京 都 大 学 防 災 研 究 所 年 報 第 50 号 B 平 成 19 年 4 月
Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 50 B, 2007

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MyLnNyUp^u+hEuZtyOɇBǪ}>Ǧſ+KulyhEuZBȆǥƝp^u)+6ǰɧ$Ǝŋ¿ơ+ɹɿBɣƷ>žğŗ)œɖȰ+ɹŦp^uɣƷɹɿ)ØBÏ4+%hEuZtyO+Č,ű(>?)ƿǪ}>Ɇɇ,œɖȰ+ɹŦp^u)Ê>ɣƷ+eFDVBȆɘ+Ƃǁɿ&Ȼ$ǗŌƌǨ>&);=Ǝŋ¿ơ+ɣƷ)9hEuZtyO+ČÏ0Ǫ}>ɆɇBëƣɹ+ėƍɣƷ)ǰɧeFDVBɃƖ>&);!$ėƍɣƷƙǹĎŽ>&Bɕ< )4) ȹȮèěɹŦp^uėƍɣƷlVMyLnNyU^ZȄ
1.

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Ț$ (ħĺ<, 2005)āę+TV]n%,ɣƷɿBŋĢȍʁ6 ŋ¿ơ5%+ƣɹɿBɣï¤Èɗ)ȤǮ>;(Ġ,ōƍƓȢ+ȫţƷ$ > (ɷƣ<, 2006)p^u+ŬÅƂǁ,ŒƜȹ(ǙűƣɹBǙƅ)Ɗǅ(ėƍȞ«B9<ěBȍʁTmqvTry);!$ 1 ŋ¿ɍ)ʄ -ȼƒ 16 Ȑ+ƆµȴǻĠ%,ćţɰĕƆ$

ƣ:·ǊǷƣ(' 11c\_xNBǦ$tDuZFn%ȍř$

ŭ%ȕǧ16 ɔ+łŔęɆ>ƣɹɿ+¾ƷƀɄ,ĤǺĊǦŸ+ċ>9ȫɕŔB9<5ȼƒ 17 Ȑ+Ǆȱ 14 Ğ%++āę+TV]n%,+¾ƷƀɄBƂǁɿ+,ÞŜǒɆBǙƅ)Ʋɿ 1000 mtBǡ ćzƌǨ),ɧƏƣ:ǅɬƣ%ǅÈɗ(ƍțɱȚƘBĎŽ>8),ɹȉ+ȵƎǒǵ%¾Ʒ

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(

ĦĈ+TV]n+ɣƷôǙűƣɹ%,ōƍŁƟ+ƓȢ+6)ƺ?>ƣɹɿBɧɊĭ,ĦĈ9ɤ%,(ŻĮ%°ǹ+ĝ

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8+ťɩ(ƿĶ&(>ɹŦp^uB¾Ʒɹɿ%Ȅ>Ɇɇ)"$,

1974 Ȑ)Ȍɝ (1974) ,8$KulyhEuZB

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Nagy, 1978; Kitandis and Bras, 1980; O’Connell and),ɡČ%>

Clarke, 1981; Refsgaard, 1997)ʄ

ȇ<?(ǙűƣBÁ8$¾Ʒɹɿ-ĝʌǤɨɹȉȰ+Ȏ+ȆǒǵBƿż)ɣƷ(1980) ,ǋœɖ+Mcl]E\NGHip^uB>8),ȹȮèɹŦp^uBɹƨƾ)ǰɧũƤé$KulyhEuZBǰɧp^u+Ƃ

ɹȉȰ+ƣɹɿBɣƷ>ȥɩ>ǁɿBǗŌƌǨ>ɆɇBǪ}$>5ĝʌ

ȦŔ<,ɹƨƾ+ŻĮ(ėƍɣƷBɚŀ$ɬ<+ʆ+ùÒ (1982a, 1982b, 1983) ,ǝɺÀƎɇƣɹBƿż&đȹȮèɹŦɣƷTV]nBª)KulyhEuZBȅȍ$Œɹ)ǰɧ>&&－1－9)ɡƃdFW+ɧ:ȵğɹ1+ɧBŎV]nɆǫŐ)ɐǑǨƎB$ >5ÜȐ)(!$ɹŦɣƷ+ȫ°ŒƑBȩɐǑǨƎBǗŌƌǨ>ǰKulyhEuZBɧ

>&

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Ƃǁɿ&&9)+<DySyiuKulyhEu

>&);!$ɹœɖ+p^u)Ê>ĉĩ

Z (Evansen, 1994) Bȝ²ǯĖƴ+ǋŪ(ɹŦp^uBɃƖƣɹɿ+ɣƷBŒā%>ȑƑ>)ǰɧfsoZȹȮ&ɣƷ+ȫ°ŒƑBǗŌƌǨ

ɐǑǨƎ+Ǝƽ

>ùÒ (ʄ -Moradkhani et al., 2005; Weerts et{al., 2006; Romanowicz et al. 2006; Vrugt et al. 2007)

žğ),ïļ2ęʅ+ŌþȋȘ)¯ǅ>+ÐƸ)ƈC%%ïļȯ¡+ǅ ȡČɶ(¦ɇ&(>Friedland>ȹȮèɹŦp^u+hEuZtyO)"

ɛǇ+;

žğ&)Ɍʇ%Ř=)Ƃǁɿ+Ǝ&ɐǑǨƎ+ƎȄ(1969) ,+ɛǇ)ƿęʅïļ+ŌþBƂǁɿ+$,

5°ɷɆɇ,ɓ 9++ÜȐ)(!$ "Ǝ)ɫ+ùÒƒɄģ?$BǪ}$>ɹœɖì+hEuZ""ɐǑǨƎ&Ƃǁɿ&Bū)Ñ8>Ɇɇ
>5?);!$ȇ<?>ƌǨɿtyO&$,ʄ -Mcl]E\NGHiè+ǰKulyhEuZ);>ƌǨɿ&ǖ>ȹȮèɹŦp^u)DySyiuKulyhEuZB&Bɳʇǯ)źɕ$ ><)Dee and Da Silva

ȅȍ Kim et al. (2007) +ùÒ:HBV &ą-?

(1998) ,Friedland (1969) );!$Ǫ}?Ɇɇ>ȹȮèɹŦp^u+ƂǁɿBǗŌĕƆ> WohlingB¯ǞɣƷ)Á7eFDVBƌǨɃƖ>;=et al. (2006) +ùÒ>Œɧǯ(ɆɇBǳª$?+Ɇɇ9ȹȮè>ɹŦp^u%ïļ>Ƃǁɿ2$BhEuZtyOɌʇ,đȹȮèɹŦɣƷTV]n+ƂǁɿB¾+ƿż&>+%,(ɹƨƾ+ǝɺɿB.&"Ʒɹɿ%Ȅ>Ɇɇ&$ȆȰ+lVMyLn+Ƃǁɿ&6($ĕƆ>ǵ)+Ȉǟ>5

NyUp^u)eFDVKulyhEuZBȅȍ>â¿ȹȮ>ƂǁɿBhEuZtyO%ĄȽ)Ř

ªȚ>TV]nBëƣɹ)ǰɧěɹŦp^={!Ņʄ&$,SAC-SMA p^u)Ⱦȹɇ+u)Ê>eFDVBĘɼ>&+ČBȹƚ^ZȄBǰɧ Seo et al. (2003) +ùÒ>>5ɹǒǵ+¾ƷɹɿBɧ

+ùÒ%Ľɧ$OôŽɹ+ɣƷ)Ï4ØBȹƚ>

>p^u+Ƃǁɿ,ƨ

Ȱ% 6 Ą%=ɹƨƾBOt\`%ȶȹȮèɹŦp^u),ǰɧ?$

(

ZFj+



$hEuZty

Ɍʇ+Ėƒ,~+Ǧ=%>đȹȮèɹŦɣƷTV]n)" $ 2. %¬Ơ%ïļ|ǨɆȆɹ?BǥƝ>p^u)hEuZtyOBřɇBǰɧȆɘƨƾ+lVMyLnNyUp^ǰɧŅʄ9>ʄ -Fread and Ming (1993)uBęʅéŐ%ȨŎ>ɆɇB 3. %ŧ2>4. %,ɐ

, FLDWAV p^u)ȁǷ< (2001) ,ȆɘŠǙèǑǨƎBÁ7TV]nɆǫŐ+hEuZtyOɇ&Mcl]E\NGHip^u)Shiiba et al. (2000)$ȹɴKulyhEuZBȅŦ?B9&)eF,[Fam\NGHip^u)??Kuly

DVKulyhEuZBȅŦ>5. %,áƾǯ(ėhEuZBǰɧ$ƍɣƷ+DuRtWnBŧ2>6. %,Ǫ}>řɇ>ėƍǥƝp^u+ƂǁɿB

hEuZtyO+ƿż&>?<+Ɇɇ,â¿ȹ+ëƣɹ (833 km2 ) 1+ǰɧôBŎ7. )Ȯ>ƂǁɿBȵƎǒǵ+¾Ʒɹɿ%Ȅ%>ǵ%$Ɍʇ+ôʇB5&8>

ɟ?$>5ɹœɖ+ƂǁɿB2$hEu

ZtyO+ƿż&>;=9Ř={Ų(2Ƃǁɿ+ƎŤ!$ɹƨƾBïļ>

ǯ(Ɇɇ&

2.

