5 3 ! #)@ 2) > ) A A @ @ 5@ %5@ " @ 5@ ;
@ + D''4E A "
# ) 1 '.$ " 1 %"@ @ # 0 3 /KR/S ! 3 13 #( ? DC @ ...E ++ ;@ % A #@ 5@ ; @ /0@ @ AT: D'' E %"# - 2 -@ 5"@ $ A @ 15 D'''E /"# # " # # ? ,# " !7! A
A *4@ $' E >! 7 # !" )@ % @ C+ ! @ 5/ 3 @ %+ D''$E ! " ! " ? %
@ # @ " #" -, - . @ D E@ ' 4 ! @ 3 D'&'E
# " . * @ @ 4 ! @ 3 D''*E 7 #
A . 1 & @ BBB@ . ! @ 3 D''&E : " - #? + /"
# ,? 5+ :@ ; "@ ; 9 @ ; 76 @ :: 0_ DE@ , 1 -, 2 * DC @ .$ 44E 7" 9# C @ !" ! @ 3 ! @ ! D44E J !7! A
A @ *E >! 7 # !" )@ % @ C+ 0# @ 79@ 3@ /0@ /@ ! D'.'E ) # #
0# 9
@ >@ '. '. - . & @ 'DE@ '4. 0# @ 79@ : @ ;+@ @ %- D444E ;" % # C -, - . @ 0DE@ 0# @ 79@ @ 5+@ 7 @ 50 D44E "
,? %#@ 3 DE@ &' ( ) 2 3 * 3 2 * 5 0& 1 3 , 3 () 3 /KR/6 D $&*.E : @ % 0 @ % D'.'E % @ " @ ? + # ,? A: ! : : DE@ & -, DA" # 1 @ 4&E , 7 # ! #)@ % @ + 0 @ % D444E # #) ,? A 9 !## DE@ * / * 1 3 3 0 3 /SR/>3 /OOO D $ E /"
7 )# > / ; 0 @ % D44$E ) ! 9 ## ;) @ ,? 7@ : + @ :
DE@ ) D '$ E 5 0) M ! @ 1 T 0 @ % 0# @ 79 D''$E % 3 - @ -, - . @ DE@ & 0 @ %@ @ 5@ /@ ! D''E , & ! ( 3 D>!7! 8( % '$@ $ E >! 7 # !" )@ % @ C+
*
V
0 @ %@ : @ %2@ ; @ 7/ D''E 8 ) ! 9 ## ;) @ ,? -0 !@ ! !"@ 9 0 DE@ - D 4E ++ ;@ % B @ : - @ 0 D''E # # #) " ? + # ") ! + 13 +@ @ $'&
" 2 $
3 !! Susan H. Cannon and Joseph E. Gartner "?
;61F@6F;
0 ( #
" J# )
# " # # ) "J@ ) @ # " # @ # # # ( # # #
) @ # ( @ "
# " ( @ # " # ) ##" @ 1.$D F2 ;66F; 1F)..).
)
# ( ( " ? " J
) " # @ ( " #
!# $W
"??
"? D $ $ ! *$
1 $
The process #) " : " D3 @ 44E@ 0# 9
> D:# 7 "@ 44E@ 8 D # "@ 0 %"@ 8 ! > )@ 44E@ -"#"# : " " + D0 A @ ''E@ : : " "# + D # "@ + T @ + 7 # !" )@ 44 E@ " D @ '*'S 0@ '.@ '.&S : @ '.'S ;
@ ''.S @ 44E@ ; !" # D@ '&S 5 @ '. E D9" $@
!# $W
"? D $ $ ! *&
D "? ? 9
9 #
"#
D7 @ E
"#
44 " $ S $ 4*$ #
"# " D9" $'E D9" $'E , )@ "
" $ S " ) "# @ ) "L# ) )
# @ " # # ) " "# )@ " # D! @ '.E
# ##"
) # " ##"
"
&
2 $ 3 !!
V $
D "?-? % @ )@
"# ( -) # # @ #@ " J # # # ) " " $
# # )
"# " J ) 9" $' ; )
"# ) @ @ # " @ "L#
)
7 D E "L# "# # # # (
"# ) (#)
# ) D9" $'E@ " " ) ##
# ) # " )
"# " ) # ) "??
> A
;" ) !7! A
A .$E >! 7 # !" )@ % @ C+ @ !- D44E
#) " -, - . @ (@ @ !-@ ; @ /%@ :@ / D44E +
# ( @
7 9 @ 1 :# * @ "@ 44
.
2 $ 3 !!
V $
@ !-@ 2 @ %:@ A @ : D44 E 0(
#@ ! 2 : "@ . @ -@ &.. @ !-@ 7 @ 5/@ - ! @ +@ " @ ;: 7 @ 5+ D44E " ) 44 ! : ) % ( @ ,? ; ) @ A: !@ 0A % DE@ - . 1 2 1 3 3 1 D+/7 !# A" # @ %8:E + # / 7 @ !-@ 7 @ 5/@ A
@ @ A @ : D44 E 0(
" #
"
#@ >!+ ,? %# 3 DE@ * 5 0 1 &' ( ) 2 3 * 3 3 /KR/63 , 3 () D &.E : @ % @ !-@ 7 @ 5/@ %" @ :7@ :#@ 5+ D44 E - &' ( ) 1 * ! 6KK53 1 D>!7! 89 % 4 4E >! 7 # !" )@ % @ C+ @ 5@ %"@ 5@ + @ / D44 E 9
) @ D5" ) @ 44 @ ;E @ 7; D'&E 9 " @ ; !" 1 . @ '@ &$ @ 5+@ 7 @ 50@ A @ :@ : # @ + D44E /
) " )@ # # @ )@ , &4 ) #
@ # @ >!+ ,? %# 3 DE@ * 5 0 1 &' ( ) 2 3 * 3 3 /KR/63 , 3 () D 4.$ 4'*E : @ % @ :@ A @ 3@ : @ A@ 9 @ 9@ %#@ @ %@ 3 D44E !+ 9 ! # % # A ,1&@ E >!
+ #"" @ 0 @ -#@ 5 D'*$E . I 3 I I3 D>!7! A
A . E >! 7 # !" )@ % @ C+ -)@ 5+ D'.4E /J# # 0 ( " J
"# @ '@ *&* , "" "@ /7@ @ %@ A#@ %@ 3"#@ - D44E + # " ) @ -@ 4 5 @ +: D'. E # " ) 5% % ,? ; " ; A DE@ 0 D $&*E 5 0) M ! @ 1 T 2 #@ 78 -)@ 5 D'&*E ( 1 0 * 5 ! 0& 1 3 66R6=3 ,3 1 D ''.E 0 % " # "#@ @ 8 3 @ ,5 D44E 9
? ) 7 % ) " 1 : "@ > D'* E :!# @ > ! > )@ 3 @ > 3 @ : ! @ + D''E + )" "
#
@ A" %# . 4 @ ("@ 3)@ 5 D44E " # !+ * @ "@ '.'' :
)@ 5+ : @ + D44 E , )
# # ( 9
% - * @ '@ 4 '4&4 : @ : D'.'E " ! 7 # !" )@ % @ C+ A
@ @ @ !-@ A #@ 23 D44E 4& ! ! ( 6KK/ D>!7! 0 % " # , % 4 'E >! 7 # !" )@ % @ C+ %"@ !3 #@ 0/ D'.&E # "? /
: ") ,? 5/ 79 0# DE@ ! (" , 2 * 3 3 D% / 7 ) 1 C,,@ *$.4E 7 # ! #) + #@ ; " @ 8 ! @ A 5"@ 5@ -@ ; D44E ! * 0 3 -& 1 3 1 D+ # A
1 @ 'E 7 # ! #) + #@ ; " @ 8 !#@ 2:@ % @ 55@ ! #@ 5@ #@ 0/@ : )@ % !#" @ D44E )
# "# "# ) 8 % 1 . @ *@ ''$4 !# @ 2: D'&E /O>O ! ( . 3 1 D>!7! A
A &$4@ &E >! 7 # !" )@ % @ C+ !# @ 2: 0@ %A D'&.E - $ , 3 1 D>!7! A
A 44E >! 7 # !" )@ % @ C+ ! )@ %+@
@ !-@ 0@ %A D444E
# )
#)? "
"" # # @ J @ &.' !" @ ! D44E 3 ( ? +
; 1 9 :!# @ ; ! > )@ , ! @ / D''$E 9 ,? 5/ 2) !# DE@ 4 1 2 - D 4E , + # 0 9 @ 9 (@ 0+
!# $*W
"?' 1
.$
! @ 95 D'.E 9 #
# ,? -+ :
)@ - ; @ 13 @ 5/ 3 @ 0+ % DE@ ! - * D>!+ 9 ! # 7 ## % 08*@ 4 4E >!
