Development of Rating Curve for High Water Level in an Urban Stream using Monte Carlo Simulation

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* ᕽᬙ᜽พݡ⦺Ʊ ☁༊Ŗ⦺ŝ ᩑǍƱᙹ ([email protected])

Received March 26 2013, Revised April 16 2013, Accepted May 6 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵ǤͶǤͳͶ͵͵ ǤǤǤ

Prqwh#Fduor#Vlpxodwlrqⴂ#ⴲⱧ㬚#ᦂ⢚㬖㉚ⴖ#ኞ⟖Ⳃ#Udwlqj#Fxuyh#ᇚ⇚

׌ஂজȵଗট֫ȵࢂઽଵ

Jong-Suk Kim*, Sun-Kwon Yoon**, Young-Il Moon***

Development of Rating Curve for High Water Level in an Urban Stream using Monte Carlo Simulation

ABSTRACT

In this study, we proposed a methodology to develop Rating Curves for high water level using rainfall generation by the Monte Carlo Simulation (MCS) technique, optimized rainfall-runoff model, and flood routing model in an urban stream. The developed stage discharge Rating Curve based on observed data was contained flow measurement errors and uncertainties. The standard error (Se) for observations was 0.056, and the random uncertainty (2Smr) was analyzed by ± 1.43% on average, and up to ±4.27%. Moreover, it was found that the Rating Curve extensions by way of logarithmic and Stevens methods were overestimated to compare with the urban basin scale. Finally, we confirmed that the high water level extension by random generation of hydrological data using MCS can be reduced uncertainty of the high water level, and it will consider as a more reliable approach for high water level extension. In the near future, this results can be applied to real-time flood alert system for urban streams through construction of the high water level extension system using MCS procedures.

Key words : Monte Carlo Simulation, Urban Stream, Rating Curve, High Water Level

Ⅹಾ

ᅙᩑǍᨱᕽ۵ࠥ᜽⦹⃽ᮥݡᔢᮝಽMonte Carlo Simulation (MCS)ᨱ᮹⦽༉᮹ၽᔾʑჶᱢᬊᮝಽ↽ᱢ⪵ࡽvᬑ-ᮁ⇽༉⩶ŝ⪮ᙹ᭥⇵ᱢ

༉⩶ᩑĥෝ☖⦽Łᙹ᭥Rating Curve ᯲ᖒჶᮥᱽᦩ⦹ᩡ݅. ݡᔢᮁᩎ᮹š⊂ᯱഭಽᇡ░᯲ᖒࡽᙹ᭥-ᮁపłᖁ᜾ᮡᮁప⊂ᱶ᮹᪅₉᪡޵ᇩ ᨕŁᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥԕ⡍⦹Łᯩᮭᮥ⪶ᯙ⧁ᙹᯩᨩᮝ໑, š⊂⊹᪡᮹⢽ᵡ᪅₉(Se)۵0.056ᮝಽ, ྕ᯲᭥ᇩ⪶ᝅᖒ(2Smr)ᮡ⠪Ɂ±

1.43%, ↽ݡ± 4.27%ಽᇥᕾࡹᨩ݅. ੱ⦽, ᱥݡᙹḡჶŝStevensႊჶᨱ᮹⦽Łᙹ᭥ᩑᰆᮡࠥ᜽⦹⃽ᮁᩎȽ༉ᨱእ⦹ᩍᙹ᭥ᨱ঑ෙ⪮ᙹప ᯕŝݡᔑᱶࡹ۵ྙᱽᱱᯕᯩ۵äᮝಽᇥᕾࡹᨩ݅. ษḡสᮝಽ, MCSᨱ᮹⦽݅ప᮹ᙹྙᯱഭǑ⪶ᅕෝ☖⦽ᙹ᭥-ᮁపšĥłᖁ᮹ᩑᰆႊჶ

ᮡŁᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥqᗭ᜽⍽໑, ᅕ݅ᝁ഑ᖒᯩ۵Łᙹ᭥ᩑᰆᯕa܆⦹ᩡ݅. ⨆⬥ᅙᩑǍ᮹đŝ۵MCSᨱ᮹⦽Łᙹ᭥ᩑᰆ᜽ᜅ

áᔪᨕ MCS, ࠥ᜽⦹⃽, ᙹ᭥-ᮁపšĥłᖁ, Łᙹ᭥ᩑᰆ

1. ᕽು

and Ray 1966; Rantz et al. 1982; Clarke 1999). ᙹ᭥-ᮁపšĥ łᖁ᮹ }ၽ ၰ ᅕᱶᮡ š⊂ᯕ ᬊᯕ⦽ ᙹ᭥ෝ ⊂ᱶ⧉ᮝಽᕽ