O7|{G`l"$(/

%,Čɶ
Ɍʇ%ɧ

>ƣ+ƂǁɿBĕƆ>đȹȮèɹŦɣƷTV]n,ɯƍ

+Ɇɇ,ɣ

Ƥè+ȹȮèȰȹɹp^u&Ȇɘ+ėƍǥƝp^Ʒ+t`ZFnǢ(>&ɣƷôɹœɖu%Ėƒ?>ɬƣɹƨƾBƿż&TV]n+p^u)ƺ>8ƣ+ƂǁɿBĕƆČ(ħĺ<2005) ,?<+p^u)

$ȣȔĆ

Ŷ

ñǵ>"5=ɹœ+Ćŵp^u&[np^u&BȀğ$>Ɍʇ

ɖ+p^u)Ê>ìȀǯ(ĉĩBhEuZtyO%,?<+ØBĘɼ>ȥɩ(ɹ&Å¿%ɣƷɃƖ(?-Ȇɘ+ƂǁɿBhEuZ

Bƿż&$~+ÍʇBƈ8>

$ɹœɖ+ƂǁɿBĕƆ($5&

tyO>Č,ţȹ)ȚÃ%(đȹȮèɹŦɣƷTV]n+Ėƒřū,Ō+Ǧ=+ɛǇ,TV]nɆǫŐ)Á7ìȀǯ(ĉĩB%>51/25,000 +ǒéƋ)Éį?$>ɪ)Ęɼ+ĉĩBhEuZtyO%ƌǨɃƖȆɘBǚŦ?Bğɹǵ%ȹ¶>ȹ¶>&);=¦ò%>ȑƑ>"5=TȆ 3 km ~Ž+žğ),+Ǣ 3 km ~)(

－2－

>;

)ȆB<)ȹ¶>")â¿ȹ¦ȑ

250 m +ȧĝƀɄB9&)īÐčȗɇ%ɯƍɆĎBòǨ®Ȇßȹ)ɹȍ>ȰȹɹBǚŦ> (Ŀ

t
n

n

Δt

Δt

ƣ<2001)??+Ȱȹɹ,Ǽɖƛ 250
× 250 m +àéœɖ+Šğ%=®àéœɖ)ȫɈtc < Δl /Δtc > Δl / Δt

Δl / c

n-1

n-1
c Δt

ʈɈʈǙ¿ɹȨɖɹp^u (ɷƣ<2004) Bǰɧ
>

j-1

Δl

l

j

j-1

Δl

j

l

®Ȱȹɹ)ǰɧȹȮèɹŦp^u);!$Ȇßȹ1+ƵɆɹȍɿBïļ>?Bȍʁ&>Fig. 1 Multi-step, Multi-reach stabilization method
for Muskingum Cunge modelėƍǥƝp^u),?5%Mcl]E\NGHip^uBɧ$Ɍʇ%KulyhEuZBȅ

ȍ>)!$Ƃǁɿ+ŋ¿ƌBƤé+Ő%É
ŧ%>lVMyLnNyUɇBɧ>&)ǩēƶBɧđȹȮèɹŦɣƷTV]n+Ėƒ&+ĪāƑ)$,Ⱥø (ħĺ<, 2005) )Éŧ$

"

>+%

%,ŸɸɌʇ)Àʆ>lVMyLnNyUɇ&

3.

 m−1
m

(6)

&(>)m : ɓŌþ+ɹɿɹƛfsoZ ( = 5< (5) Ő)> X ,>Žŧ+Ǧ=ɌTV]

n%,Ȇ+ğɹǵ ;/ɞ 3 km ɍ+Ȇǒǵ%



ɹ



xo
1
1−
(7)
2
BcIΔl
&>&);=Ǝǐ¯ĻBȸɳǯ(¯Ļ&${X=

&%>=+®Ȇßȹ)ƿ$~)ŎlVMyLnNyUɇBǰɧ>(xoB

ɿ%=Ɍʇ%, xo = xn−1
j−1 &>5(2)đȹȮèɹŦɣƷTV]n+ėƍǥƝïļ),lȆɘBȹ¶$I
N[s]Δl : ïļ+â¿V]\j [m] %>xo ,Ĺŷɹ=<xD|IX

VMyLnNyUɇBɧ √  m1 

[m−1/3 s]B : ȆȲ [m]Δt : ïļ+ŋ¿V]\j.$5/5#QfsiIX

3.1

dx
=m
dA

/ 3)i : Ȇ+čȗ [rad]N : Manning +ƪǹæƎ$ 3. %+ŻĮBŧ2>

+ęʅȨŎ)"c=?-+Ȇɘ p Ą+Ȇßȹ%Ėƒ?>žğ),Ƃ

Multi-step, Multi-reach gpI
X6t:

ǁɿ&+ŋ¿ȾBŎŐ?? p Ą"ƺı

lVMyLnNyUɇ,(1) Ő)Ŏ½ǋ(Ƥé>&)(=Ȇɘƨƾ+ɹɿBïļ>8)+Ő%ƣɹɿBïļ%>ǵ)+ȈǢ>

,3.4 )ŎęʅïļB¦&)(>Δl & Δt +&=Ɇ);!$,Ci (i = 1, . . . , 4).&"+ȆßȹBĘ +ɹǍB j ǒǵŽ3
ɹǍB j − 1 ǒǵ&>ŋĢ n +ƣɹɿ xn
j [m /s]nn,ŽɹǍ+Õ©Ɓö xj−1 xj ɹǍ+ŬÅƁö ;/ǋǢ+ƵɆɹȍɿ dn<n
xn−1
j (n − 1j+¿+ȼÛƵɆɹȍɿ) B9&)lVMyLnNyU
ɇ%Ō+;)ïļ%> (ǔȷ<, 2006)

n
n−1
n−1
+ C4 dnxn
j = C1 xj−1 + C2 xj−1 + C3 xjj) C1cΔt/Δl − 2X
2(1 − X) + cΔt/ΔlcΔt/Δl + 2X
C2 =2(1 − X) + cΔt/Δl2(1 − X) − cΔt/ΔlC3 =2(1 − X) + cΔt/Δl
2cΔt
C4 =
2(1 − X) + cΔt/Δl: X ȯ+ǐ)(!$ïļȫ|Ǩ)(>&>
ɵ< (1999) ,lVMyLnNyUɇ);>ėƍ
ǥƝïļ+|ǨƑB°ɂ>Ɇɇ&$Multi-step,Multi-reach ɇBǪ}$ =Ɍʇ%9+ɆɇBĬ
ɧ>&)Multi-step, Multi-reach ɇ+ɩǵ(1)

,Δl/Δt ɹ?+ǶȒƸǹ c &34ǿ(>;) Δl & Δt BòǨ>&)!$?);=

< C4 ,
C1 =

3.2

Ci (i = 1, . . . , 4) : X ȯ+ǐ)(>+BɊɌʇ
(2)+ǰɧʄ%,Δl & Δt +ŬÅƟǨǐB??®Ȇßȹ+Ǣ (ɞ 3 km)1 ŋ¿&$ ɹ?+Ƕ(3)

ȒƸǹ c  Δl/Δt ;=9ű žğ),ïļ+â
¿V]\jB cΔt &$ǌ&>Ɇɹ?+ǶȒ

(4)
(5)

Ƹǹ c  Δl/Δt ;=9ǅ žğ),ïļ+ŋ¿V]\jB Δl/c &$ǌ&>
ʄ -Fig. 1 + (c < Δl/Δt) +ʄ%,ïļ+â¿%>c ,ɹ?+ǶȒƸǹ [m/s] %=lbyO+

V]\jBȹ¶$ >Multi-step, Multi-reach ɇ%－3－

,(1) Ő+ɩʀ% ((j−1)+cΔt) ǒǵ+ɹɿB5Ñ8

d3

?BŽɹ+Õ©Ɓö&$") ((j − 1) + 2cΔt)
ǒǵ+ɹɿBÑ8>?Bã=Ɂ-Ñ8>2ǒǵ+ɹɿ xn
j Bȇ>(d2

ïļ+â¿V]\jB

d1ȹ¶>žğ),(j − 1) ǒǵ& j ǒǵ+¿+ŬÅn−1&+ɹɹɿȥɩ&(>%,xn−1
j−1 & xjɿBƤéȉƮ$?<+ǐBÑ8$+řū,â¿V]\jBȹ¶>žğ&Ȅɥ%>

3.3

n

x2

n

Upstream

x3n

d4

x4n

n

d5

n

x5n

x1n Downstream>Fig. 1 +(c > Δl/Δt) ,ŋ¿V]\jBȹ¶>žğ%=

nnFig. 2 Example of river channel network composed ofﬁve segments[E?$('-~P cTFg 

Multi-step, Multi-reach ɇ,ïļ+ŋâ¿V]\j

BȾ>&);=ȆǥƝïļ+|ǨƑB°ɂ>ïļ+ŋâ¿V]\jȾ>&,Ž
ɹ

<ɹ)Ď

%,(



)KulyhEuZB

A3,m = C3nt

ǰɧ>žğ),Ƃǁɿ+ŋ¿ȾBęʅéŐ%Ȩ

)(=+55%,KulyhEuZBǰɧ>
&%((>Ť!$Ō+;(Đȭȥɩ&

m
nt



m−1
nt





; m = 1, . . . , nt , A2,0 = 0

(14)
(15)