+ #"" @ 0 @ ! @ 1 D'&$E * ( , & A D>!+ 9 ! # 7 ## % A10@ E >! + #"" @ 0 @ ##@ ; @ 7% D''&E ) # " ,? 3 DE@ &' ( ) 2 3 * 3 2 * / 0 1 3 ! 3 1 3 @RO D $E + # ! #) / @ 1 T ##@ @ ; @ 7%@ : @ -/ D444E # " # " ,? 79 0# 1 1 DE@ &' ( ) 2 3 * 3 D .''&E ++ ;@ % 0@ 07@ ,, D'.E ! J# "(
# # ! " - *4 3 13 #( ? DC @ 4$ E , + # -)
# !##@ #" #@ 1 B 0@ 07@ ,, D'.&E J# ( " ,? 5/ 79 0# DE@ ! (", 2 * 3 3 D% / 7 ) 1 C,,@ 4$E 0 @ // A @ AA D''E # -"#"# : " " + . @ @ &' 0 @ !: 2@ 57 D44E A (
# A#(# 1 % #) : " % ! - @ (*@ &$.& B @ %% D'.E ! D,+-! 1 @ $&E , + # -)
# !##@ #" #@ 1 B
'
Roy C. Sidle '? '??
;61F@6F; )
# " #
- @ @ "@ # ) ## D@ 5 @ 444S !@ 444S 7" @ 44E 0 # D0# @ '.'E@ 3 D% 1) @ '..E@ !# D,@ '.$E@ 9 # + D !I@ ''*E@ 5 D8" !"@ '.$E@ 3 A" DQ"@ '''E ;"`" !" # % D;"@ '&*E@ ,
# @
) (# # (
# " # @ " " )
#) #
) "
@ " " # ) # " " # ) D # @ '.S ! @ '.S !@ 444S 7 @ 44E 9 # # ) D) E@ # @ "
# 9# #
D@ )@ " @ # " E ) ## D@ ,@ ''S ! 0"@ '''S !@ 44E # ) # # #
# D@
) ## @ # @ # #
"E D@ ; ")@ ''4S : ) ;"L @ ''&S 7 !@ 44E ! #)
# ) # # # ##"" # " D " "# E F
D9" *E "@ ) # "#
# # ( ! " ) ) " ) D@ :@ '.S 0# @ '.'E
'? '? ?
)DD)6. FD #;C)#);6 16). ; DF1).6. . !
+ #" ")@ J# ##"
# # ) ) " "#
3
# #" 1
!# * W
'?
)L ! '$
+ # " ) ! D'.$E
" 4 4 FF) S #
) ""
4 FF) , 1 B@ # #
# #"
@
) 4 D$$4 FF) E # 1 + # D8=3 " A #@ '&*E , " # D)#) # $$ ) E # #
#@
"# ) "# D E ) + @ J# # (#) $$ ) S "@ #
"
" "
@ # ) ) " :) " # "
) " " ##"
) "# 4X " D; @ 44E "@ ") # " # #" # " , ) (
# @ " "# ) D$ ) E # ( ## # " ) D! 0"@ '''S !@ 44E 4 #
#
) "# ) # D@ E # # " 9 " J# #" ##"
# + # " ) # "# % " *4X@ ) " $' # #" # " #
D% @ # "@ 44E > ) # @ # ) " #
D # "@ % @ 44E + " # !+ - * @ "@ $& ** ;@ 3/ ")@ 0 D''4E A # " # 1 . @ (@ 4' & ;
@ !1 -
@ % D'.&E ##"" " # #" # 8 @ @ $ ; )@ %/ 0 @ 50 D''E # # "#
)
@ # #"@ #
! " 0 1 ! 8 @ *@ ''$4. ; @ +@ :" @ @ ) @ /@ 0@ 5@ I @ + D''E 3 " 7" A
#@ ? D . 3 #+!+ +@ *(@ & ; @ : !@ :/ D'* E 3 D>!+ 9 ! # % # % 18%@ . E >! + #"" @ 5""@ +2 ; @ :5 5 @ : D'''E
") # # #) - * @ @ 4'4$ ; @ :5 A @ D''.E % " # ; " ? ,# (
"# D>" " E !# (# "# ; " @ C# @ ; @ 9@ !) @ 8@ -@ :+ D44E 3 ) " ? + # ( " ) . & @ " @ &''* ; "I@ 3+ D''4E ! -F 1 , D+
E >1/!8 , -)
# A
@ -"
# A
@ A ;"
"@ /% @ ;% D'&&E &4 ! ! D>!+ 9 ! # % # A ,1'4@ & E >! + #"" @ , " 9 % / ! @ 8@ >
4
V *
;"
"@ /%@ @ 7%@ @ :+ D'&*E 1 & D4 E ;" " 3 :@ A @ 8% @ 1 D'.4E % )" #
. 4 @ '@ & @ !- %"@ !3 D444E ( @ " ) @ 1 :# - * @ "@ 4 @ @ 3@ @ @ T; D444E 9" "" " # '''
# ) @ "@ '4$'* 7 )@ - :@ 09 D'.E ! I , 0 D>!+ 9 ! # % # A ,1&@ E >!
+ #"" @ 8@ > 7 )@ % D'.&E C ) ,? :7 + 2! %# DE@ D .&4E 5 0) M ! @ # @ >2 7"@ %A 5 ; D''4E 3 " 7,!
#? + # ")
% ##@ -) - . @ *@ ' 7" @ %- D44E J# 2 ,@ D''E +
) " . A @ @ & V 5W ,@ 53 D'.$E :" )@ 9 @ 8 : )@ % ;"L @ 5: D''&E # ) " . @ /-@ $'** :
@ A- D'&$E /# # # # ) ; " @ C# " 8=3 "@ 3 A #@ +5 D'&*E , "# # ) ) @ 1 0@ 1 B 0 - . @ @ * 8@ T D''E , "# ##) )
# # # #@
#@ ? D . 3 #+!+ @ '@ *$&. A# @ @ 7 #ZP @ %@ %" @ C@ C@ % D44E # ? !
7 @ ! 1@ "@ $ 4 A@ 5 0 @ +5 D'' E #( ? 2 ,( D3# % # !## ! 1 &@ & E 3# @ 3# @ 1 B A
@ ,A 0@ 3 D''.E J# ( " J
/"#)" * @ @ $*$ %@ + 1) @ % D'.E + !#? : ) ) # ) . 4 @ '@ .'* %@ + 1) @ % D'..E : @
# ## "#" !# " # . 4 @ @ $$ %"@ !3 #@ 0/ D''E /
" 8 %? /# RQ ! /OQS D>!+ 9 ! # 7 ## % A10.4@ $4E >! + #"" @ A#(# 1 9 % / ! @ A @ 8% ! @ / D'. E + " # )
# # #) * -F ! A - D ''4&E /0 @ - ""@ -, ! @ /@ 5 " @ @ @ ! D'.'E A #) ! " D, )
## E # . A @ /@ *&. V 5W !@ % D'.4E 0 ! * - D>!+ / A" # 1 A10'$@ $ E >! + #"" @ A#(# 1 9 % / ! @ @ 8% !@ % D'. E !
" "#" " # + ? . . ) @ /@ &''$ !@ % D''E + # #" #
# -, % @ /@ $ !@ % D''E + # J# ) @ *@ .'&'4 !@ % D444E 0 # " )? + # " "
* ( 6/ 12 1 D>!+ 9 ! # A
# %:%!A@ $$*E >! + #"" @ % #) : " % # ! @ 9 @ 8
4.
V *
!@ % @ : D44 E 3 2)""@ 5 - 3 . A @ *"D$E@ $$ !@ % @ +! D44E A J#
#
,? % ! DE@ -, 1 . ) ! D, > 9 ) % # 8 % # ! 1 '@ *$E +; , A @ 8 @ >2 !@ % 0"@ 0 D'''E !" J# " ? D . 3 #+!+ +@ @ .$4 !@ %@ A #@ +5@ 8=3 "@ 3 D'.$E A D0
% " # : C @ 4 E + # 7 )# > @ 0 @ !@ %@ ) @ @ 3"@ QQ@ + @ 01@ 3 @ 5@ 3@ 0A@ 1@ %1@ @ 5% D44 E , # " "? /# # # # % 0 @ *J-@ .4 !"@ +@ !@ !@ : @ 2 D''*E J#
# @ # "# @
8 # 9 " ) ''* * *4 # ( ! ! /OO> 0 1 3 @RQ3 * 3 D 44*E + # ," -)
)@ ! A"@ :1 !)@ A+ B @ DE D''&E ! * D0 % ## #" 1 '@ 0 % A
E ; " : ) /
@ C# " !)@ 7 % )@ !+ D444E > ? ,## #" # 1
P@ % 5
!@ ; . @ /@ '$& ! @ 9 D'..E +
)= # 1 , @ @ $&$. ! @ 95 ! @ 1 D'&&E 1 7 , 1 3 D% / 7 ) C @ 3@ E 7 # ! #) + #@ ; " @ 8 ! @ 95@ 9 @ %3@ :# @ 9: D'.E : 8 ,? %3 / DE@ 1 ! - & A D **E -"# % @ !