սėॡ

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Fig. 1. Flow chart of high water level Rating Curves using MCS procedure

ᮁపᮥᛞíᔑᱶ⧁ᙹᯩ݅۵ߑᰆᱱᮥaḡŁᯩᮝ໑, vᬑ-ᮁ

⇽༉⩶᮹᯦ಆᯱഭǍ⇶ၰá᷾ᯱഭಽᕽ⪽ᬊࡹŁᯩ݅. ੱ⦽

Ñ᜽ᱢᯙᙹᯱᬱšญၰĥ⫮ᮥ᭥⦽ʑⅩᯱഭaࡹ໑, ⇶⃺ࡽ

⦹⃽ᬕᬊᨱࠥᔍᬊࢁᙹᯩ݅(DeGagne et. al. 1996; Moyeed and Clarke 2005; Apel et al. 2006). ၙǎŝ ᮁ౞, ᯝᅙ॒

ݡᇡᇥ᮹ᖁḥǎᨱᕽ۵⦹⃽᮹ᮁప⊂ᱶᨱᯩᨕฯᮡיಆᮥ

ʑᬙᯕŁᯩᮝ໑, ๅ֥⪮ᙹʑᙹ᭥-ᮁపš⊂॒ʑⅩᯱഭᙹḲ ᨱฯᮡ⚍ᯱෝ⦹Łᯩ݅. ᙹ᭥-ᮁపšĥᨱݡ⦽ᩑǍ۵19ᖙʑ ᇡ░ᅙĊᱢᮝಽ᜽᯲ࡹᨩᮝ໑20ᖙʑᱥၹᇡᨱ۵ฯᮡʑᚁᱢ

ၽᱥᮥᯕൊ⦹ᩡ݅. ⩥ᰍḡᙹ⩶┽᮹ᙹ᭥-ᮁపšĥłᖁ᜾ᮡ

aᰆձญ᦭ಅᲙᯩŁ, ⦹ӹ᮹ḡᙹ᜾ᮝಽ✚ᱶḡᱱ᮹ᮁపᮥ

ᇥᕾ⧁ᙹᨧᮥĞᬑᨱ۵ᙹ᭥ෝᩍ్ǍeᮝಽǍᇥ⦹ᩍbb᮹

Ǎeᨱbʑ݅ෙḡᙹ᜾ᮥᱢᬊ⦹Łᯩ݅(ISO, 1998). ə్ӹ, ᯕ్⦽ᩑǍ}ၽ᮹ḡᗮᱢᯙၽᱥᨱࠥᇩǍ⦹Łᙹ᭥-ᮁపšĥ łᖁ᜾᮹⩶┽ၰྜྷญᱢ᮹ၙ᪡ʑ᳕ႊჶ᮹ྙᱽᱱၰ}ᖁႊᦩ ᨱ ݡ⦽ ᩑǍ۵ əญ ฯḡ ᦫᮡ ᝅᱶᯕ݅.

ǎ᫙᮹Ğᬑ, Bailey and Ray (1966)۵ᙹ᭥-ᮁపšĥ᮹

}ၽ⪚ᮡłᖁ᜾ᮥǍ⦹ʑ᭥⧕⦹ඹᇡ᮹ᙹ᭥-ᮁపšĥෝ

⇵ᱶ⦹Łᔢඹᇡ᮹ᙹ᭥š⊂ᗭʭḡᙹ໕⩶ᮥ⇵ᱢ⦹۵ႊ᜾᮹

⇶₉-႑ᙹႊჶᮥᱽᦩ⦹ᩡᮝ໑, Rantz (1982)۵℉ࢱᮁప᮹

ᔑᱶᯕaᬊ⦹ḡᦫᮥĞᬑ↽ݡš⊂ᮁప᮹2႑ᯕᔢᮥ᫙ᔞ⧁

ᙹ ᨧ݅۵ ᳑Õᮥ ᱥᱽಽ ᙹ᭥-ᮁపšĥłᖁ᮹ ᩑᰆᨱ ݡ⦽

ႊჶᮥᱽᦩ⦽ၵᯩ݅. DeGagne et. al. (1996)ᮡᙹ᭥-ᮁప

šĥłᖁ᮹ᩑᰆᮥ᭥⧕Ğ⨹ᱢᱢ⧊༉⩶ŝ࠺ᙹၹĞŝ⠪Ɂᮁ

ᗮe᮹ Ğ⨹ᱢ ༉⩶ŝ Manning᮹ ႊᱶ᜾ᮥ ᯕᬊ⦽ ᩑᰆᮥ

ᱽᦩ⦹ᩡ݅. Clarke (1999)۵ᙹ᭥-ᮁపšĥłᖁ᮹ᱢ⧊⇵ᱶ

᜾᮹ๅ}ᄡᙹᔑᱶᮝಽᇡ░ᩑe⠪Ɂ⪮ᙹప⇵ᱶ᮹ᇩ⪶ᝅᖒ

ᮥ ᇥᕾ⦹ᩡᮝ໑, Moyeed and Clarke (2005)۵ Bayesian MCMC (Markov Chain Monte Carlo) ᱢ⧊ʑჶᮥᯕᬊ⦹ᩍ