A4 = C4 nt

ā>ȥɩ>Multi-step, Multi-reach ɇBǰɧ>&ęʅ+Ōþ:ŋ¿V]\j+ȲȾ>&

+C1 1 −!$ūŌïļBƈ8>žğ),ɛǇ
Ɍʇ+;

A2,nt |A2,m = C3 A2,m−1 + C2 1 −

A2 =

(16)

&(>?);=Multi-stepMulti-reach ɇBǰɧ®Ȇßȹ+lVMyLnNyUŐB (8) Ő+Ƥé+Ő%Ȩ&%>

(>ȆßȹBâ¿ǯ)ȹ¶> Fig. 1 + (c < Δl/Δt)

3.4.$5/5#<xkmu+PVB5Ę $6>Multi-step, Multi-reach ɇ%,Žŧ+Ǧ= c/Δt "ɹ)ȃ(<ɹɿB
Ñ8$ Ť!$īşǯ)Ñ5>Ǎ+ɹɿ xnj ,(1) ŐBɎ((!$5 (1) ŐB¦ƚǯ)¦-ɐǑɿ%> xnj&ÄǑɿ%>+Ƽ+ɹɿ&+ÀæBƤé+Ő (8)
n
n−1
n−1
xn
+ A4 dnj = A1 xj−1 + A2 xj−1 + A3 xj
j

A1 = C1nl
A2,nl |A2,m = C1 A2,m−1 + C2
1−


A3 =

m
nl

1−



) (8) ŐBʆɷȆɘƨƾ+ɹɿ

Bïļ>

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Figure 2 ,5 "+ȆßȹȆɘBĖƒ$



n
B xn
4 &?-Ȇßȹ 2 +Ǎ+ɹɿ x2 ,+A23 xn−1+ A24 dn
2
2

(10)

m−1
nl

(17)

&(>( A +ú)" 2 &
(11)

ɏ$
(12)

Ǝň,?

Ȇßȹ 2 Bƿż)$Ñ8æƎ%>&B>Ȅɥ+ŐB®Ȇßȹ%Ėƒ?-Ȇɘƨƾ+ƣɹɿBŌ+;&(>)nl (= Δl/cΔt) , Multi-step, Multireach ɇ)



2
n
n
2
n−1
+ xn−1xn
2 = A1 x3 + x4 + A2 x3
4m; m = nl , A3,0 = 0nl
A4 = C4 nl$Ơɕ>%,½ǋ+8>ʄ -Ȇßȹ 3 +Ǎ+ɹɿB xn
3 4 +ɹɿm−1nl; m = 1, . . . , nl , A2,0 = 0

A3,nl |A3,m = C1 A3,m−1 + C2

+C3

)'+;

>ʄ%>??+Ȇßȹ), (8) ŐBǰɧ
(9)





+C3

)ȵƎ+Ȇßȹƺı>ȆɘBƿż)žğ(8)

+&+ (8) Ő+æƎ Ai (i = 1, . . . , 4) ,

yLnNyUɇ);>ėƍǥƝïļɇBŧ2"

Fig. 2 )ŎȆɘBƿż)$~+ÍʇBƈ8>

%Éŧ>&%$

A2 =

Ž%,.&"+ȆßȹBƿż)žğ+lVM

>â¿ȹ¶Ǝ%>Ȅɥ)ŋ¿V]\jB nt (= cΔt/Δl) ȹ¶>žğ+æƎ,
m−1
A1 = A1,nt |A1,m = C3 A1,m−1 + C2n tm
+C1 ; m = 1, . . . nt , A1,0 = 0)
(13)
nt

－4－

⎡

1

⎢
⎢ 0
⎢
⎢ 0
⎢
⎢
⎣ 0
0

−A11

0

0

1

−A21

−A21

0

1

0

0

0

1

0

0

0

)ęʅȨŎ%>
0

⎤⎡

xn
1

⎤

⎥⎢ n ⎥⎥ ⎢ x2 ⎥
⎥⎢
⎥
⎢ n ⎥
0 ⎥
⎥ ⎢ x3 ⎥⎥⎢⎥−A41 ⎦ ⎣ xn
4 ⎦
0

1

xn
5

⎡

A13

A12

⎢
⎢ 0
⎢
=⎢
⎢ 0
⎢
⎣ 0

A23

0

A22

A22

A33

0
0

0

⎡

0

A14

⎢
⎢ 0
⎢
+⎢
⎢ 0
⎢
⎣ 0
0

A43

0

⎤⎡

xn−1
1

⎤

)Rn ,¾ƷdFW+ǅBŎ (r × r) Ōþ⎥⎢⎥⎥
0 ⎥ ⎢ xn−1⎥⎢ 2⎥
⎢ xn−1 ⎥
0 ⎥
⎥⎢ 3
⎥
⎥⎢
⎥
A42 ⎦ ⎣ xn−1
⎦
4

0

0

0

0

0

0

0

A24

0

0

0

A34

0

0

A44

0

0

0

&@%(20) ŐBTV]nɆǫŐ(23) ŐB¾ƷɆǫŐ&$¾ƷɿB9&)ƂǁɿBǗŌƌǨ>

xn−1
5

A53

0

+ęʅ%>

0⎤⎡

KulyhEuZ+DuRtWn, Kalman(1960) )⎤n;!$Ǫ}??~ěěɹŦɣƷ+ȹɝ)9

d1

⎥⎢
⎥
⎥⎢
⎥
⎢ n ⎥
0 ⎥
⎥ ⎢ d3 ⎥ (18)⎥⎢⎥0 ⎦ ⎣ dn4 ⎦0 ⎥ ⎢ dn
2 ⎥

0

A54

dn
5

(18) Ő)Ŏ; )xn
j Bɹ <Žɹ)Ď !
$ū)(<2$ęʅȨŎ?-Ĩɀ+æƎęʅ,Ž
ĸ±ęʅ)(>+%ÎęʅBȝ²ǯɤ)Ñ8>
&%>+ÎęʅBɽɀ)ŐBkN_uȨŎ?-Ǝƽǰɧ?$(20) Ő)BÄǑ+ǨƎ&$>Ɍʇ+ǰɧʄ%,D n dn+ƌǨ);!$Ƙ>eFDVBĘɼ) ?

%Ƃǁɿ (ƣɹɿ) BƌǨɣƷ>&ɉ5%Ɍʇ%,(20) Ő& (23) Ő)ɐǑ+eFDVĜ˛ (p × 1 Ōþ) B  (26) Ő& (27) ŐB??TV]nɆǫŐ¾ƷɆǫŐ&Ƃǁɿ&ɐǑ+eF
DVBȻ$ƌǨ>KulyhEuZBȅȍ>&BĘxn = An xn−1 + D n dn

>ǨƎ

Ĝ D n dn BȹȮèȰȹɹp^u%ļǨ+ô(19)&(>?BTV]nɆǫŐ&$ŌŹ%ŧ2>

xn = An xn−1 + D n dn + B n ˛ + ‰n

(26)

y n = Hxn + C n ˛ + ” n(27))B n , (p × p) Ōþ+æƎęʅ%>ÂƩŐ

KulyhEuZ+ʆ+ŐBǰɧ>+ȜƑBŊ>8¾ƷɆǫŐ)9 C n ˛ (C :4.
4.1

*$hS3.5,3&w`

r × p Ōþ+æƎęʅ) +ĜB $~+ȅŦBę ot]:

4.2

u93.5,3&

lVMyLnNyUɇ+ƂǁkN_u xn (p × 1 ŌɐǑǨƎ ˛ BÁ7TV]nɆǫŐ)ƿ$,~þ) ,ŋĢ n &&9)Ƥéǯ)Ⱦ>ɿ%=œ)ŎǰKulyhEuZBɲɧ>+Ȝǯ(ɖȰ+ɹŦp^u%ïļ>ƵɆɹȍɿB dn (p × 1)
&$p^u+ȫ°ĜB ‰n BBȨā>TV]ndFW?-¦ɇ%>?,ƌǨ2Ƃǁɿ xn &ɐǑǨƎ
T T
˛ n BȻ$Ɔ(kN_u z n = [xTn ˛ n ] (2p × 1 Ōþ) BǨÌ+ z n BKulyhEuZ%Ō+;xn = An xn−1 + D n dn + ‰n

(20))ƌǨ>9+%> (Jazwinski, 1970)

+; )Ȩ&%>)An & D n , (p×p)

 
ẑ −
n = Φn ẑ n−1 + D n dn+ŌþBŊ"æƎęʅ%>5Ǧſ+KulyTP−z (n) = Φn P z (n − 1)Φn + Qn



hEuZ%, ‰n +șƃƖÈƑBǨ$+Åǀǐ&ÔȹĻęʅBŌ+;T−T
K z (n) = P −z (n)Ln Ln P z (n)Ln + Rn

)ƟǨ>




−

−1

(29)
(30)

E{‰n } = 0(21)ẑ n = ẑ −n + K z (n) y n − Ln ẑ n

(31)

E{‰n ‰Tm } = Qn δnm(22)