" " @ A+ ! @ 95@ 2 @ 2@ @ 1@ 0
@ %7 D'..E 3 J# # )
# @ *@ ''. ! @ 1 ! @ 95 D'&*E @
@ ) A#(# 1 ,? % DE@ . - D ''E @ -"# M % @ !
" " @ A+ " @ C D''*E ) 1 0 D$ E , , : " @ 2"@ 1 @ %; :@ 09 D''.E A # #"
@ #@ 8 ? + # @ @ ' 4
@ + 2@ %: D'.$E J# 9
@ 4 ) @ @ '$' " "@ 1+ % @ % D'..E ! @ @ 1 B . @ @ *4
!# **W
'?' 1
4'
" "@ 1+@ 3 @ :7@ @ C5 D'.E #
# " ) "
"# 1 B * 6 0 1 - 1 , 3 A, (3 + @ 9 D'.$E
! " 1 . @ @ *. !I@ - D''*E " 1.$D F2 1F>> 6G ; #C;6@)
+ # ( #
)
##"
# " * "") "
)
##"
#
) D@ 4X
) $4 ) E A
)
##" "" @ 8@ " @ ( ##" "") " # + " @ # # ""
# J# ) # - ) #" #)@ " " #@ @ " # # # "" "#" (??
$ !
##"
#
) "# )
@ ##"
#
) @ " # #@ ; 5 D'''E #
@ # "
"# 7! 0 7
" 3@ % + D''&E K"
? ,? : " % 9 DE@ * 0 3 D E ++ ;@ % , @ %:@ 3-"@ %7@ :I @ 55@ B @ 3 D'' E
# ? )# D+ #E - @ ("D E@ & , @ %:@ !#@ !A@ C#@ 50 D''.E 8 I# " . @ /D.E@ '&'. 5# @ 3/ D'&&E !8 * ' ( 3 1 3 1 D>!7! A
A $4@ * &.E >! 7 # !" )@ % @ C+ 5# @ 3/@ 2 #"@ %+@ :# @ 7: D'.&E ,(# " % #) : " ,? 5/ 79 0# DE@ ! (", 2 * 3 3 D% / 7 ) 1 C,,E 7 # ! #) + #@ ; " @ 8 5 @ : D''*E : # ## #
) ; " 5 @ : D E + #(# - .
!# &.W
(?* 1
5 @ : ; @ :5 D''*E : # ## #
#)@ " : "@ ; " @ ? D . & 3 +@ / @ * 5 @ : 9 @ A D E + 44) ) ) % @ ; " 1 - + 5 @ : 5 @ A D44E
" 1 1, -@ *DE@ $ ' 5 @ : A @ + D''$E 9 !7! 0 % " # , % ' @ .$ E >! 7 # !" )@ % @ C+ :")@ D'.E +) )
#
,? , -7 * - $ 2 * -7 D1 &@ &&.E , + #
-) "# % # :")@ @ 2 @ !@ 8"@ 7 D''E A # # @ * 0 ;;0,!7! A
A .$+E >! 7 # !" )@ % @ C+ ! "
@ %/ D'.$E
# # % ) /
A " * @ '@ *$4 ! @ A - @ 1 D44E # # " . & @ *D*E@ 4'4' ! " @ 37@ ! @ /@ 1 @ - D'$.E 8 # %) " 1, -@ @ *.$&4* !)@ 5 D'4E D4* E C 0 =# ;"#" ! "@ - D''$E ) - 8) ( D'$ E % @ % " @ 7 ) @ D'&.E :## # # # , 1-@ +G*@ $*' @ D'.E / " ? ! # " " # @ @ $&.' @ D''E ! ( D,+-% : ! E , + #
-) "# % #@ /# A )#!7! 89 % '* *4@ '* E >! 7 # !" )@ % @ C+ 0@ %C D444E 8 " "# ) ## . . , -3 1-@ 'D&E@ $.$' 0 @ :! D'.E % ) )# "
: ! - D. E :!# @ > ) 0 @ ! 0 @ 5@ !@ :/@ ,@ 53@ !@ %@ ; "@ 0+ D44 E %#
@
" # & @ @ ***
* $ Johannes Huebl and Gernot Fiebiger
*?
.616)CG FD 1F6)6F;
,
@ @ " D+@ 44E #" # " ## " " # ( + # " # "# ## " ) " # " DB @ '.$E? # " " +# " #" @ " #" D-" ! @ 444S 2 @ 44E , " # # ) (
I#
# @ " ##
" )
# # #
# " D9" .E 8#
# I#
@
# # # # ) # # @ # "
# "
f
f f
f f f
3" D #@
E , @ "# @ !#(# # "#
" L#
" , 0 #" " , ## #
# 3 V 7 W !" @ ! D'&E? ;
B ? / " C "") 0 # "" & (, @ * 5 @ @ $ V 7 W !" @ ! D'&E C # 2 " ;
& , &@ /@ 4&* V 7 W !" @ ! D'&$E , B # ## !)
0 # " 3 "" ,? (& () 3
@ , "# V 7 W !)@ 5 D'E . I . ! C @ C V 7 W ! @ 7 D'$4E . , D +" E ! C @ C V 7 W ) / D.'E %" @ #
#
@ - & B ,7 * 3 A )# 6 "6 ; "" @ 0 V 7 W T @ 2 !
@ 2 D'.$E - #" ,? + DE@ 0 - 3 ! ( *, 3 3 D $ $$E "" @ 5 B @ 9 D'.$E /"
+ ,? + DE@ 0& - 3 ! ( *, 3 3 D .E "" @ 5
! 1 4 5 Francesco M. Guadagno and Paola Revellino -?
;61F@6F;
8 $* :)@ ''.@
" " ! @ K"#@ ! @ ; # % D " ,)E D9" 'E #" D* E@ " # # @ "# #
, " #(# # ")@ # " # ") ) # # - # # ) ") J# ) "#" @ )
"# C"" A 9 " 7 #)@ " # # ) ) J# ## #) ) J
#
" ## " # ) J # @ #
# # #
@ 7 ) V ,W #
@ ! @ +@ % @ %@ ;"@ A@ # @ 7@ 9 # @ ,@ 7@ 7@ , @ %@ 1 @ A@ A@ ; D''&E 9 # =
$*
! 1 4 5
V '
" # ''& A !
0T 1 #) . 3 3 /@R6K D E V ,W #
@ @ A @ :@ A@ ;@ A@ 3 D444E "# # )
## @ ,) * Q 0 3 1 F DC @ 4' E @ 3 # @ A@ 7" @ 9:@ C @ + D'.*E A
"
"
## . 0 @ V ,W @ :@ % @ %@ 3"#@ A@ 1 =/ @ / D'&$E !" # N
A !
DE . 0 @ /@ '.. V ,W
@ 7; 1
@ A D44E 8
# )
## ? ! ''. # ) - @ @ $*' A @ :@ 7" @ 9:@ -@ ; D''.E A )
$ :) ''.@ @ " ,) - . -, & @ "(@ ' C@ A D444E 9 N # "
## : 3 @ ! ! DE " # % . @ (DE@ $ V ,W / @ 3 7" @ 9: D''.E ! # ##
"# - . -, @ "(@ $4 , @ 9@ =+ @ ;@ A# @ !@ !# @ A D'&$E ! "#" # # # ! " + . 0 9 :@ &. 5 @ +: D'. E ,? ; " / A DE@ 0 D $&*E 5 0) M ! @ 3 9 @ 9@ 7" @ 9:@ + ) 1
$.
! 1 4 5
V '
C @ + D''E 3 A ,? ! / 3" @ 1 V ,W C )@ +@ D'$$E >6 B " 3 () )@ (@ .$ V 7 W 0@ +7 ! @ %!5 D'.*E A"# - . @ *@ 4'
/ --- 03
Reinaldo GarcõÂa-MartõÂnez and Jose Luis LoÂpez
/?
;61F@6F;
##"
# C" # # ''' #"
" #" C" 3 + # D0# @ 44E 8 * # @ ''' " " ##"
) " $4
# ! C @ #" " # " ! 8 # " "
) ) # + " $@444 @ @444 "
) *$@444 " "J /# # >!U D3 P @ 44E 9
##"
# #
# @ #" # # ( @ # " # "
" @ C ") #
# " @ " J@ @ # # # # C #" # @ ) @ # " 0
)
"# #
938 "
" J "
)
# ) ( +
"# " )
: 5 8 -" DE@ &' ( ) * + # A ! ; - 44$
$4
/?
--- 03
V 4
)>1.$D F2 )0);6. ; 6; #)1
9
% # 9" 44 +#")@ > ) "
##"
$4
--- 03
V 4
D /?-?