ᙹ᭥-ᮁపšĥłᖁ᜾᮹ๅ}ᄡᙹ⇵ᱶŝᇩ⪶ᝅᖒᮥᇥᕾ⦽ၵ

ᯩ݅. Apel et al. (2006)ᮡ German Research Network National Disaster projectෝ ☖⦹ᩍ ࠦᯝ᮹ Rhine Riverෝ

ݡᔢᮝಽMonte Carlo Simulation ႊჶᨱ᮹⦹ᩍWeibull- distributionᮝಽ༉᮹ၽᔾ᜽┕ᮝಽᱽႊ᮹❭ƕ⪶ශᮥᔑᱶ⦹

ᩍ⪮ᙹ᭥⨹ࠥෝᇥᕾ⦹ᩡᮝ໑, Afshar et al. (2009)۵Genetic Alforithms ʑჶŝMonte Carlo Simulationᨱ᮹⦽᭥⨹ࠥ

ʑၹ ↽ᱢ᮹ ⪮ᙹ᭥ ⇵ᱢ ʑჶᮥ ᱽᦩ⦹ᩡ݅.

ǎԕ᮹Ğᬑ, Yoo (1999)۵ɩvᙹĥ᮹4}ᵝ᫵ᙹ᭥⢽ḡᱱ ᨱ ݡ⦹ᩍ ⦹⃽ ᮁᙹ᮹ ☖ᱽʑ܆ᮥ Łಅ⦽ ᙹ᭥-ᮁప łᖁᮥ

ᮡእๅ}ᄡᙹᱢKernel ⫭ȡ༉⩶ᮥ☖⦽ᙹ᭥-ᮁపšĥłᖁ

᯲ᖒ᮹ႊჶುᮥᱽ᜽⦹ᩡ݅. Kim and Lee (2008)۵ᄁᯕḡᦩ

⫭ȡᇥᕾᮥᯕᬊ⦹ᩍᙹ᭥-ᮁపšĥłᖁ᮹ᇩ⪶ᝅᖒᮥᇥᕾ⦹ᩡ

݅. ੱ⦽Lee (2008)۵Ӻ࠺ᅙඹ5}ᙹ᭥⢽ḡᱱᮥݡᔢᮝಽ

ᙹ᭥ಽᇡ░ᮁపᮝಽ(model 1) ᮁపᮝಽᇡ░ᙹ᭥ಽ(model 2) əญŁ ᧲ႊ⨆ᮝಽ(model 3) ⫭ȡᇥᕾᮥ ᙹ⧪⦹ᩍ ᙹ᭥-ᮁప

šĥ᜾᮹ᔩಽᬕ༉⩶ᮥᱽ᜽⦽ၵᯩᮝ໑, Lee et al. (2009)ᮡ

Ӻ࠺vᱢ⡍Ʊၰḥ࠺ḡᱱᮥᵲᝍᮝಽᙹ᭥-ᮁపšĥłᖁᮥ

ᯕᬊ⦽Ğ֥ᄥᙹญ✚ᖒపᄡ࠺ᨱš⦽ᩑǍෝ⦽ၵᯩ݅. Kim et al. (2009)ᮡ⦽vݡƱᨱᖅ⊹ࡽADVMᮥᯕᬊ⦽ᩑᗮᱢᯙ

ᮁప⊂ᱶ ᯱഭ᪡ እƱ⦹ᩍ ᙹ⊹༉⩶ᨱ ᮹⦽ eᱲᮁప ᔑᱶ᮹

ᱢᬊᖒᮥ á᷾⦹ᩡᮝ໑, Lee and Kwon (2010)ᮡ ᝮ⊹ ᙹ᭥

š⊂ᗭ᮹12֥eš⊂⦽ᙹ᭥-ᮁపšĥłᖁᮥၵ┶ᮝಽRMA2

༉⩶ᮝಽᙹ໕łᖁᮥ༉᮹⦹ᩍᙹ᭥-ᮁపšĥłᖁᮥᦩᱶ⪵᜽┅ʑ

᭥⦽ʑⅩᩑǍෝ⦹ᩡ݅. Kim et al. (2011)ᮡᅖ݉໕}ᙹಽၰ