P z (n) = [I − K z (n)Ln ] P −
z (n)

(32)

)E{·} ,ÅǀǐƯĵBȨδnm ,Nwc\K+^uZ%=Qn ,TV]ndFW+ǅBȨɆ¾ƷkN_u y n (r × 1 Ōþ) ,æƎęʅ$~+;)ẑ n (2p × 1) , z n +ƌǨɿ%=K z (n)(2p × r) ,¯ǅTV]n+KulyQFyP −z (n) ,z +ÔȹĻęʅ%>ŽŐ+ ’ – ’ +ÉĞ, z n : P n(p × p) Ōþ+ęʅ%>
H n (r × p) Bɧ

(28)

)Ȩ

y n = H n xn + ” n(23)BƦŋ¿V]\j (n − 1) +ƀɄB9&)ƌǨ&
Bɏ>5˘n (2p × 2p)Ln (r × 2p)D n dn(2p × 1)Qn (2p × 2p) ,??¯ǅTV]n)>ƂǁƌęʅƂǁɿ <¾Ʒɿ1+Ⱦºęʅ)” n ,¾ƷdFW%=TV]ndFW&ȄÄǑ+ǨƎkN_uTV]ndFW+ÔȹĻęʅ%ɥșƃƖÈƑBǨ$Ō+;

=~+;)ƟǨ>

E(” n ) = 0(24)

E(” n ” Tm ) = Rn δnm

(25)

－5－



˘n =

)ǨÌ>



An

Bn

0

I


Ln = H n


Cn

(33)


D n dn =

4.3





D n dn

Qn =

0


Qn

0

0

0

(34)

+10& U n , V n , S n tAIX(2)eFDVBɓŃžğ+hEuZtyOƦĈ+ƌǨɿ x̃−n x̃n &eFDVÄǑ%>&Ǩžğ−|3.5,3&+hEuZtyOƦĈ+ƌǨɿ X̂ n X̂ n &+ÀæB−

ŽÉ+ǰKulyhEuZ,(26)(27) Ő%Ȩ
?>ì)$īǰƌǨɿBȇ>8+Ȝǯ(¦ɇ%>

ƂǁɿkN_u&+eFDV

kN_u?? (p × 1) +ŌþBŊ  " p ǅ(>Ɍʇ+ɛǇ)$,ïļ>ęʅ+ŌþX̂ n = x̃−n + U n˛

(44)X̂ n = x̃n + V n ˛(45)&ǨæƎęʅ U n & V n (p × p Ōþ) BÑ8>
&BĘ

>

−

X̃ n & x̃−n &+Àæ,(37)(42)(44)(45) Ő (2p × 2p) )¯ǅ>8ïļȯ¡ǅ(><

+ɛǇBġȳ>8Friedland (1969) ,ęʅ−X̂ n − x̃−n = U n˛+ŌþB (2p × 2p) )¯ǅ>&(ƂǁɿkN



_u xn &+eFDVkN_u ˛ B (p × p) +Ōþ= An X̂ n−1 − x̃n−1 + B n ˛+55%ūŌÑ8>ɆɇBǪ}$ >+Ɇɇ,

= (An V n−1 + B n ) ˛ȹɴKulyhEuZ&ą-?Friedland (1969) +Ǫ}~ě;=ȜɛǇ1+ǳª (ʄ-Hsieh&(>+%U n & V n−1 &+Àæ,
U n = An V n−1 + B n

and Chen, 1999 ; Ignagni, 2000) :Friedland (1969)&,(!Ɇɇ%+DuRtWn+ȅŦƈ8<?

(47)&Ȩ?>Ȅɥ)X̂ n & x̃n &+Àæ,(40)(43)(44)

$~%,Friedland (1969) )ȝ2$½óǯ
(ȅŦɆɇBŎ Igagni (1981) +Ɇɇ)Ť!$ȹ(46)(45) Ő

<

ɴKulyhEuZ+ȅŦ£ǫBǥ X̂ n − x̃n = V n ˛(1)−= X̂ n − x̃−
n + K̃ x (n) −H n (X̂ n − x̃n ) − C n ˛−*$Z cT@qcT3.

Ő) >ɐǑǨƎ+Ĝ (eFDVĜ) BɓŃžğ= U n − K̃ x (n) (H n U n + C n ) ˛ȹɴKulyhEuZBȅŦ>)=5 (26)

&(>

(35)

y n = H n xn + ” n(36)+ɛǇ)ƿeFDVĜBɓŃǦſ+Kulx̃−
n = An x̃n−1 + D n dn

(37)

−
−
P̃ x (n) = An P̃ x (n)ATn + Qx

(38)



−

T
K̃ x (n) = P̃ x (n)H T
n H n P̃ x (n)H n + Rn

P̃ x (n) =







−1
y n − H n x̃−n−
I − K̃ x (n)H n P̃ x (n)−1&ǨÌ?-V n & U n &+Àæ,V n = U n − K̃ x (n)S n(50)&(>(47)(49)(50) +ĸ"+ŐB6?-V n−1
ĸ"+ŐBĪÇǯ)¦&);=(44)(45) Ő)
> U n & V n BÑ8>&%>
(3)

(39)
(40)

β et



_u%=P̃ x (n) ,eFDVBɓŃ$ƌǨ x̃n3.5,3&ɐǑ+ǨƎĜ β BǗŌƌǨ>ɆǫŐB~)ȅŦ
>5˛ +ǶǉɆǫŐ,ˆ
ˆ− = ˛
˛
n
n−1

(41)

)x̃n ,eFDVBɓŃ$ƌǨƂǁɿkN&>˛ +¾ƷɆǫŐ)"(51)$,eFDVBɓŃžğ+FdkTryB~+;) r n (r × 1)&ǨÌ+ÔȹĻęʅ%>

r n = y n − H n x̃−n")eFDV ˛ ÄǑ%>žğBƭǨ>e−ƌǨɿ X̂ n & X̂ n ,−(42)X̂ n = An X̂ n−1 + D n dn + B n ˛−−X̂ n = X̂ n + K̃ x (n) y n − H n X̂ n − C n ˛ (43)−= y n − H n X̂ n − U n ˛FDVÄǑ%>&Ǩžğ+ƂǁkN_u+

+;

(49)

B9&) U n , S n , V n BÑ8>Ő)(!$ =+

)(>

−

(48)

Sn = H nU n + Cn

xn = An xn + D n dn + ‰n

5 S n (r × p Ōþ) B

+TV]nɆǫŐ&¾ƷɆǫŐBƭǨ>

x̃n = x̃−n + K̃ x (n)−5,3&z>yhEuZ,Ō+;




(52)

(52) Ő+ɀǆ 1 Ĝ&ǆ 2 Ĝ)?? −C n ˛ & C n ˛
B

?-



−

r n = y n − H n X̂ n − C n ˛+ (H n U n + C n ) ˛)Ȩ?>

－6－


(53)
(54)

= S n ˛ + vn

(55)

4.4

ȹɴKulyhEuZ,ęʅ+ŌþB¯ǅ>&(>+%+ (55) ŐB ˛ +¾ƷɆǫŐ&ûɷ$−>)v n , (y n − H n X̂ n − C n ˛) %ǨÌ>*$3.5,3&&(Ƃǁɿ&ɐǑǨƎBūŌƌǨ%>

p Ōþ+kN_u%=v n +ÔȹĻęʅ,Ō+;Œİ+ɛǇ%ğɳǯ(ƌǨɿBȇ>8),P x :)Ȩ?>

P β +ŬÅǐBǰƞ)ƟǨ>ȥɩ>?,Ž
ŧ+DuRtWnBĐ³ǯ(ɛǇ)ǰɧ>−T
E{v n v Tn } = H n P̃ x (n)H n + Rn

(56)ȹ)ɺ2ǵ%>

?;= ˛ BǗŌƌǨ>8+KulyhEuZ
,Ō+;

)(>
(57)

−

−
T
H n P̃ x (n)H T
n + S n P β (n)S n + Rn

ˆ − + K β (n) r n − S n ˛
ˆ−
ˆ =˛
˛
n
n
n



−1



<½ǋ(Ɇɇ%Ñ8;=|ǨhEuZty

O+DuRtWnBǪ}$
(58)
(59)



ȹɴKulyhEuZ+ɛ%eFDV+ÔȹĻęʅ P β BǇǵBŀǭPxT
K β (n) = P −β (n)S n ×



Dee and Da Silva (1998) ,ƌǨô P β +ŬÅǐ)ǅƺ>&P−
β (n) = P β (n − 1)%ţ>+DuRtWn,ȹɴKulyhEuZ&Ȅɥ)ęʅ+ŌþB (r ×r)
)ɫ

$ïļ

";=Ų(

řū%Ƃǁɿ&eF

DVBƌǨ>&%><)ƌǨeF

P β (n) = I − K β (n)S n P −β(60)DVBƂǁɿ+Ƕǉ)hE`e\N>&);−ŽŐ+Ǚ%P̃ x (n) & r n ,eFDVBɓŃKu=eFDVBɓŃKulyhEuZ+ïļBŸ

lyhEuZ%Ñ8>&%>5S n , (47)