( > %
Kilometres
D /?/? : (# # # > D E A#" : # ''' DE A#" # ''' D #
#E
/?( .
!# 4&W
$
( 9" 4' 44
# : $@444#
/?( /?(?
.)#);6 +16)1.6. .
; ( # '''@ " ##"" "
9" 4* 4 " 4 ) ##""
" #" " !# A +" / I 1"P " # 7 8 7"
&4 &'4 ** & & $* * **& .& $ &. .
*4 '4 *4 $4 . & 4 4$ 4&$ 4* 4 $ 4 4
$ * 4& 44 & & . $ $*
$
--- 03
V 4
" " # 4 4 " # #)
7 DXE@ " " ( " +
# @ @ ( " " ) @ # # # RR == 9 # # )@ A
" ! 5" $4X " @ 4X # @ 4X @ 4X ( !
7 4X " @ $X # @ $X @ 4X ( 8 # D. &$ E " "
7 . # /?*
).6#6) )>1.$D F2 .+1C).
4 " "
# >
7 " J # "
) D' $E@ "# @ " " " ) # + # " $44 )
" J @ -/@ # # J C ! D7 @ 44E ;
) I" " #"
#)
7 @ @4 F
## #) @ , # " "# " 8 # #
"# ) ) ) # # ) ##""
) @ "@ @
# 9" 4 " 3 ! 5" " D #" E # 7 D:#" E " ''' 9 #" " # #
"# ) ) # $ " I# " , ##
** *
.$4 44
0 # $44)
D FE
/ #
D FE
#
$ D FE
# $4X # # D FE
*$ *
@4 @*&4
@4&. @&$
@&4 *
!# 4.W
/?* ) $ $
D /?? 1" ) D "E 3 D E :#" D E ! #
$
--- 03
V 4
# S " S ## " )S % # S C 4 " % @ "# # #" " " " > @ (# # # $ # " '''
@ "
"# # #" "
##"
# , ## # "# #@ ( #
# ) ) )
##" # /?-
.616)C). DF1 #6C6F;
: " ) 1C,!,!@ # ! @ 55 D'$&E , , ##@ 1 T 0# @ 79@ 3 @ :@ / @ 3!@ : @ ;+@ ; @ 53 D44E &' ( ! ) 1 /OOO 1 I) D>!7! 89 % 4 E >! 7 # !" )@ % @ C+ 0 @ :7 D'$ E + # - 3 . A @ "D*E@ # @ '$'$* B @ 8@ 9 P@ :@ A@ 7@ 2#@ ! D''E * ) -) D% 5 (E /#" A P## 1# @ K"
6! + 6
Chyan-Deng Jan and Cheng-Lung Chen
?
;61F@6F;
+ " ##"
''* )
- ) ) )
) # # / 1. D F2. ; 62; C !
*@444
" # ) &$ ! ' " 3 # ")@ # ##" " * # ) " " ) D #E # # @ # # "# ## " @
" ##@ " ## # # # ##" " D
#E
" @ ") @ #( ## +) " D
#E # @ # ##"
#
? 6! + $ $
!# W
Rainfall intensity (mm/hr)
Rainfall record at Alishan
Duration of rainfall (hr)
Hourly rainfall (mm)
D ?"? % )" )
- + ! 9 # @ #
" "
Time (hr)
D ?'? - " ) " " ) " " )
- " " ) + Q " " # 44
6! + 6
V
Hourly rainfall (mm)
$ *
July, 1996
August, 1996
D ?(? - " ) )
+ ! " )
7 -
+ @ " ) " 44$F @
# # # , " ) D #E # 44$F @ )
##"
D #E # 8 # )@ " 44$F @ ##"
@ " @ 44$F @ # " ) # " (##
# ) 9
@ ") & 4$.F @ # " $ " D44$F E
D " $ E@ ##"
# ") & , @ "
" $44 @444 4F @ # " 44$F + "
)
" $44@444 @ $ ") & + J#
##"
#@ # #" ") #" " #
J "#
44$F "
? 6! + $ &
!# W
6 ?? ! # # & @ # #" ) )
- ) " + D''.E "
# DE "
+ #( D E 1" 1" F
7
" DE
+ #( D E -) ) DX E 1" 1" F
7") D E
+ #( D E 1" 1" F
$4 $444
4444
4444
44 44
1+ . 1
1+ . 1
1+ * 1
1+ 1
1+ 1
44$44 1+
$44
1
1+ $ 1
$44
$44@444
@444@$44
@$44
' 44&*
.'. 44 ' 4
. * 4
$ $ 44 &
'$ 44 & 44$
*
*
&
&
&
&
.* 4 4
$ 4*4
. 4$.
$ $ 4'
*& * 44.'
&4 44
'$ & 44$
%
" ##
1,-)
8
1
+ #( # D E 1" 1" F
1+ & 1
1+ 1
1+ . 1
3 #( ##
%"
1
/ \
1
+ #( # D E 1" 1" F
& 4$
*& $ 44&$
'* 4
& * 44'
'$ & 44$
3 " ##
1"
9 4X #""
9 4X #""
+ #( # D E 1" 1" F
1+ 1
1+ ' 1
1+ $ 1
T
1
) #H 1"
DE
*44
*44.44
.44@444
@444@44
@44
+ #( D E 1" 1" F
4 4 ,1
$4 . 4$'
4$& . 44'
$ * 44
' $ 4.
'$ & 44$
1+ 1 1 ) ##" " " ) #(
# 8 ) 1 > ) D1>E ,1 ,
$ .
6! + 6
V
@ # ) ) )
) ##"
# , # @ ) ) J# # @ # @ ##"
#@ " "
, ## # @ @ ) "# #"J# ) !U ' # "#" @ #) # % ) >!U $
) -) "# # % *4 @ #) 1 " ")@ # & # @ $@444 " -) @*'4 # ) @ #) 1, -) D-) E %) 1"
" # ) S # "# + ) # "# 4$@444 DX E /
4@444 # /# )
) 8 >!U
#
" @
) >!U D44E #" ) )
- # )
/
& +""@ '$' + " )
/ @
" @* ) " @4&$ @ '$ I" @ @ * " # )
)@ .@44 " ) D3 5@ 444E
) #" ) )
/ '$' >!U 44 D'$'E D@ " >!U . D44EE #"
) #" ) )
/ "# #" ) )
- #" ) "#" # " "
@
@ '$' + )@ "# # " " @ ) '$'@ J# # ''*
!# W
?
6! + $$$
" )
- @ #"
) D E #" ) & ) " @ 1 " ") # %) #"
) "
$ # "@ # T"@ )@ A" " " : ") D9" @ # # E #"
) D E@ " # " # ) @ 4
, # " # ) @ 8+ #
+
" # ##"
# D9" '@ #
# E #" # "# ) @ # #" " " " 1 )@ #" @ #
#"
#
$4 ) " $ ) - @ " # )
)@
# D5 5 @ 44E ,
# @ @
" @ " ) " " #
"# # )# #" @ 1 > )@ 1 " - > )E
# D"# A ! #) ! 0 ! #)E # # " @ ) # " # #"
" > 8+@ 44 " " # "# #" ## # = #)
) #"
" ?'
F; @.F;.
# ")@ #
9" ' : 5
#
?*
1)D)1);).
@ 1 D'.4E )" #
. 4 @ 'DFE@ & @ 5 !) @ 8 D44E 9 )@ @ V W @ A0 D # E D''&E ,( & ) 0
D$ E ! 0 ;" "@ 9 ) ;" " + #"" 9 ) A
#@ V W @ A0 D # E D''.E ) 1
D' E "# + #"" @ @ 0 ! + # @ @ V W "@ T D''&E ,
" #" ) )
- * / # ! ( 1 3 T 3 ( D $ E 1 " - > )@ @ V W @ !5@ - "@ 1@ @ -@ @ 0;@ -@ :3@ !@ !@ -"@ 5@ - @ :5@ @ :@ ! @ A@ 3"@ @ 3@ 5 D44E 3
@
" J ) #)
#@ '@ * .*$ @ 1% !@ - D'.E 5 0) M ! @ 1 T 9@ 5@ 3"@ -@ 0"@ :9@ T"@ !2 D44E # #
##"
# # ''' )@ #"@ V W 3@ !@ @ T2@ 3 "@ 5 D'''E ! ) # #" ) )
- ) 1 1 , @ /DE@ V W 3@ :3@ "@ :-@ -"@ 9/@ 3"@ T-@ @ 0@ -"@ 7@ 3@ -- D444E .0 1 &' ( , 1 D1 !## # ) A
- : ''' +" % @ $ E 1 !## "#@ @ V W 3@ :3 5@ 9! D444E # # "# ) ) ) ? )
- - . @ "*@ '4& 3@ :3@ 5@ 9!@ 0"@ D''*E @ # @ #
) &. @ "(@ V W 3@ !0 D''.E % )
- ''* @ DE@ .44 V W 3"@ 29@ !@ 3@ - @ 0 D''.E 0 * C &' ( ) & 0 D% @ E 1 !## "#@ @ V W ! @ 0 D'E 9 @ 7 )@ 1 > )@ @ "# + #"" @ @ V W @ 25@ !"@ T:@ 0@ -T@ 3@ 5; D''*E 7,!F7A! # )
#" ) )
- @ # #
) &. @ "(@ $$* V W 0@ ! D''E 0 1 D% E 1 !## "#@ @ V W
!# .W
?* 1
$*
0@ 01@ T@ T@ @ @ 3@ : D444E # # " "# ) ' ) ) - T
8# 44 9 " ) 44 " #" " D@ $ S @ 4 S @ 4*$ E # " D@ $ S @ 4 S @ 4 E # "# # " # " I" 9 # "# #@ #
# "
( # ) # "# D9" ' 4E "
(
# "# @
( 8 " @ " # "#
? DE "
S D E # # #S D#E " #S DE " # 9" # " 9
5") 44@ ##"
5I %@ # " Q I %
D9" E # Q I % 5") . F . F@ # " # . 5") &&$ F " *$ 4 $ @ # 4 $ 9" " # ## # "# # ) #
?" . !