ᇩȽ⊺⦽⦹ᔢᮥ ᅕᯕ۵ ⪮ᙹ░ ᜾ᔾᮥ Łಅ⦽ ⬂݉໕ ᔢᨱᕽ᮹

ᙹ᭥-ᮁపłᖁၰ݉᭥ᮁప⬂ᇥ⡍ᩩ⊂ᮥ᭥⦹ᩍᮁ⦽᫵ᗭ༉⩶ᮥ

}ၽ⦽ၵᯩᮝ໑, Kim et al. (2012)ᮡ༉௹⦹⃽᮹ᙹ᭥-ᮁపšĥa

Łญ⩶ᮥᯕ്݅۵ᱱᮥ₊ᦩ⦹ᩍᯱiၰᦵၹ⦹ᔢ᮹ᔑḡ⦹⃽᮹

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u x X U

45^o u

1.0 F_X(x)

F_U(u)

F_U(u) ; F_X(x)

Fig. 2. Relationship of random number _Ɠ and quantile value _Ɩ Łญ⩶ ᙹ᭥-ᮁప šĥෝ ᇥᕾ⦽ ၵ ᯩ݅.

ᙹྙᩩ⊂᮹ᱶ⪶ࠥෝ׳ᯕʑ᭥⧕ᕽ۵ᙹྙš⊂ᯱഭ᮹᧲ᱢ

⪶ᅕ᪡޵ᇩᨕḩᱢᯙ⊂໕ᨱᕽࠥŁಅࡹᨕ᧝⦽݅. ə్ӹᬑญӹ

ᮡ ၙ⯂⦽ ᝅᱶᯕ໑ ᯕෝ ᅕ᪥⧁ ᙹ ᯩ۵ ႊᦩᨱ ݡ⦽ ᩑǍa

ḡᗮᱢᮝಽᙹ⧪ࡹᨕ᧝⧁⦥᫵ᖒᯕᯩ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵

᭥⨹ࠥʑၹᙹྙᄡᙹ(hydrological variable)᮹༉᮹ၽᔾʑჶᯙ

MCS ʑჶᮥᯕᬊ⦹ᩍŁᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥᱽÑ⦹Łš⊂

ᙹ᭥-ᮁపšĥłᖁᮥᅕ᪥⧉ᮝಽ៉, ࠥ᜽⦹⃽ᨱᕽ᮹⪮ᙹၽᔾᨱ

⦹Łᯱ⦹ᩡ݅. ݅ᮭFigure 1ᮡᅙᩑǍᨱᕽᝅ᜽⦽MCSෝᯕᬊ⦽

ࠥ᜽⦹⃽᮹ Łᙹ᭥ Rating Curve }ၽ᮹ ᩑǍ ⮱෥ࠥᯕ݅.

2. Monte Carlo simulation

2.1 Random Number Generation

ᅙᩑǍᨱᕽ۵᭥⨹ࠥʑၹ⪮ᙹప༉᮹ၽᔾᮥ᭥⦹ᩍMCS ʑჶᮥᯕᬊ⦹ᩡᮝ໑, ᯕ۵ᇩ⪶ᝅᖒᮥ݅൉۵ᙹ݉ᮝಽᕽ݅᧲⦽

⪶ශᇥ⡍ಽᇡ░✚ᱶᄡᙹ(variable)᮹⪶ශᇥ⡍ෝ༉᮹⦹۵ߑᯕ ᬊࡹŁᯩ݅. MCSෝ᜽⧪⦹ʑ᭥⦽ʑᅙ᳑Õᮡᨕਅ⦽Ǎᖒ᫵ᗭ ᮹ᄡ⪵a݅ෙǍᖒ᫵ᗭᨱᩢ⨆ᮥၙ⊹ḡᦫ۵ࠦพᱢᯙǍᖒ᫵ᗭ