ɸ%>;(49)(50) Ő%Ñ8>&%>"5=eFDV

DuRtWnBeFDVKulyhEuZ&;/ȹ

BɓŃKulyhEuZ% x̃ BƌǨeFDV

ɴKulyhEuZ+ʆ+ŐƌǨ+8+KulyhEuZ% ˛ BƌǨ?<

hEuZBȅŦ>+ǐB (42) Ő& (43) Ő)ǃȍ?-eFDVBɃƖƂǁɿ x̂−n x̂n BƌǨ>&%>

(4)

(61)

ˆ
x̂n = x̃n + V n ˛n(62)5 <+Íʇ%ɧ >eFDV (p ŌþkN−b−n ≡ E[x̃n − xn ](67)

&ǨÌ>bn , x +ƌǨɿ x̃ )Á7eFDV%=>&)Ǜ>(61) & (67) Ő

eFDVɃƖĈ+ƂǁɿkN_u&eFDVkN_
u+ÔȹĻęʅ P̂ x P̂ xβ ,~+Ő%ïļ%>−ˆb−n ≡ E[x̂n − xn ] − E[U n ˛ n−1 ]−−TP̂ x (n) = E{(x̂−n − xn )(x̂n − xn ) }−T= P̃ x (n) + U n P −β (n)U n−Tˆ−P̂ xβ (n) = E{(x̂−n − xn )(˛ n − ˛) }= U nP −β (n)= −U n ˛
(63)

(68)
(69)

+Àæ>+%hEuZtyOƦĈ+eFDVƌ
Ǩɿ,
−

(64)

P̂ x (n) = E{(xˆn − xn )(xˆn − xn )}= P̃ x (n) + V n P β (n)V Tn< b−n & ˛ &+¿),

(Igagni (1981)

(65)

(70)

ˆ UT
b̂n = U n ˛
n n

(71)

−

ˆ − ˛) }P̂ xβ (n) = E{(x̂n − xn )(˛n(66)~ŽB5&8>&ȹɴKulyhEuZ,(37)(72)

P̂ b (n) = −U n P̂ β (n)(73)") (49) & (50) Ő< (66) Ő%e< V n ,V n = U n − K̃ x (n)[H n U n + C n ]FDVBɃƖ>ʆ+DuRtWn%!( uZ);>ƌǨɿ&ɳʇǯ)ǖ>& Friedland−P̂ b (n) = −U n P̂ β (n)&(>< (41) Ő%eFDVBɓŃƌǨɿBÑ8(51)ȹɴKulyhEuZ+ƌǨɿ,ǰKulyhE−ˆ UTb̂n = U n ˛n n&(>5eFDVƌǨɿ+ÔȹĻęʅ,

T(1969) );!$źɕ?$<eFDVKuly

ȹɴKulyhEuZ+Ơɕ%ɧ  ˛ &,(!$*$hMB|WS< (60) Ő%eFDVBƌǨ(61)>Ɍʇ%,+_u) B

−ˆ−x̂−n = x̃n + U n ˛ n= V n P β (n))Đȭ(?$(74)&(=¾Ʒ),eFDV( &Ǩ ( C n = 0 ) ?-V n = [I − K̃ x (n)H n ]U n

>

－7－

(75)

&(>+ V n B (62) Ő)ǃȍ>&%eFD
VɃƖĈ+Ƃǁɿ x̂n +ƌǨŐB~+;

)ȇ>

B

ǐeFDVBɃƖĈ+Ƃǁɿ+ÔȹĻę−ʅ P̂ x (n) &(>&Bɏ>

&%>

ȹɴKulyhEuZ,+ P b )ƱǾ>eF
DV+ÔȹĻęʅBǗŌĕƆ>DuRtWn&(!

ˆx̂n = x̃n + V n ˛n$ >eFDVKulyhEuZ%,P b  P x

ˆ= x̃n + [I − K̃ x (n)H n ]U n ˛n&Ȅâ¿Ėƴ%Ƙ>&Ǩ(81) ŐBɧ $ P b= x̃n − [I − K̃ x (n)H n ]b̂n B½ǋ)ƌǨ>

−= x̃−n + K̃ x (n)[y − Hxn ]−P−b (n) = γ P̂ x (n)−[I − K̃ x (n)H n ]b̂n−−P̃ x (n) = (1 − γ)P̂ x (n)= x̃−n − b̂n+K̃ x (n)[y n − H n (x̃−n − b̂n )](81)−
%γ , P b & P̃ x +¶ğBò8>VKsɿ+f(76)

soZ%= 0< 1 +ǐB&>γ  1 )Ü?-

%x̃−n ,eFDVɃƖƦ+ɣƷƂǁɿ%>ƦeFDVƌǨ+KulyQFyƱƿǯ)ǅ(=ŧ+ȹɴKulyhEuZ%, x̃−n B (37) Ő%Ñ8¾Ʒɿ&ɣƷɿ&+ĩ+ƀɄ,ŗ)eFDV+ĕƆ)"5=eFDVĜBɓŃǦſ+KulyhEuɧZBŒę>&);= x̃n−1 BÑ8?BŬÅǐ

+KulyQFyƱƿǯ)ǅ(=¾Ʒɿ&ɣ&$ŋĢ n +ƂǁɿBɣƷɆeFDVKƷɿ&+ĩ+ƀɄ,ŗ)Ƃǁɿ+ĕƆ)ɧ

ulyhEuZ%,x̃−n BÑ8>İ)~+ŐBɧ(>(>&)(>Ɇγ  0 )Ü?-Ƃǁɿ>&)γ  0 +&,eFDV,ĕƆ?(+%eFDVKulyhEuZ+ƌǨô,eFD>x̃−n = An x̂n−1 + D n dn

(77)

?,eFDVɃƖĈ+Ƃǁɿ x̂n−1 BŬÅǐ&$x̃−n BɣƷ>&Bɏ>?);=īƆVBĘɼ(

Ǧſ+KulyhEuZ)(>~)eFDVKulyhEuZ+DuRtWnB
5&8>

+eFDVƌǨɿBƂǁɿ+ǶǉŐ)hE`e\N• Ƃǁɿ&eFDV+ɣƷx̃−n = An x̂n−1 + D n dn

(82)BŸɸ%>+%ȹɴKulyhEuZ)ȝ2$ï

−b̂n = b̂n−1(83)

ļ+řūŲ((>eFDVKulyhE• ɣƷô+eFDVɃƖ>&&9)eFDVBɓŃKulyhEuZ−

uZ+ƌǨô,+Ưĵ);=ũīǰƌǨ&(>&)Ǜȥɩ%> (Dee and Silva (1999))
bn BƌǨ>8+KulyQFy K b (n) ,(58)Ő+ɽɀ) −U n B´$K b (n) B U n K β (n) &ǨÌ?-TK b (n) = P −b (n)H n ×−−1[H n P̃ x (n)H n + H n P −b (n)H n + Rn ](78)

&$Ñ8>&%>Ȅɥ)(59) Ő+ɽɀ)−U n B´>&%b̂n +ĕƆɆǫŐ,Ō+;

)

(>
−

−
b̂n = b̂n − K b (n)(y n − H n x̃−
n + H n bn ) (79)~ŽeFDVKulyhEuZ)

>Ƃǁɿ

x̂n &eFDV b̂n +ƌǨɇ%>
<−−P̂ x (n) = P̃ x (n) + P −
b (n)

(84)

• ÔȹĻęʅ+ɣƷ−P̃ x (n) = An P̃ (n)ATn + Qx (n)−−1P̃ x (n)P̂ x (n) =
1−γ
−
γ
P−
b (n) = 1 − γ P̃ x (n)(80)+Àæ>?,eFDVBɓŃ$ƌǨƂ−ǁɿ+ÔȹĻęʅ P̃ x )eFDV+ÔȹĻęʅ P −
b

－8－

(85)
(86)
(87)

• eFDV+ĕƆT− T
Kb = P −b (n)H n [H n P b H n−−1+H n P̃ x H T
n + Rn ](88)−−b̂n = b̂n − K b [y n − H n (x̃−n − b̂n )](89)• Ƃǁɿ+ĕƆ
−K x = P̃ x (n)H T
n−eFDVBɃƖƂǁɿ+ÔȹĻęʅ,(63) &(79) Ő−x̂−n = x̃n − b̂n−1
×[H n P̃ x (n)H T
n + Rn ](90)

xn = (x̃−n − b̂n )+K x [y n − H n (x̃−n − b̂n )](91)• ÔȹĻęʅ+ĕƆ
−P̃ x (n) = [I − K̃ x (n)H n ]P̃ x

(92)

5.

*$3.5,3&wy Qfl
3!2%/

Katsura River Basin(833 km2)

lVMyLnNyUɇ);>ėƍǥƝïļ)eF
DVKulyhEuZBȅȍ>~)+Du
RtWnBƫ6ĥCđȹȮèɹŦɣƷTV]n)

Lake
Biwa

;>ɹɿɣƷ+áƾǯ(řūBŧ2>āıŋĢB n&n − 1 +hEuZtyOĈ+Ƃǁɿȇ<?$>Ƃ×BƭǨ>
Step 1 n − 1< n 5%+¾ƷěBȍř>

Tenryuji

Step 2 ®Ȱȹɹ)ǰɧȹȮèɹŦp^uBŒ

Kameoka

Katsuraę®Ȇßȹ1+ƵɆɹȍɿ dn Bïļ>
Step 3 lVMyLnNyUp^uBŒęŋĢ n+ƣɹɿ x̃−n Bïļ>

Gauging Sta.