$.$
!# $W
DE
D E D ?*? !" # "# # DE ! # "# D E " # "# D # " # " 4$ @ # "# 4 " D E #E
Elevation /m
9
- D44E
29 Jun,00 5 May,01 30 Aug,01 19 Nov,02
1090
30 Aug,00 22 Jun,01 30 Jul,02
1085 1080 1075 1070 0
50
100
150
200 Distance /m
D ?-?
# ) # "# 5I % Q I % 9
- D44E
$.*
7 8 1 $
V
D ?/? "
( Q I % 9
- D44E
+
D ?? !# " 9
D444E
#" "
" D) # # E )@ # @ # ) #) J # ) " @ ) @ ( + # "#@
" #
" #"
! ) @
" #@ # #" " #
"# > # @ ( # " " # S # # S #) #) # A " # "# " # .$ + # ) 5")@ "
!# $W
?" . !
$.&
DE
D E
D#E D ??
5I % Q I % DE A # D E # D#E A ? 0@ 9K . 5") 44
$..
7 8 1 $
V
*$ 4 ) "
" (
) " ?'
)F.6F;
9
( @ # # ( # D"@ ''*S !# @ '.'E?
$
# 7 @ " # ##"
# )
7 " ) "
) @ " ) # ) 0, 3 ( @ ##"
# " # " # # # " # (
+ ) "@ # #) ) @
"#" # " ) " +##
# " ) # # @ # #" J )@ " #
" " D E " E V W :I @ 55 D'' E -7 ! ( ! D>!7! 8( % .E >! 7 # !" )@ % @ C+ K@ 1 0@ B- D''4E N + !## A @ ;I V W !# @ 2: D'.'E 3 , & ! ( 1 ( ) , 3 + + D>!7! A" # AA+'E >! 7 # !" )@ % @ C+ @ D'''E :## # " ,? 1R 1 I ! ( D '$E ," : " - M /
@ +!@ A % # ,"@ 2) > ) @ ;Q@ B "@ ;9@ 0"@ 5! D444E ! ( 1 D 4E # A @ ;I V W 0@ TT@ 5@ @ -@ 03@ - @ T@ B "@ %T D44E !
# " #) 1 . ) 1 @ DE@ ' V W 0@ TT@ 5@ @ -@ 03@ B "@ %T D44 E + ") # "#" ##"" " #@
" "#" # " ) # # @ DE@ 4$4 V W 0@ TT@ 5@ @ T@ ;T D44E ! ( -" !## # ) A @ @ V W 0@ 05@ B@ !@ 0@ 5T D'. E 1 . ! ( .7 . 3 D: 3 " ," 7# ) M ) )@ . E +#) !##@ ;I@ !## A @ ;I V W 0@ 9K@ -"@ 2-@ "@ A@ @ 5@ -@ TA D44E :# # Q I % ) 5I " 7") 1 ,& @ 'D*E@ &&$ V W
$'
7 8 1 $
V
0"@ 5!@ 2@ B@ @ 3K@ B@ ! D''4E ! ( , C ,3 $ !## A @ ;I V W 0"@ 5!@ @ 3K@ 2@ B@ B@ !@ 3"@ 5 D''E ! ( 0 1 , 1 !## A @ ;I V W T@ 2 D44E % # 5I " 7") :!# @ +#) !## V W T@ B1 D'. E I ! ( * - * D: 3 " ," 7# ) M ) )@ $E +#) !##@ ;I@ !## A @ ;I V W B@ ! D44E # " " ,? %# 3 DE@ &' ( ) 2 3 * & 3 + : @ % B@ Q; 3"@ 5 D'.'E ! ( C 3 $ * , D 44E " ) A @ "@ V W B@ Q; 3"@ 5 D'.'E ! ( C 3 $ * , D 4 4&E " ) A @ "@ V W
& . Terrence P. Rollerson, Thomas H. Millard, and Denis A. Collins ?
;61F@6F;
) ) #
# D- @ '.E ! # "" ) " ) @ "
# "J # ,
)@ # " ) )
, )@ )
# @ # "@ "@ F
C# " , 9 *4 *4 @ C# " ,
;
A" " ; ) ! " , #" " " ) (
# D9" E 0 " "@ ")
'44 ) # " " A # # "
" " : ) @ " " ##" :"# C# " , %@ # " @
#@ @ @ "@ @ # "@ "@ F
#
)
/ 3 # C# " , :"# # $4 # ) ) ( 0 # " )
# ) A # @
S "@
# @ " # ## "J # " , ) # # # S @ # " 9"
# # " ??
>9
# " ) ,2;,% D @ 44S 2 #" @ 44E ) " #@ # @ " # " " @ # #) ( ) " ) " # " )
D9" $@ # # E
) )@ ;" )@ ; " % @ /7@ :@ 2+@ A"@ 5@ @ 3@ !"@ + D'''E 0 /OO>2 ! D9 A ## : A
@ 9 A ## ## % 1 E 8 9 )@ !@ 8% % #@ 5+@ :" @ 5/@ 8"#@ +C D'&'E 9 % D! 'E ,? %50 " D#
E@ / : /3KKK3KKK . + 7 # !" ) @ C# " % @ D''E ( 2 * 3 % 1 0 D3 : % 1 &*E : ) 9 @ C# @ ; " % @ @ @ ;@ : @ - D''&E ,(# # ; "
"# / 0 ! (3 ! 3 1 3 >! 7 # !" )@ % @ C+@ + # ! #) / @ 1 T % @ @ @ ;@ : @ D''.E A
) ) ) ; " @ C# " C@ 9 D'.$E
! " 1 . @ DE@ *. T @ 5 1@ -0 D''$E . I , 0 2 ! . + 8 # ;
@ C# @ ; "
$ 9 .: 4. 3 5 Markus N. Zimmermann ?
;61F@6F;
, ! + # " ) @ #
@ "# " % " #" ) " # #" D@ B @ ''&E !" )@ ! )# ) I
" '.& !# "
" ( D@ - @ ''4S %# B @ ''E ) D@ %#@ ''4S ## ; @ ''&E , ) # #
J# # # " #" D@ B - @ ''E + " "
)
# " D@ B @ ''& S %#@ '''E !"# !U 4 $ E & A
:) " #" D+ ; @ 444E , @
##"
! A" 8 # >!U 4& @ # ## " " 4$X
!# W
? 6 --- . 3
*'
D ?? J ) # #@ '.&
+## ) I# # #
# #
"
??
6 --- %
+ ''' - # "
I#
!# .W
?* 1
*
0 " # ( " " ?*
1)D)1);).