௝۵aᱶᯕ݅. ݅อ, อ᧞ᄡᙹॅe᮹ᔢšᖒᯕྕ᜽⧁ᱶࠥಽ

᯲í ᳕ᰍ⦽݅໕ ࠦพ᮹ aᱶᮥ ᱥᱽಽ ⦽ MCS۵ ⓑ ᪅ඹෝ

ၽᔾ᜽┅ḡᦫíࡽ݅. ə్ӹอᯝᯕ్⦽ᄡᙹॅe᮹ᔢšᖒᯕ

እƱᱢⓑĞᬑᨱ۵ᔢšĥᙹෝၵ┶ᮝಽ݅ᄡప⪶ශၡࠥ⧉ᙹෝ

ᯕᬊ⦹ᩍᄡᙹॅe᮹ᩑšᖒᮥ ᮁḡ᜽┅۵äᯕᵲ᫵⦹݅Ł⧁

ᙹᯩ݅. ᯕ్⦽šᱱᨱᕽMCSʑჶᮡᇩ⪶ᝅᖒᇥᕾᮥ᭥⦽ʑᅙ

⪶ශᇥᕾʑჶࠥǍಽᕽᇩ⪶ᝅᖒᮥw۵Ŗ⦺ᱢᯙ༉⩶᮹bǍᖒ

᫵ᗭॅᯙ ᯥ᮹᮹ ᄡᙹᨱ ݡ⧕ ⪶ශᱢᯙ ✚ᖒᮥ Łಅ⦽ ⧕ᕾᮥ

a܆⍡⦹۵⧕ᕾႊჶᮝಽᯙ᜾ࡹŁᯩ݅. ᯕ్⦽MCS ŝᱶᨱᕽ

b⪶ශᄡᙹ᮹ᇥ⡍⩶┽ᨱᱢ⧊⦽ӽᙹෝၽᔾ᜽┅۵äᯕaᰆ

ʑᅙᯕࡹ໑, ᯕෝ᭥⧕ᕽ۵ᯝ݉0ŝ1ᔍᯕᨱᕽɁᯝ⦹íᇥ⡍⦹۵

ӽᙹෝ⇵⇽⦽݅ᮭᯕӽᙹෝᱢᱩ⯩ᄡ⪹⦹ᩍ✚ᱶ⦽⪶ශᇥ⡍ෝ

঑෕۵ӽᙹಽၵЙᨕᵝ۵ႊჶᯕྕᨨᅕ݅ᵲ᫵⦹݅(Kim, 2008).

MCSʑჶᮡəᇥ⡍✚ᖒᯕ᦭ಅḥ⪶ශᄡᙹॅ᮹⧉ᙹಽᱶ᮹ࡹ

۵ᔩಽᬕ⪶ශᄡᙹ᮹☖ĥᱢ✚ᖒŝᇥ⡍⧉ᙹෝ⇵ᱶ⧁ᙹᯩᮝအ ಽᯱᩑĥ᮹ᇩ⪶ᝅᖒᮥ ᇥᕾ⦹۵ߑᱢ⧊⦽ႊჶᮝಽ᦭ಅḡŁ

ᯩ݅. ᩑᗮ⪶ශᄡᙹෝ᭥⦽ӽᙹෝ⇵⇽⦹۵ߑᔍᬊࡹ۵ႊჶᮝಽ

ݡ⢽ᱢᯙႊჶᮡᩎᄡ⪹ჶ(inverse transformation method)ᯕᯩ

ᮝ໑ݡᇡᇥ᮹MCSᨱᕽᵝಽᔍᬊࡹ۵ႊჶᯕ໑ᯕ۵٥aᇥ⡍⧉

ᙹamÞßᯙᩑᗮ⪶ශᄡᙹᨱݡ⧕٥ᱢᇥ⡍⪶ශᯕᯝভ᮹

⪶ශᄡᙹ᮹s۵݅ᮭEq. (1)ŝzᯕ٥aᇥ⡍⧉ᙹෝᩎᄡ⪹

⦹ᩍ᨜ᮥᙹᯩ݅. Figure 2۵ᩎᄡ⪹ჶᮥ༉᜾ᱢᮝಽӹ┡ԕᨩ݅.

Ɩ á _±^àÎÞƓß (1)

⦽⠙0ŝ1ᔍᯕ᮹Ɂ॒ᇥ⡍(uniform distribution) ⪶ශᄡᙹ

|᮹ ٥ᱢᇥ⡍⪶ශᯕᯕ໕ ݅ᮭ Eq. (2)᪡ zᯕ ӹ┡ԝ ᙹ

ᯩ݅.

®ÞƓß á Ɠ (2)

Eq. (2)ෝᯕᬊ⦹ᩍᯥ᮹᮹ᩑᗮ⪶ශᄡᙹ(continuous random variable) ෝ ᭥⦽ ӽᙹෝ ⇵⇽⧁ ᙹ ᯩ݅. ᷪ 0ŝ 1ᔍᯕ᮹

Ɂ॒ᇥ⡍ ӽᙹෝ ⇵⇽⦹ᩍ ᭥᮹ Eq. (2)᪡ zᯕ ᩑᗮ ⪶ශ

ᄡᙹ᮹⪶ශᇥ⡍⧉ᙹ᮹ᩎᄡ⪹Eq. (1)ᨱݡ᯦⦹໕ᩑᗮ⪶ශᄡ ᙹ᮹⪶ශᇥ⡍ෝ঑෕۵ӽᙹෝၽᔾ᜽┍ᙹᯩ݅. ᯕ᪡zᯕ

ᩎᄡ⪹ჶᮡ0ŝ1ᔍᯕᨱᕽ⇵⇽ࡽɁ॒ᇥ⡍ӽᙹෝbᩑᗮ⪶ශᇥ

⡍᮹Quantile ⧉ᙹᨱݡ᯦⦹ᩍe݉⯩༉᮹⧁ᙹᯩᮝအಽݡᇡᇥ ᮹ᩑᗮ⪶ශᇥ⡍ᨱݡ⦹ᩍᵝᨕḥ⪶ශᇥ⡍ෝᨕಅᬡᨧᯕၽᔾ᜽

┍ ᙹ ᯩ݅.