Yodo River Basin(7,281 km2)−

Step 4 n-1 %Ñ8eFDV b̂n−1 (= b̂n ) B9&)
−−eFDVBɃƖ> (x̂−n = x̃n − b̂n )

−−Step 5 Ƃǁɿ+ÔȹĻęʅ P̃ x (n)P̂ x (n) &eF
DV+ÔȹĻęʅ P −b (n) Bïļ>

Step 6 ŋĢ n +¾Ʒɹɿ y Bȍř>

10 km

Fig. 3 Locations of gauging stations in the Katsura
River Basin

Step 7 (88) Ő < (92) ŐBŒęeFDVƂǁɿÔȹĻęʅBĕƆ>
Step 8 Step 2 %ȇɹŦp^u+Ƃǁɿ&Step 7%ĕƆȆp^u+ƂǁɿBŬÅƁö&$
n + 1 5%+ɣƷɹɿBïļBŒęStep 6 %ƍFky_ (1993 ȐFky_) +ȋ"Bïļƿżėƍ
&1992 ȐFky_,ĺėƍ%=1993 ȐF
ky_,ȵƎ+gNʆƹ>ėƍ%>

ƌǨeFDVB9&)ɣƷôBɃƖ>
Step 9 Step 7 %ȇeFDVɃƖĈ+ƂǁɿBŬÅ
ǐ&$n + 2 5%+ɣƷïļBŒęȄɥ)ɣƷôBeFDVɃƖ>+ɣƷïļBȥɩ&>t`ZFn5%ã=Ɂȍʁě)" $,ɹȉ 13zŭ%¾Ʒ?ǒŽɿ (ŋ¿ȹ¦ȑ: 1 ŋ¿) BīÜʂɇ%â¿ȉƮ
9+Bɧ

>hEuZtyOřɇ+ƑȑBɕ<)>&Ɍʇ+ɚǯ(+%ɣƷě)"ŒƜě&ȄěȹȮBɧƂǁɿ+ĕƆ)ɧ

6.

Hj7u6.1

na7IXdK$9>ƣɹɿ,Ȉ)Ǐ<(ă=ëǒǵǒǵ+¾Ʒɹɿ (ŋ¿ȹ¦ȑ: 1 ŋ¿) &6.2 (2) %Ëǒǵ+ɹɿBhEuZtyO)ɧ

eFDVKulhEuZBȅȍđȹȮèɹŦʄBŎ

ɣƷTV]nBëƣɹ (ëǒǵŽɹ: 833 km2 ) )eFDVKulyhEuZ+fsoZ)" $,T

ǰɧ>ïļƿżÅ¿+ 1992 Ȑ& 1993 ȐǾŋ,Ž

V]ndFW+ȹĻB 10 [m6 /s2 ]¾ƷdFW+ȹĻɹ)ŗɩ([nƺı(

B 100 [m6 /s2 ]eFDV+ÔȹĻęʅ+ǅBÈǨ+%ŏƧɹ×%ɣƷƑȑB÷ź%>5Fig. 3 )Ŏ;)ŗƣ

>fsoZ γ B 0.5 )ƟǨđȹȮèɹŦɣ)!$ȵƎ+ɹɿ¾Ʒŭƺı>+%ɹǍƷTV]n+fsoZ,Ä+ùÒ (ħĺ< 2005) %%hEuZtyOČ+Žɹ)Ï4Ø:ȵȄǨfsoZ&ȄǐBɧƎǒǵ+ɹɿBĕƆ)ɧ
>(



žğ+Č('Bȹƚ%đȹȮèɹŦɣƷTV]n,ëƣɹ+ȆɘB 193 +Ȇßȹ)ȹ¶$=eFDV

6.2

J;RU

(1)

*$hN;

KulyhEuZ+ŗ(ęʅïļ+Ōþ, (193 × 193))(>

Figure 4 ) 1992 Ȑ+ėƍFky_Bƿż)$eF
DVKulyhEuZBǰɧôBŎt`Ɍʇ+ǰɧʄ%,1992 Ȑ 8 õ 18 Ȍ 0 ŋ < 23 Ȍ

ZFnB?? 0, 1, 2, 3 ŋ¿&$ɣƷ&

0 ŋ5%+ 5 Ȍ¿+ėƍFky_ (1992 ȐFky_) &+ëǒǵ+ɹɿBŎ$

1993 Ȑ 8 õ 14 Ȍ 0 ŋ < 19 Ȍ 0 ŋ5%+ 5 Ȍ¿+ė

yhEuZ+ô (Bias ﬁlter) &ȝ²>8)e

－9－>5eFDVKul

800'92, Katsura, 0-hr

700

400

500
400
300
200

350
300
250
200
150
100

100
0

50
0

20

40

60

80

100

0

120

0

20

40

800

'92, Katsura, 1-hr

400

500
400
300
200

0

20

40

60
Time [hr]'92, Katsura, 2-hr

100

350
300
250
200
150

0

120

0

500

20

40

60
Time [hr]

400

500
400
300
200

80

100

120

Bias filter
Kalman filter
Observed
Simulated'93, Katsura, 2-hr

450Discharge [m3/s]

600
Discharge [m3/s]

80Bias filter
Kalman filter
Observed
Simulated

700

350
300
250
200
150
100

100

50
0

20

40

60

80

100

0

120

0

20

40

Time [hr]800'92, Katsura, 3-hr

500

Bias filter
Kalman filter
Observed
Simulated

700

60Time [hr]

400

500
400
300
200

80

100

120

Bias filter
Kalman filter
Observed
Simulated'93, Katsura, 3-hr

450Discharge [m3/s]

600
Discharge [m3/s]

120

50

800

350
300
250
200
150
100

100
0

100

100

100

0

80

Bias filter
Kalman filter
Observed
Simulated'93, Katsura, 1-hr

450Discharge [m3/s]

600
Discharge [m3/s]

500

Bias filter
Kalman filter
Observed
Simulated

700

60Time [hr]Time [hr]0Bias filter
Kalman filter
Observed
Simulated
Bias'93, Katsura, 0-hr

450Discharge [m3/s]

600
Discharge [m3/s]

500

Bias filter
Kalman filter
Observed
Simulated
Bias

50
0

20

40

60

80

100

0

120

Time [hr]

0

20

40

60
Time [hr]

80

100

120

Fig. 4 Analysis (0-hr) and predictions with 1, 2, 3-hr
lead time for 1992 event at Katsura

Fig. 5 Analysis (0-hr) and predictions with 1, 2, 3-hr
lead time for 1993 event at KatsuraFDVBĘɼ( Ǧſ+KulyhEuZ (KalmanƌǨëǒǵ+eFDV (Bias) 9ȻÉ$>ﬁlter) &JhsFyTmqvTry (Simulated) +5hEuZtyOǣĈ+¦ƚô)ǘɚ>&ôBȻ$Ŏt`ZFn 0 ŋ¿+ɣƷ(eFDVKulyhEuZ&Ǧſ+KulyhEuZA hEuZtyOǣĈ+¦ƚôBŎfcu),

&+－ 10 －,3&C'û<??9¾Ʒɹɿ)Ü

'92, Tenryuji, 3-hr

700
600
500

400

400
300
200

350
300
250
200
150
100

100
0

Bias filter (g = 0.25)
Bias filter (g = 0.50)
Bias filter (g = 0.75)
Bias (g = 0.25)
Bias (g = 0.50)
Bias (g = 0.75)
Observed'93, Katsura, 3-hr

450

3Discharge [m3/s]

500

Bias filter
Kalman filter
Bias filter (two stations)
Kalman filter (two stations)Observed
Simulate

Discharge [m /s]

800

50
0

20

40

60

80

100

0

120

0

20

40

60

Time [hr]

80

100

120

Time [hr]Fig. 6 Prediction results with 3-hr lead time. Comparison of the results ﬁltered with observed discharge only at Katsura and both at Katsura
and Kameoka (two stations).