; @ @ -@ @ 2"@ -%@ 3@ 8 D444E > #) - 6 ''' + (+ . +@ "DE@ $. V 7 W ;07 D44E ! 1 , 2 . + + 2""(((+ (+ +"," " " , + ;" "6 0 " 7 @ ;@ ! ;00@ ;>0+3@ ;%A D''&E - 2 D ( ( D V 7 9 #W + 2""(((+ (+ +" "" " (+ 9 @ ! B @ : D444E %"#" RR;6# ==@ :" 6 0"6#
" D; " " %"6E? / 7
"#" " 9
+ (+ . +@ D$E@ . V 7 W 7@ A D444E &( 2 - & ) .) D7 # ; @ 7**E > ) ; @ ! V 7 W - @ 0@ %#@ @ % 6@ >@ B @ : D''4E 0, /OQ@ ! ( ( 2 . 1 . D,+-! A" # ' @ 44E , + # -)
# !##@ #" #@ 1 B -@ + D'E ) C 9 " 0"@ B"6 #@ ! V 7 W - @ > D44E 7 # " "" # C 6 " %" ! 6 4 5 " : @ ," 7 )@ > ) ; V 7 W A ##@ + 2 @ - D44E - " ! ,? %# 3 DE@ &' ( ) 2 3 * 3 D $.E : @ % %#@ D''4E 1 ! ( D: C+0 /-@ 1 4E /-@ B" #@ ! %#@ D''4 E ! ( /OQ@ () 2 D,+-! A" # 1 ' @ &&.E , + # -)
# !##@ #" #@ 1 B %#@ D'''E / # # ) @ -@ &&& %#@ B @ : D''E '.& ! ? # " ) . @ *@ &$.' ##@ ; @ 7% D''&E ) # " ,? 3 DE@ &' ( ) 2 3 * 3 D $E + # ! #) / @ 1 T 0@ +@ 5 @ !@ :3@ T "@ A D''.E 0 :#7 -@ ; B @ : D44E +
# ? + # ")
! * / 0 1 ! ( 3 ( D '$4E
*
$ 9 .: 4. 3 5
V
B @ : - @ 0 D''E # # #) " ? + # ") ! + 1@ @ $'& B @ :@ :@ A@ % @ - D''&E :" # "" ) RR ==S N
0 "#"
$4 ) " # +
@ #
"
#
"
@
" #
# * @ ) #
* *
) ; N
+ )
# # O RR# # . . .
) ) # ##"
# # " ; " ## "== ) " " 9" #
# ) ;F16+ . ; )>1.$D F2 )0);6.
1 B= 1 , ) 8 # # ) @ # "# ##
# # 7
!# *W
'? . **
D '?? ) % " D>9E@ D:9E@ D39E ) # ") ; # D;%E D E 1 ") ) " )
A
# A : " 7 " ) " 9 7# D:@ '$@ '$.E A # A # # I# !.; ; G..
) % D9" *E * $ )
## 4 )
: " 7 = " #
@
# ) D:@ '$.E @ # @ "# )
## #)
@ ) " D9" *E@ " I#
# D-" %@ ''$E ! ) ) % ) @ # + # # #) : " 7 D9" *E # # " ) )
## " 4 1 # " #
@ " )
) " ) )
## , ##" @ @ * 4 * D-" %@ ''$E 3 # # ##" )
##
# ;
) @ I# ) D9" *E + # # " ) # "# RR) == D" / F7 + #@ ''E ,
44$4 )
## ## ) 4# " #
# # # )
##
# " $ "# ) $ 4 # " " # ) % D5 ; @ ''*E@ # " ")@ # ")
D# ) + 444E
*44&44
&44.44
@444@44
@444@44
@444@44
@444@44
@444@ 44
@44@ 44
@44@$44
@ 44@*44
@$44@.44
+ D ) ;AE
*&4 $4
.4 *4
@4.4 *4
@4 &4
@4 &4
@'4 *4
@$ 4
@ 4 *$
@'4 *$
@$$4 .4
@**$ *$ 7Q&.'
7!$44
7Q&&4
7Q&&
7Q&.'
!
!
7!***
7!**.
7!**'
7! 4&
3 ) "
#
#
3
3
#
3
3
3
3
3
#
' &. @ 4* ' & @ 4.$
' & @ 4.$
' &4 @ 4'* ' & @ 4.
' & @ 4.
' & @ 4.
' & @ 4..
' & @ 4..
' & @ 4. ' & @ 4..
3" D 1E@ " D 0E ) %
! ) ( # S "@ $ " # ! ) ( # S "@ $ " # ! ) ( # S "@ $ " # ! ) ( # S "@ $ " # ! ) ( # @ "@ $ " # /# S "@ " # ! ) ( # S "@ $ " # ! ) ( # @ "@ $ " # ) %
/# S " @ " #S " ) "
6 '?? % #
)
" / F7
+ # D''E
:#1) + D''*E
" / F7
+ # D''E
" / F7
+ # D''E " / F7
+ # D''E
;" D''E
;" D''E
" D44E
" D44E
" D44E
:#1) 5 D''E
% #
$@$44$@&44
*@444*@'44
*@*44*@'44
*@$44&@44
&@ 44&@&44
.@$44'@444
'@*444@44
@.4 .4
$@**4 &$
$@.'4 44
$@'&$ .4
*@$'$ '4
&@.4 '$
.@&$ 44 7Q&.'4
7Q&'&
7Q&.'
7Q&.'
7!$*
7Q&..'
7!*'
7!$4
#
#
#
#
#
#
!#
#
' * @ 4.
' *4 @ 4.
' * @ 44
' &4 @ 4'*
' & @ 44 ' * @ 44
' &. @ 4* ' & @ 4. ) %
! ) ( # S " @ 4 " #S " ) " /# S @ .* " # ; !@C)6
+ ##" ) D9" *.E
7A% " ) # ) " ? # ) " $4 @ "J ! ) # " 1!/% D1 !## / % # "#@ E % # 7 5 " '?/
1)D)1);).
;"@ 90 D''E . &' ( 0 . 1 ! D>" @ $ E ;" / @ !1. D F2. 6 #F@;6 .6? +) );. , ; F0)10)2
/ " ) # : " ! -
" " # ) # " # #) $4@444 ) 44@444 ) D @ '.&S / @ 44E #) '.4 # ) # #
!# &W
(? )! # .? + ,
*.'
6 (?? # #
. :)@ '.4@ : " ! - " 3 :"" D'.E
/
C " "# # D E
+ J# D E
# DE
# ; A)
## A
$ 44 44 4
*4 *44 $4 $ @444
4'$ 44 4 4$ 4 44$
) / " )
) ! 7 # !" )@ # "@ 44E
" ' '.4'. "
/ ''& * ! #
A
' @$44 ;A
#
' :)
'.*
19 %
8 , '.4 . :) 19 %
:)
'.
*'
# .? += 2 = @.
V &
D (?? 8 !7!@ ' :)@ '.4
" " "
" # # ) " " # " # + # # 0 D'.'E #? DE " # ) @ ) " ) ) @ # " ) ( " 4 " " S DE @
!# &W
(? ! *'&
D (?"? 8 !7!
@ " ) ) " # # " )
## " # ! " 9 " )
" # )@ ) ! # ) " # "
) ) #) # D &S 9 # 0 @ '.S !# @ '..S 0@ '.'E "
# " " @ # ) " ) ) " / " # =
D5 @ '.S A @ '.$S ; ) 0@ '..S 0@ '.'E @ )
## " ) # " #
# @ A " " :") % )@ :") % ) # # " # # "# ! D9" & &$E @ A @ 4 & ! % D &S 5 @ '.S A @ '.$E 0 $ # @ # " "
*'.
# .? += 2 = @.
V &
) S ! " 9 " )@ #) ) ( " 4 "
" D0@ '.'E - " # @ "# # ! " 9 " :") % ) DA @ '.$S !# @ '..S 0@ '.'E # "# # ) # = # # , :") % )@ " $44@444 ! % DA @ '.$E ! ) ) " # =
" # D9" &$E 8 " # @ #"" " " 4 * " $
" D:I C @ '.*E@ # ) " ) ! D9" & &$E (??
.
49 5
9
#) : " ! -
# " # " @ # # # " ## D# &E
: " ! - # "
#? DE # " "# S DE "
S DE # S D E # " "
; # " "# : " ! - '.4 444 8 ' : #@ '.@
"
) # # # # = # @ #@ # D0 @ '.E +
"#
" ! 7 # !" )@ # "@ 44E (? ?
.
49 5
: : " ! - )
" " " #
!# & W
(?
D
&4
# # # @ # )
" # )#) # # " # # # + " )
" D@ '.4 '. E@ L#" "#
" # # # " # @ # # # 9
A !# D'.$E
: " ! -
) " @ # # , ) @ @ # # ") (#)
# ) ) # # ") D@ A !# @ '.$S !# @ '..S .E ) # ")
@
) ) # # # ") (@ ) # #@ ") (@ @ ) "" D9" & &$E 7 ) D@ 7)@ '.S 9 #@ '.$S A @ '.$S :I
C @ '.*S !# @ '..E : " ! - ) " #)
@ " ## # % D@ -) @ '&.S C#@ '.$S C# !# @ ''&S C#@ '''E )#) # #( ")@
!# &$W
(?" !
&
D (?"? ) # # # : # '. " % D+E ) ( # D) # # "E ) " ( ) D "E " )
#
) # # D;E
") ) # # 9
A !# D'.$E
&
# .? += 2 = @.
V &
) ")@ ) D9 @ '. E
: " ! - #
" D9" &*E : ) # - @ " ) #" #
# # " " " 8 #) # : " ! - '.4 1 9 " % @ ) " $ X ( # #) D9 #@ '.$S !# @ '..E (?"?
1 ! A !