2.2 Quantile Estimation

ࠥ᜽⦹⃽ᱽႊ᮹MCSᨱ᮹⦽⪮ᙹ᭥⇵ᱶ⊹ᨱݡ⦽ᇩ⪶ᝅᖒ

Ƚ໦ŝŁᙹ᭥Rating Curveᩑᰆᮥ᭥⦹ᩍᯥ᮹᮹ᇥ⡍⩶ᮥᱢᱶ ᇥ⡍⩶ᮝಽaᱶ⦹ᩍ᭥⨹ࠥ᮹ᇩ⪶ᝅᖒᮥᱶపᱢᮝಽ⧕ᕾ⦹۵

ŝᱶᮥᔍᬊ⦹ᩡ݅. ᯝၹᱢᮝಽኩࠥ⧕ᕾᮥ☖⦹ᩍĥᔑࡹ۵ᰍ⩥

ʑe á ÎîƎᨱݡ⦽ᖅĥ⪮ᙹపᮡaᱶࡽ٥aᇥ⡍⧉ᙹÞƖ_Əß á Ə á Î àƎ (ᩍʑᕽ, Ə۵እⅩŝ⪶ශᯕ໑, Ǝ۵ၽᔾ⪶ශᯥ)᮹

ᩎ⧉ᙹෝᯕᬊ⦽⧕ෝᔑᱶ⧉ᮝಽ៉⇵ᱶ⧁ᙹᯩ݅. ᅙᩑǍᨱᕽ ۵ᩑᗮ⪶ශᄡᙹಽᇡ░Quantile sᮥᔑᱶ⦹ʑ᭥⦹ᩍš⊂vᙹ పᯱഭ᮹ᱢ⧊ᖒ⠪aෝᝅ᜽⦹ᩡᮝ໑, ↽ᱢᇥ⡍⩶ᮝಽGumbel ᇥ⡍⩶ᮥ₥┾⦹ᩡŁ, ᇥ⡍⩶ᄥಽӽᙹ[0, 1] ၽᔾ᮹ŝᱶᮥ☖⦹

(4)

Fig. 3. The study area of the Wooyi stream basin located in the North-east Seoul, South Korea. (a) represents location of Wooyi stream in Seoul, and (b) is drainage sewer system.

Table 1. Watershed Present condition of Wooyi stream basin

Watershed Name

Watershed Area (^Ï)

Watershed Length ()

River length () Local river Total

Wooyi 28.76 11.75 8.33 8.33

Daedong 4.18 3.47 1.60 1.60

Gaoh 2.24 2.81 2.02 2.02

Whagye 4.40 2.80 2.80 2.80

ᩍ⇵ᱶࡽᯥ᮹እⅩŝ⪶ශᨱݡ⦽ᩎᄡ⪹⇵ᱶჶ(inverse problem estimation)ᨱ᮹⦽Quantileᮥ⇵ᱶ⦹ᩡ݅. ₥┾ࡽGumbel ᇥ⡍

⩶᮹٥aᇥ⡍⧉ᙹ(CDF: cumulative distribution function)۵

݅ᮭ Eq. (3)ŝ z݅.

ÞƖß á

å

^à^ƙ^Ɯ^ƚ^{à ć}^{Ɩ à Ɩ}^ķ ^×^ƛ^Ɲ^ƞ

æ

⁽³⁾

ᩍʑᕽ,Ɩ_×᪡ķ۵bbGumbel ᇥ⡍⩶᮹᭥⊹ๅ}ᄡᙹ(location parameter)᪡Ƚ༉ๅ}ᄡᙹ(scale parameter)ᯕ໑, ⢽ᅙᯱഭ±_Îì z ì ±_§ (_§ᮡᯱഭ}ᙹ)ಽᇡ░⇵ᱶࡽๅ}ᄡᙹ᮹⇵ᱶ⊹ෝbb

ýƖ_×᪡^ýķಽ ᱶ᮹⦽݅.