Fig. 7 Eﬀect of the parameter γ on prediction resultwith 3-hr lead time and bias estimationªľ < 40 ŋ¿Ĉ~ě,eFDVBĘɼ>Č
ǐB&!$

>&A

>hEuZtyOBŒ

ęĈ+ƣɹɿ,TV]ndFW&¾ƷdFW
+ǅB

)&>

)ƺ$

=+ïļʄ%,¾ƷdFWBƱƿǯ)űƟǨ$ >8)
¦ƚô¾Ʒɹɿ)Ü

ǐ)(!$>ƌǨ

eFDV+ŋìʅ,¬*JhsFyTmqvTr,!=&ā?>30 ŋ¿Ĉ+gNƦĈ%,ėƍ+ɷ
B&!$

Ž=Ȱ%ƌǨeFDVƖ+ǐ>+)ƿgNŋ+JhsFyTmqvTry¾Ʒô)Ü
ûƛ9>ô)(!$(2)+%ɣƷôBű>brv,3&25

N;>eFDV

Figure 6 ,t`ZFnB 3 ŋ¿&žğ+ǲ

+ǅ,ʄ -gN)Ü ïļªľĈ 40 ŋ¿+ɻŉǒǵ) >ɣƷô%>ëǒǵ+ɞ 5 km Žô%û?-eFDVɞ 70 m3 /sJhsFy&ɹ)ǲɻŉǒǵ,Ǖ>eFDVɃƖB>žğ

¾Ʒɹɿ&+ĩɞ 100 m3 /s %>&(

y&¾Ʒɹɿ+ĩ+ŋìʅ)ʃņ$<JhsFžğ5ëǒǵ%ɹɿBĕƆ>ž

y&¾Ʒɹɿ&+ĩ+ɞ 7 ¶ǫǹ%ƌ$ >&ğ&ǲɻŉ <ɞ 10 km Žɹ+Ëǒǵ%9ɹɿBĕ)(>Ɔ>žğ)" $4 Śʃ+ïļôBŎ$ >Ō)ɣƷô)ǘɚ>t`ZFn 1 ŋ¿+ëǒǵ%ɹɿBĕƆ>žğ)5ǘɚ>&žğeFDVBĘɼ>&);!$ėƍ+ɷ Ž

eFDVKulyhEuZ+ô,JhsFyTmq

=Ȱ:ǬÿȰ+ɣƷ¾Ʒɹɿ)Ü#5g

vTry+?;=¾Ʒɹɿ)Ü#NǣƦ9eFDVBĘɼ>&);!$ɣƷôȹɆŝƖ?¾Ʒɹɿ)Ü#B÷Ǒ&Žɹǒǵ+ɣƷ)9ČBÏ4$>ɣƷ+t`ZFn 3 ŋ¿+žğ)ǘɚ>&eFDVBĘɼ( Ǧſ+KulyhEuZ+ɣƷ,

$

>&

>?,ɹëǒǵ%ɹŦp^u+eFDV

&Bɏ>5Žɹ+Ëǒǵ)9¾ƷƀɄ>žğ),<)ɣƷôĎŽ>
Ɍʇ%ę!TmqvTry,hEuZtyO+

JhsFyTmqvTry+ô&34ǖhE
uZtyO+Čû<?( &A >?,

÷źBɚǯ&$¾ƷƀɄB9&)ƣɹɿBĕƆ&$93 ŋ¿Ɛă$ïļí£?-ƣ+ɹɿœɖȰ+ɹŦp^u)ǅ

,ȑ(ă=ƽǒǵ+Ƅɮ%>¾ƷɹɿBɧƺ>8%>?)ƿ$eFDVK

hEuZtyO?-;

ulyhEuZ,ɹŦp^u)Ê>eFDVBǗ

ɹɿ¾Ʒɓ

ŌƌǨ$ƣɹɿ+ɣƷBɃƖ>+%t`+ȊZFn 3 ŋ¿+žğ%9hEuZtyO+Čā

hEuZBȅȍȹȮèɹŦp^uBɧ?>;=°ǹ+ĝ ėƍɣƷBŒā%>ȑƑ>Ȅɥ+çĎ, Fig. 5 )Ŏ 1993 ȐFky_+ô

(3)

%9û<?>Ȉ)JhsFyTmqvTry+ôîƹǯ)¾Ʒɹɿ;=9ǅ(!$

>ïļ

>+%

$ɧ

>¾ƷɹɿBėƍɣƷ+Œɒ)$$

hEuZtyO+Č,Žɹǒǵ)9Ï0+%ŤɭėƍɣƷ!Ǚűƣ)+10& γ 8C$9eFDVKuly>&)eFDVKulyhEuZ),eFDV+ÔȹĻęʅ+ǅBò8> γ &－ 11 －

fsoZ>Žŧ

500
400
Discharge [m3/s]

9ɟ?$

0-hr
1-hr
2-hr
3-hr
Observed
Simulated'93, Katsura, Augumented Filter

450
350

>&

ɽŔ+řɇ+>,ŗ)ɐǑǨƎĜ (eFDVĜ)+ÔȹĻęʅ+Ř={300)=¯ǅTV]n);>KulyhEuZ,?BǗŌĕƆ$ +)ƿ250

eFDVKulyhEuZ%,Ƃǁɿ+ÔȹĻęʅ&200

Ȅâ¿ĖƴBŊ"&Ǩ$ƌǨ$

150
100

Ɇɇ,ɳʇǯ),Ɩ50

ulyhEuZ+ʄ%,ǗŌïļ$Ñ8ÔȹĻ

0

0

20

40

60

80

100

&

>ƦŔ+

>Ħ§+ǰK

ęʅ+ǐŬÅǐ&3&C'Ȅǐ%>&B°

120

Time [hr]ȏ$Fig. 8 Prediction results for 1993 event at Katsura
with Adaptive Kalman Filter=ŬÅǐ+ƟǨɐǑǨƎĜ+ƌǨ)ǅØBÏ4ȑƑ>ɹŦɣƷ+Œɒ%,ǢÅ)A!$ʆƹǯ)ɣƷ&hEuZtyOBã=Ɂȥɩ=ŬÅǐ)ǅƺ(

eFDV

KulyhEuZ+Ɇɇ,;=Œɧǯ(řɇ%>&+TmqvTry%,+ǐB 0.5 )ƟǨ
%,γ +ǐB$ɣƷïļBę?ɣ

Ʒô)Ï4ØBĘķ>
Figure 7 , 1993 Ȑ+ėƍBƿż)t`ZFnĘ>5;=ǅ(ɹ1+ǳªBƭǨžğ)ęʅïļ+Ōþ¯ǅ(&

DVKulyhEuZ+ȈǢ&

>

7.

ǵ9eF



3 ŋ¿+ɣƷô%>γ B 0.250.50.75 &Ⱦ$ïļ$ >γ ǅ(?- P b ǅ(=đȹȮèɹŦɣƷTV]n+¾Ʒɹɿ^ZȄ

KulyhEuZ%eFDVƌǨɿBĕƆ>İ)¾

řɇ&$Ȇɘ)ǰɧlVMyLnNyUp

ƷB;=ťŃ>&)(>"5=γ ǅ3^u+hEuZtyOɇBǪ}~)Ɍʇ%Ŏ

eFDV,;=Ȫ)Ⱦ>+çĎ,eřɇ+¬ɩ&TmqvTry+ôʇB5&8>

FDV+ƌǨô (Bias)<°ȏ%>+

,?3'üǜ%,( );>ɣƷô+γ +ǐ,íýǯ)òǨ>
%, γ = 0.5 &$(4)(Ɍʇ+ǰɧʄ$Ȉ)ɛǇ,(&Ę>u93.5,3&z>ɣƷô+<ȓƘɆɇ%=ɽŔ+Bȝ²$B9&)â¿ȹȮ>ƣɹɿ+ŋ¿ƌBęʅŐ%Ȩā>ɆɇBŎ
2. lVMyLnNyUɇ%ɣƷ>ƣɹɿBhE
uZtyO%ĕƆ>ƿż&5ɹŦpeFDVKulyhEuZ,4. )Ŏ; )ǰKulyhEuZ

1. ïļ|ǨřɇBȅȍlVMyLnNyUɇ

ȥɩ>Figure 8^u)Ê>eFDVBTV]nɆǫŐ) ƣɹɿ&&9)ƌǨ2ƿż&
3. Ƃǁɿ&&9)ɐǑǨƎBƌǨ>hEuZty,1993 Ȑ+ėƍFky_Bƿż)ǰKulyhEOɇ&$ǰKulyhEuZBŎuZ);>ëǒǵ+ɣƷôBŎ$>ïļªľ

%+ǃǂɇ&$ęʅ+ŌþB¯ǅ)< 40 ŋ¿Ĉ)ā?>ėƍ+gNȬÜƂǁɿ&ɐǑǨƎBƌǨ>ȹɴKulyhEu

Ĉ 30 ŋ¿Ĉ,eFDVKulyhEuZ+;)£űȩB

Z+ȅŦBŎ<)eFDV+ƌǨɛǇ>&9(ǰKulyhEuZ+ɣƷô,ɾ)Ȉ$;=ïļČɶBĝ8Ɇɇ&$e

ď%>5Fig. 4 )ŎǦſ+KulyhEu
Z (Kalman ﬁlter) )ȝ2$®t`ZFn%ǰK
ulyhEuZ+ɣƷ¾Ʒɹɿ&Ü#
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ÓǸǅ³ɊĭùÒŭȐɄ, 49, B, pp. 13 – 26.

ɇ,ȵƎǒǵ+ɹɿ¾ƷƀɄBȄDuRtWɷƣĒƉǊ Ăʊ ­ (2004) : ɈʈȫɈʈɹ?

n%Ȅ>&%$ɹɿƀɄBƳ:+ÆĖBȅȍɹɿɹƛÀæŐ+ªȚ, ƍĐ³ʇȺ
Š, ǆ 48 ¸, pp. 7 – 12.

&);!$ɣƷôĎŽ>ŅʄBŎ)Ɍʇ%Ǫ}Ɇɇ,ɹŦp^uÖɌőŞʉ ǠȭƔƗ (1992) : ėƍɹŦɣƷ))Ê>ɣƷ+eFDVBKulyhEuZ+D

>Œİǯ¢Ǉ&+¦òɇ, ƍĐ³ʇȺŠ, ǆ 36~Ž+;¸, pp. 567 – 572.