" @ # # @ " #
) : " ! - #
" # # " " #
) "
#
# # " " @ #" )
" # "
" "" + " # # # # @ # "# # )#) " !"# # " # @ 9 @ '.4 ! 3 #
" @ " "
4 '.4 # # ) " ## @
"# " ) " #) J
# " " ) "#
" "" #
) " # #DE # # ! 3 ) '.4 # D!# @ '.. E ) # " " # " "
" ) "
" ) # # X #) D # RR# == E # ) ## )
)
# ( # ) "#) ) ! " ) " # "# D!# @ ''$E , # @ " # X #) D # RR # == E # ) # (
# ( # ! )
" @ ) " (# ) #" )
# ) ) ) + " #" ) " " RR # == : " ! - # # )
!# &$W
(?" !
&$
D (?'? 7 " : " ! - D+E " '.4 1 9 "@ ! " 9 "@ "@ :")@ A @ " D;E " '. ) # # D A !# @ '.$E DE " #" # " " % ) D !# @ '..E
&*
# .? += 2 = @.
V &
@ #" # " ) # # # D@ '.4 ! " 9 " @ !# D'..EE ) # # " ##"
# #)
" @ # #
# " # " #
" D@ :I !# @ '..S !# @ '.. E (?'
C)F#F1+ #6. FD 6+) -*/ )>1. D F2.
! " :") % ) ) '.4 #" (# # (# ) 0 #
" 1 9 " )@
" ) # ) #@
@ #
@
^ ) #
) ( #@ ##)@ ( "#" @ "#
" , # # #
# 5 D'.E 3 D'.E + % @ 1 9 " ) # ( ) # . # ) " $ # #) "# # # )# ##) " #
% % # D9" &E " @$4 F + @ #
"# " 4X " " D3 @ '.E 1 9 " " " % @ #)
# ) " . # "# % ) " # I" ) " #@ " ) # #)# # @ @ # " ! 7 # !" )@ # "@ 44 E ##)# " @ #" @ #" >!U D9 ) -@ '.E + " )@ 1 9 " ! " 9 "
) ) " 44 @
) ) @ " " 44 )
@ ) " #@
) ) " #) ") ) , $ ) ;" 1 ) #
" %
# "# % @ A !@ " ) ) )
" !7! D;E A ? ; 5 @ >! + ) /
&4
# .? += 2 = @.
V &
" L# " " # # " " # " 1 '.4 " # #" # ) " >!U$ A C# " D9 ) -@ '.E ;) 8# '.@ 8/ " . "
" % 9
:) '.4 8# '.@ 8/ ) &&
"@ @ " % D!#" @ '.E + A :") % )@ '.4 @ # "
) * >! 9 ! #
! % @ " # A " @ A#(# A 3 ## $ " @ ) " @ "# RR == " (# #
"# ##) #) ; '.4 ''4@ >!U
#" ) '.4 @ # #@ " " " # # @ # "# "#" 1 9 " ) D9" & &.E@ # "#
# "
" ! 3@ ) " " " " # " # (?*
D1)H@);G ; #C;6@) FD 1C) )>1. D F2.
3 : " ! - ##" !+E
) @.44 @ # (@ " &*@444 # " D7 A @ '.$E ! " Dad . E : " ; @ 0 D>!+E
" # D!# "# @ 44E @ # " # " "# .4X " # ) $4X #
" "
(?/
F; @.F;.
+) '.4 " " # " : " ! - ) #
" " # " # # " # ) )@ " " @ # # ) )
# #) " @ # # # )@ "
# / " # # # @ # #@ # # #) #) ) @ "# # # #) @ # #) ! 7 A 8L#@ @ 8 ; )@ !% :) @ ; D444E + 2 ! /OQK - 6KKK D>!7! 9# ! 4*44@ E >! 7 # !" )@ % @ C+ ; )@ !% 0@ %; D'..E ,
)
## " @ )
## @ ! ) " ( " . :) '.4 " : " ! -@ >!+ I @ "/@ 4 * ; "@ :: A @ + D'.E -F I . + D>!7! #" .$4@ E >! 7 # !" )@ % @ C+
@ 2+ A @ A D''4E +# ' :) '.*@ : " ! -@ 0 # ( @ ' @ $'*
# 1"PG@ 7@ C#@ 50@ % @ 0, D''E + " " #"#
P # @ :# ? ,# I . @ "-@ $ * @ % D'.&E *&/OQK * ! ( + I 3 D>!7! A
A @ ' E >! 7 # !" )@ % @ C+ @ %@ :""@ %@ %" @ : D'&$E : " ! - # ? # "" @ *(@ . "@ 5 D'.E ' ( /Q3 /OQK3 - + 3 D>!7! #" .$4;@ * E >! 7 # !" )@ % @ C+ @ %3 D'''E * /O3 /OQ6 D>!7! A
A $.*@ &$E >! 7 # !" )@ % @ C+ "@ 9 #@ 3- D'. E /
" : " ! - @ 'D E@ @ 'D$E@ "@ 3 @ 3; D'.E ! ) 1 ( ) , + - D% @ &4 E 9 / #) : +#)@ % 4@ !@ 0+ / @ %@ )@ :+@ 9#@ %5@ 3 @ :+@ @ +@ ! 0 I##@ +: D44E ) 0 ! 9 #@ 3- D'.&E #
# . ,( - . @ (@ $* 9 #@ 3- 0 @ : D'.E )# " # # # # . :) '.4 " % @ 0 * - 1 I D## : " '4.@ $E A" # 0 % # ,"@ "" @ 5 9@ 5-@ :@ :@ =+@ %/@ 7 )@ % D'.E % #
" # ! '.4 " : " ! - # @ 0 . @ *@ * 9 @ %3 D'. E * D. E -@ +"@ Q 9 )@ ;3@ -@ : D'.E I - /OQK + 2 ! /KK D>!7! A
A '@ $ E >! 7 # !" )@ % @ C+ 7 @ 73 A @ D'.$E * 1 ! ( 8 & ! /OQK3 - ! , 3 D>!7! 0 !") A &@ E >! 7 # !" )@ % @ C+ 7)@ 2/ D'.E ! ) 1 9 ! " 9 " " " '.4 " : " ! - D$ E :!# @ > )
! ; 7#@ - D''*E & , /Q3 /OQK3 + I 3 D>!7! 8( % '**&&@ '4 E >! 7 # !" )@ % @ C+ 7#@ - D''.E % # # :) .@ '.4@ : " ! - # @ 0 . , @ -@ $$4* - @ 5- D444E A # I"@ :") % @ : " ! -@ 0 D' E :!# @ ! > )@ 9 -" #@ ;A ! @ + D''4E %# # # : " ! - # @ 0 . 1 @ (@ $ - @ %A@ : @ @ C#@ 50 D'.E * /Q D>!7! A
A $4@ 4 4E >! 7 # !" )@ % @ C+ -)@ 5- D'&$E A * * &' ( 3 + I 3 D>!7! ;" .;@ 4 E >! 7 # !" )@ % @ C+ -)@ 5-@ @ % D'&.E * I 3 * ) ! - D>!7! A
A
4@ & E >! 7 # !" )@ % @ C+ , @ %:@ %@ :/@ 3-"@ %7 D''&E
,( - * @ "@ .$. , @ %:@ !#@ !A@ C#@ 50 D''.E 8 I#
# . @ /@ '&'. 5@ %5@ !# @ 2:@ 1 @ 2:@ : @ -+ D'.E , 3 -F3 D>!7! A
A $4@ * &.E >! 7 # !" )@ % @ C+ 5@ %5@ :) @ 9@ @ D'. E ! # # " '.4'. " : " ! -@ 0 @ (DE@ 4@ (DE@ $'
!# &W
(? 1
&&
5 : ) "# D''E - + !& A) I * C D4 E !