᭥᮹ Eq. (3)ಽᇡ░ ĥᔑࡹ۵ ᯥ᮹᮹ እⅩŝ⪶ශýƏᨱ ݡ⦽

ᖅĥ⪮ᙹపƖ_Ə۵ ݅ᮭ Eq. (4)᪡ z݅.

ýƏá

å

^à^ƙ^Ɯ

^ƚ

^{à ć}^Ɩ^Ə^ý^ķ^àý^Ɩ^×^ƛ^Ɲ

^ƞ æ

⁽⁴⁾

ᯕĞᬑᖅĥᩑ⦽ƌ֥ᨱݡ⦽ᙹŖǍ᳑ྜྷ᮹᭥⨹ࠥ^ý«۵݅ᮭ

Eq. (5)᪡ zᯕ ᱶ᮹⧁ ᙹ ᯩ݅.

ý«á Î à ÞÎ àýƎß^ƌá Î àýƏ^ƌ (5)

᭥᮹ Eq. (5)ಽᇡ░ ⇵ᱶࡹ۵ ᭥⨹ࠥ^ý«᮹ ʑݴsÞý«ßᮥ

Taylor ɪᙹෝᯕᬊ⦹ᩍᔑᱶ⦹໕Eq. (6)ŝzᮝ໑, እⅩŝ⪶ශ (non-exceedance probability)ᨱݡ⦽ʑݴsÞýƏß۵݅ᮭEq.

(7)ŝ z݅.

Þý«ß j Î àãÞýƏßä^ƌ ⁽⁶⁾

ÞýƏß j

å

^à^ƙ^Ɯ

^ƚ

^{à ć}^Ɩ^Ə^{à Þý}^Þý^ķß^Ɩ^×^{ß ƛ}^Ɲ

^ƞ æ

⁽⁷⁾

3. ݡᔢ⦹⃽ᮁᩎၰᮁప⊂ᱶ

3.1 ۩ঃ෇వକલ

ᅙᩑǍ᮹ݡᔢᮁᩎᮡᬑᯕ⃽ᮁᩎᯕ໑, ᮁᩎ໕ᱢ28.76km²,

ᮁಽᩑᰆ11.75kmᯙࠥ᜽⦹⃽ᮁᩎᯕ݅. ᯕḡᩎᮡ1998֥, 2001

֥ŝ2003֥ᨱ⪮ᙹ⦝⧕aᯩᨩ޹Ŕᮝಽᰍ⧕šญᔢḡᗮᱢᯙ

༉ܩ░ยᯕ⦥᫵⦽ᮁᩎᯕ݅. ᬑᯕ⃽᜽⨹ᮁᩎ᮹ᮁᩎĞĥ۵ᕽ἞

ᮝಽ۵ ᇢ⦽ᔑ, ᇢ἞ᮝಽ ࠥᅪᔑ, ԉ἞ᮝಽ۵ ᖒᇢǍ᪡ Ğĥෝ

Ğĥෝᯕ൉۵ᇢ⦽ᔑ(EL.386m), ࠥᅪᔑ(EL.721m)ᨱᕽbᮁᩎ ᮹ᇥᙹಚᮥ⩶ᖒ⦹Łᯩ݅. ⦹⃽᮹ᮁಽ⩶ᔢᮡݡℕᱢᮝಽᙹḡᔢ ᯕ໑, ⦹ඹಽḥ⧪⧉ᨱ঑௝ᮁᩎ⡎ᯕ᳢ᦥݡᇡᇥ᮹ᮁᩎᯕᔢඹᨱ

⠙ᵲࡹᨕᯩᮝ໑, ᯝᇡǍeᮡSᯱ⩶᮹ᔍ⧪ᮥᯕ൉Łᯩᮝӹݡℕ ಽǕłᯕᨧ۵Ǎeᯕ݅. ᬑᯕ⃽ᮡݡ࠺⃽, a᪅⃽, ⪵ĥ⃽᮹ḡඹ

᪡bbอӹᵲ௲⃽ᮝಽ⮹్ॅᨕa۵⦹⃽ᮝಽᕽᵲ௲⃽ᱽ1ḡඹ ᯕ݅. ݅ᮭFigure 3۵ᱢᬊݡᔢᮁᩎ᮹᭥⊹ࠥၰᗭ႑ᙹᇥǍᄥ

⦹ᙹšÑ᜽ᜅ▽᮹႑ᙹℕĥࠥᯕ໑, ݅ᮭTable 1ᮡᬑᯕ⃽ᮁᩎ᮹

ᙹĥ⩥⫊ᯕ݅.

(5)

Fig. 4. Development of the Rating Curve

Fig. 5. Result on precipitation generation by Monte Carlo Simulation. (a), (b), and (c) represent method of moments (MOM), method of maximum likelihood (ML), and method of probability weighted moments (PWM), respectively.