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9+%>ĦĈ,+řɇBɬƣƨɹȌɝ¹ɢ (1974) : ƍȺɹŦìɣƷ1+KulyhEƾ)ǰɧ>&&9)ȂǙ+tDuZFnɣƷTuZɳʇ+ǰɧ, Ǻə³¥ʇȺɄģŠ, ǆ 221 Ğ,V]n)ȅȍ>ɣǨ%>

pp. 39 – 47.

ɃƖBęȁǷ ÙǅǽŞċŽĳ äǤɨŢƕɷƣĒƉĿ_\ƣ  (2001) : ȹȮèɹŦp^u)Â#[nɹȍɿŒŋ¿ɣƷp^u)"ɌùÒ,³ùÒȟɃůÝŖřùÒ (B) 18760373(ǃȨ: ħĺêɦ)

pp. 115 – 120.

;/ (Ĳ) ƣ»Õ¼ɳĲǎƣƓȢÂÝůƒŅÚ+ɃůBȇ5)É$$, ƍĐ³ʇȺŠ, ǆ 45 ¸,ɵ ʋʍűǔŨɢưƣǱƘ (1999) : Multi-step, Multireach Muskingum-Cunge ɇBɧ ȹȮèƍȺp^ŕBƇŽ5

u+ªȚ, ƍȺƍńĀ³¥Vol. 12, No. 5, pp. 384

VR}L– 390.

ǔȷśǤɨŢƕɅ ­ɷƣĒƉ (2006) : IV

Dee, D.P. and Da Silva, A.M. (1998) : Data assimilation in the precense of forecast bias, Q.J.R. Meteo-ƍȺ³, ǠƬŮǴ.

rol. Soc., 124, pp. 269 – 295.

Ŀƣ ƻŽŰȆɷƣĒƉǤɨŢƕ (2001) : ɹǒé+Ɔ(ƎɳȨāéŐ)Â#ɹɹŦìTEvansen, G. (1994) : Sequential data assimilation withmqvTryTV]n+ªȚ, Ǻə³¥ʇȺŠ, No.

a nonlinear quasi-geostrophic model using Monte691 / II - 57, pp. 42 – 52.

Carlo methods to forecast error statistics, J. Geophys. Res., 99, pp. 10,143 – 10,162.

(Ĳ) ɋ¨ȆƣɊĭùÒXyZùÒŭ (2006) : Œ

Freed, D. L. and Ming, J. (1993) : A Kalman ﬁlter en-ƥɹŦ¦ƚYm [ĚÌ]MV_ȿ].
ħĺêɦɷƣĒƉʊ ­Ŀƣ  (2005) : đȹ

hanced real-time dynamic ﬂood routine model. InȮèɹŦɣƷTV]n+ªȚ&[nåōƍČ+ȩ

Proceedings of XXV Congress of International Association for Hydraulic Research, Tokyo.

, Ǻə³¥ʇȺŠ, No. 803 / II - 73, pp. 13 – 27.
ĝʌǈȖǤɨŢƕ (1980) : Ƃǁâ¿ɇ);>ɹŦɣFriedland, B. (1969) : Treatment of bias in recursive

Ʒ - kinematic wave ɇBǙƅ&$ -, ÓǸǅ³Ɋĭ

ﬁltering, IEEE Trans. on Automatic Control, Vol.

ùÒŭȐɄ, ǆ 23 Ğ, B-2, pp. 211 – 226.

14, No. 4, pp. 359 – 367.

ĝʌǈȖǤɨŢƕɅ ­ (1982a) : ŠǙèɹŦp^

Hsieh, C. and Chen F. (1999) : Optimal solution ofu+Ėƒ&ɹŦɣƷřɇ, ÓǸǅ³ɊĭùÒŭȐɄ,the two-stage Kalman estimator, IEEE Trans. on

ǆ 25 Ğ, B-2, pp. 221 – 243.

Automatic Control, Vol. 44, No. 1, pp. 194 – 199.

ĝʌǈȖǤɨŢƕɅ ­ (1982b) : ǝɺp^u);

Ignagni, M. (1981) : An alternate derivation and ex->Œŋ¿ɹŦɣƷ)À>ÂƩǯùÒ, ÓǸǅ³Ɋĭtension of Friedland’s two-stage Kalman estimator,ùÒŭȐɄǆ 25 Ğ, B-2, pp. 245 – 267.

Vol. 26, No. 3, pp. 746 – 750.

ĝʌǈȖǤɨŢƕɅ ­ (1983) : ȵğɹ) >

Ignagni, M. (2000) :Optimal and suboptimalėƍɹŦ+°ɶɣƷřɇ, ÓǸǅ³ɊĭùÒŭȐɄ,separate-bias Kalman estimators for a stochastic

ǆ 26 Ğ, B-2, pp. 181 – 196.

bias, Vol. 45, No. 3, pp. 547 – 551.

Ʌ ­ĝʌǈȖǤɨŢƕ (1984) : ėƍɹŦ+°ɶɣ
Ʒ)Jazwinski, A. H. (1970) : Stochastic processes and ﬁltering theory, Academic Press, New York.

>Œİǯřɇǆ 28 §ƍɳĚ¥ʇȺŠ,

pp. 415 – 422.

Kalman, R. E. (1960) : A new approach to linear ﬁl-－ 13 －

tering and prediction problems, J. of. Basic Engi-

assimilation of radar-based precipitation data andneering, 82, pp. 35 – 45.

streamﬂow observations into a distributed hydrolog-

Kim, S., Tachikawa, Y. and Takara, K. (2007) : Ap-

ical model, Proc. of symposium HS03 held during

plying a recursive update algorithm to a distributed

IUGG2003 at Sapporo, July 2003, IAHS Publ., no.

hydrologic model, Journal of hydrologic engineering,

282, pp. 138 – 142.

ASCE, Vol. 12, No. 3, pp. 336 – 344.

Shiiba, M., Laurenson, X. and Tachikawa Y. (2000)

Kitandis, P. K. and Bras, R. L. (1980) : Real-time: Real-time stage and discharge estimation by aforecasting with a conceptual hydrologic model 1.

stochastic-dynamic ﬂood routing model, Hydrol.

analysis of uncertainty, Water Resour. Res., Vol.

Process., 14, pp. 481 – 495.

16, No. 6, pp. 1025 – 1033.

Weerts, A. H. and El Serafy, G. Y. H. (2006) : Particle

Moradkhani, H. M., Hsu, K. L., Gupta, H. andﬁltering and ensemble Kalman ﬁltering for state up-

Sorooshian, S. (2005) : Uncertainty assessment of

dating with hydrological conceptual rainfall-runoﬀ

hydrologic model states and parameters: sequential

models, Water Resourc. Res., Vol. 42, W09403.

data assimilation using the particle ﬁlter, Water Re-

Wohling, T. and Lennartz, F. and Zappa M. (2006) :sour. Res., Vol. 41, W05012.

Technical note: updating procedure for ﬂood fore-

O’Connell, P. E. and Clarke, R. T. (1981) : Adap-

casting with conceptual HBV-type models, Hydrol.

tive hydrological forecasting - a review, Hydrol. Sci.
Bull., Vol. 26, No. 2, pp. 179 – 205.

Earth Syst. Sci., Vol. 10, pp. 783 – 788.
Wood, E. F. and Szollosi-Nagy, A. (1978) :An

Refsgaard, J. C. (1997) : Validation and intercompar-

adaptive algorithm for analyzing short-term struc-ison of diﬀerent updating procedures for real-time

tual and parameter changes in hydrologic prediction

forecasting, Nord. Hydro., Vol. 28, pp. 65 – 84.

models, Water Resourc. Res., Vol. 14, No. 4, pp.

Romanowicz, R. J., Young, P. C. and Beven, K. J.

577 – 581.

(2006) : Data assimilation and adaptive forecasting

Vrugt, J. A. and Robinson B. A. (2007) : Treatmentof water levels in the river Severn catchment, Unitedof uncertainty using ensemble methods: comparison

Kingdom, Water Resourc. Res., Vol. 42, W06407.

of sequential data assimilation and Bayesian modelSeo, D. J., Koren V. and Cajina, N. (2003) : Real-time

averaging, Water Resourc. Res., Vol. 43, W01411.

Real-time Flood Forecasting Incorporating Kalman Filter with Bias Correction

Takahiro SAYAMA, Yasuto TACHIKAWA*, Tomoyuki HIRATA** and Kaoru TAKARA*Graduate School of Urban and Environment Engineering, Kyoto University**Nomura Research Institute
Synopsis
As a data assimilation method of a distributed rainfall-runoﬀ ﬂood prediction system and river discharge observation data, this study proposes a ﬁltering method of Muskingum Cunge river routing models.
Application of the conventional Kalman ﬁlter to river routing models is not eﬀective because hillslopemodels have signiﬁcant impact on the ﬂood predictions. In order to overcome this problem, the proposed
method estimates biases induced by rainfall-runoﬀ models as well as state variables in the ﬁltering algorithm, so that the ﬁltering has eﬀect on the predictions with lead time of few hours. Demonstrated ﬂood
predictions at the Katsura river basin show that the bias correction improves the accuracy.
Keywords:distributed rainfall-runoﬀ model, Muskingum Cunge, ﬂood prediction, data assimilation－ 14 －