@ 5 : ) "# @ ) 5 : ) "# D''$E ! ( C DC @ . E 8" 0 8L#@ 2)"" % "# ;" "@ 5 : ) "# @ A" # 0 % # ,"@ "" 5 @ +: D'&4E * * . D$&& E 9 @
@ M @ ! 9 ## 3-"@ %7 D''*E ! ( A . I D>!7! 9# ! *'*E >! 7 # !" )@ % @ C+ 3@ 9@ " @ 5@ C @ ;@ !"@ -@ !" ) @ + D444E 3 : # @ 5 I . @ //@ $* 3 @ +2@ @ ;@ "@ D'.E A " " 1 9 " % @ 5" '.45" '. ? D . @ + @ '@ *$ 3@ A0 :""@ % DE D'.E /OQK - + 3 D>!7! A
A $4@ . E >! 7 # !" )@ % @ C+ 3 @ %/@ :@ :;@ 1 @ 3:@ 2 @ 3@ @ A5 D'.E 0 ' ( /Q ( 1 ( ) , D>!7! A
A $4@ *'*''E >! 7 # !" )@ % @ C+ 3 @ 5%; D44E ) 3 :" * 08@ 5" :I @ 55 D'. E 7 # # # # # :) .@ '.4 " : " ! -@ 0 :!# @ A) ! > )@ ! :I @ 55 D''&E
# # . @ /"@ $** :I @ 55 D444E 7 ) # " "
? ,# # # # @ (/@ * . :I @ 55 D44E A " )
) ## ) 0*1@ "@ 4$ :I @ 55 D44 E A " " : " ! -? # # # I" # . & @ /-@ 9444@ ?44'F445944444 :I @ 55 1@ 7 D'.'E ! # " " # ## "
I @ "@ & :I @ 55 C @ ; D'.*E ! ) # . :) '.4 " @ : " ! -@ 0 * @ "'@ *'&4$ :I @ 55 !# @ 2: D'..E I ( , I 3 + 3 2 * 3 -73 ) D>!7! ;" .@ . E >! 7 # !" )@ % @ C+ :I @ 55@ A @ @ @ %3@ @ 5/ D444E ! ) ## " # + # #
: " ! - . @ *@ .'. :I @ 55@ !#@ !A@ A" @ %@ /# @ D44 E &' ( ) , 3 I3 I 3 - , D7!+ !# A
&$@ .'4.E 7 # ! #) + #@ ; " @ 8
&.
# .? += 2 = @.
V &
:#7" @ 05 D''*E I 0 2 ,( 1 D!# A" # 4@ E 7 # ! #) 3 : @ %+@ 0@ %;@ ! @ + D'..E 7 )
## " )
# #
: " ! - # @ >!+ I @ "/@ $ :) @ 9 5@ %5 D'.*E !
. :) '.4 1 9 " % # @ : " ! -@ 0 ,? !+ 2 DE@ + 2 !, $ D *..*E / 0 > ) A @ ) :) @ 9 : @ -+ D'.'E %
# #
# ) '.4 " : " ! -@ 0 @ @ $& :) @ 0@ ! @ :+@ 7#@ -Q@ C @ ; D'.$E -F . 3 3 ) ! 1 1
+ 3 D>!7! A
A $@ E >! 7 # !" )@ % @ C+ : @ @ :""@ %@ @ % D'.E ) + D>!7! A
A $4@ &.'.4E >! 7 # !" )@ % @ C+ :""@ % @ % D'*E %#
: " ! -@ 0 . @ (@ .$$.&4 :""@ %@ @ % D'.E -, + D>!7! A
A $4@ $E >! 7 # !" )@ % @ C+ 1@ 7 D'.E + # #
: " ! - - 3 & . A @ 'D $E@ 1@ 7 A" )@ %! DE D''*E ! 2 - * 3 * D* E > ) 0 A @ ! 8= @ 5/@ - @ 5-@ @ 5/ D44E ! ( ! # & F 3 D>!7! A
A *4*@ ' E >! 7 # !" )@ % @ C+ A @ D'.$E , '.4 A :") %
@ : " ! -@ 0 . @ -'@ 4$* 4*' A @ D'.*E 9 # @ : " ! -@ 0 ,? + + DE@ * D *''*E + M >@ ; A @ D'''E ! ! ( ! ( - & & 1 /O3 /OQ6 D>!7! A
A $.*@ '*E >! 7 # !" )@ % @ C+ A @ D44 E % " # A#(#% # * . * 1 # &% 1 I 3 /6R/=3 * 3 7 D *E > 1# +" P :P# @ :# ) A @ 5@ %5 D'' E C ## #? + # "
# # # . @ /'@ $$. A @ !# @ 2: D'.$E "
) # # @ @ $$
!# &W
(? 1
&'
A @ 0@ %; D'''E & &( ! ( . -7 , - ! 6R53 /OQ5 D>!7! A
A $.*@ $*.E >! 7 # !" )@ % @ C+ A @ @ 5@ %5@ " @ 5@ ;
@ + D''4E A "
# ) 1 '.$ " 1 %"@ @ # !7! 0 % " # , % ' 4&$@ .4 E >! 7 # !" )@ % @ C+ !#" @ %3 D'.E / # '.4 : " ! - " - . @ /@ $ !# @ 2: D'.$E 3 : " ! -@ 0 @ >!+ * 0 - 3 ! (3 *, 3 5R=3 3 D 4' E /
/ ! #) 5@ ) !# @ 2: D'..E 3 , 3 & ! ( &1 ( ) , D>!7! A
A &+@ &. E >! 7 # !" )@ % @ C+ !# @ 2: D'.. E 3 , 3 * 1 + 3 D7!+ !# A '@ *E 7 # ! #) + #@ ; " @ 8 !# @ 2: D'.'E !8 & ! ( & 1 ( ) , D>!7! A
A &;@ E >! 7 # !" )@ % @ C+ !# @ 2: D44 E 3 @ @ # #" @ @ ) : " % @ 0 * . * 1 # R% 1 I 3 /6R/=3 * 3 7 D &E > 1# +" P :P# @ :# ) !# @ 2: "# @ ! D44E ! " : " ; @ 1 # + . ,# # . ( * @ D&E@ !# @ 2:@ C#@ 50@ A @ A D''$E 3 , 3 ) ! ( 3 D>!7! A
A $ &@ $* E >! 7 # !" )@ % @ C+ !# @ 2:@ :#ZP @ 53@ 1 I @ 5+@ % ZP "@ !@ :#7@ 5A D44E 1& ! ( I 2 3 ) 3 D>!7! A
A *4@ $' E >! 7 # !" )@ % @ C+ !# @ 2:@ C#@ 50@ 2 @ 1@ :#ZP @ 53@ ! "#@ 0@ @ 7 D E
# # C # @ 1# "? 8##"
#@ "@ - * +
&4
# .? += 2 = @.
V &
! @ 3 D'. E 3 ## #? # # " # @ @ # " I . @ @ *'& ! @ 3@ 2 )@ A@ A" @ % D44 E I C , I 3 - , 3 1 ( 1 - 4& -, D7!+ !# A &$@ $E 7 # ! #) + #@ ; " @ 8 !@ ! @ 3 D'' E I D ' E 7 ## A @ "# @ +B ! @ + D'''E 1 & , /OQK - + 3 D>!7! 8( % '**@ 4 E >! 7 # !" )@ % @ C+ !@ 7+@ 9 @ 05 D'.'E C ## "#
. @ (@ &$&* ! ," D'' E %I # . I #( @ -D4E ! ," D''*E 3 : # . I #( @ D'E " @ 5@ + " #@ 2/@ ; " @ 53@ ;
@ ! D''.E 8 @ # # #@ " ''4 " 2" # @ 5 D, E I @ "-@ *4 .4 @ %, D444E : " ! - 4 ) ? 0 = . @ "@ ' >! + ) / D44E + - D #" 9 % @ E >! + ) / @ A #@ A @ 8% C#@ 50 D'.$E 3 A # -
% @ 8% - 3 & . A @ ''D *E@ $4 C#@ 50 D'''E * * ) , ( ! 3 D>!7! ;" *@ ' E >! 7 # !" )@ % @ C+ C#@ 50 D444E 3 ,? - !" @ ; - " @ !% :#1"@ - %) @ 5 ! DE@ - I D *4**E +## A @ ! C#@ 50 !# @ 2: D''&E 8# "
: " % ? ! ) # " #) # . @ /-@ * C @ ; D'.E ! /Q - D>!7! A
A $4@ *'.*E >! 7 # !" )@ % @ C+ C @ ;@ 7#@ -@ 5@ %5@ "@ A: D'.E 1 , /Q D>!7! A
A $4@ &&&E >! 7 # !" )@ % @ C+ 0@ %; D'.E , * ! ( ! /Q2 D>!7! A
A $4@ ' *4E >! 7 # !" )@ % @ C+ 0@ %; D'.'E !
D E #" ) )
## " : " ! - # @ 0 @ . :) '.4 I @ "@ .$& 0@ %; :#3 @ 1! D'.&E : " : " ! - #) # # : #+ '. , . - @ ((@ $$&'
!# &W
(? 1
&
0@ %;@ A @ @ :#3 @ 1!@ 5@ %5@ C @ ;@ - # @ % D'.E / " #@
@ : " ! -? /J#
# @ @ ' '& 0 @ 5! @ 3 D''$E 9 !7! 8( % '$ '&@ E >! 7 # !" )@ % @ C+ B"@ A-@ + @ ;9@ C#@ 50@ ; @ -@ ;
@ + D44E - # )
"# # 0 %
: " % ! ,? 0 ! DE@ 1 C D9 7" @ 4'E 7 # ! #) + #@ ; " @ 8
A
##
'* +# "# 9 : D+9:E '*@ $' # D( E * # " J . && ) $. # "#" && $
#
$. $4 . "#" $
) && J .
)@ "#
'' " " '
@ "
" ' # # @ J @ +# ) % : & # )
# # ' # D%>E 7 # " # # # $&
&
A
#""