3.2 କ߆౸୨নր

ᙹ᭥-ᮁపšĥłᖁᮡḡᗮᱢᯙ⦹⃽༉ܩ░ยᮥ☖⧕ᕽ}ၽ/

ᅕ᪥ࡹᨕᲙ᧝⦹ӹᦥḢʭḡǎԕ⦹⃽᮹Ğᬑᙹྙš⊂ᯱഭa

∊ᇥ⦹ḡ ᦫᮝ໑ ᯝᇡ Ǎ⇶ᯕ ࡹᨕ ᯩ݅Ł ⦹޵௝ࠥ Łᙹ᭥ᨱ

ݡ⦽ᯱഭa⪶ᅕࡹḡ༜⦽Ğᬑaݡᇡᇥᯕ݅. ᅙᩑǍ᮹ᱢᬊ

ݡᔢ⦹⃽ᮡᕽᬙ᜽šԕḡႊ⦹⃽ᯙᬑᯕ⃽ᮁᩎᮝಽ⦹⃽⦹ඹᇡ

ᰆᬵƱḡᱱᨱᯱʑᙹ᭥š⊂ʑ(T/M)aᖅ⊹ᬕᩢࡹŁᯩᮝ໑, ᕽᬙ᜽᮹ݡ⦺ŝᩑĥ⦽⦹⃽šญᩑǍᬊᩎ”᮹ᯝ⪹ᮝಽᮁప⊂ᱶ ᯕ ḡᗮᱢᮝಽ ᝅ᜽ࡹŁ ᯩ݅(Yoon et al. 2008).

ᙹ᭥-ᮁపšĥෝđᱶ⦹ʑ᭥⧕ᕽ۵ݡᙹᄡ⪹ᮥ☖⧕ᕽšĥ᜾

ᮥᖁ⩶⪵⦹۵äᯕ⠙ญ⦹݅. ᯝၹᱢᯙᙹ᭥-ᮁప᜾ᮡ݅ᮭEq.

(8)ŝ zᯕ ᮁపᮥ ᙹ᭥᮹ ḡᙹ⧉ᙹಽ aᱶ⦽ႊჶᮥ ᔍᬊ⦽݅

(Lambie, 1978).

ª á ƉÞ¡ à Ƙß^ƀ (8)

ᩍʑᕽ, ¡۵ᙹ᭥, Ɖ᪡ƀ۵ᔢᙹᯕ݅. Ƙ۵ᮁపᯕ0ᯕࡹ۵

ᙹ᭥ෝӹ┡ԕ۵ʑᵡ໕ᅕᱶ⊹ᯕ݅. ݅ᮭFigure 4۵⦹⃽᮹ᮁᩎ ᮲ݖᨱᵲ᫵⦽š⊂ᯱഭಽ⪽ᬊࡹ۵2000ⴇ2010֥ʭḡ᮹ᬑᯕ⃽

ᰆᬵƱḡᱱ᮹ᙹ᭥-ᮁపšĥłᖁᯕ໑, Figure 4(b)᪡Figure 4(c) ۵ ᰆᬵƱḡᱱ ᮁప⊂ᱶǍe᮹ ⬂݉⊂ప ݉໕(Station No. 24, Station No. 25)ᮝಽ b ⬂݉໕ e᮹ Ñญ۵ 50mᯕ݅.

(6)

Table 2. Development of the Rating Curve Equations (Unit; x á ^Ðîì o á lsí )

Observed year # of Obs. data Rating Curve Equation _«^Ï

20002004 83 x á ÕÏíÖÓÞo à ÎÓíÏ×ß^{ÎíÒÐÑÏÏÐ}

ãÎÓíÏÑ ; ¡ ; ÎÕíÎÒä 0.9614

20002006 114 x á ÕÎíÒÏÞoà ÎÓíÎÒÎÑß^{ÎíÓÐÒ×ÑÔ}

ãÎÓíÏÑ ; ¡ ; ÎÕíÑÏä 0.9164

20002008 122 x á ÔÒíÑÎÞo à ÎÓíÎ×ÐÎÏß^{ÎíÓÖÓÑ×Õ}

20002010 140 x á ÔÖíÒÒÞo à ÎÓíÎÏÎÕÖß^{ÎíÓÏÖÐÏÔ}

Table 3. Stochastic characteristics of observed and simulated precipitation

Statistics Observed UQR Series (19612010 year) Simulated UQR Series

MOM ML PWM

Max. 208.1 255.2 260.3 259.3

Min. 102.3 104.4 105.2 104.9

Average 134.0 132.6 134.2 133.7

Median 127.2 124.8 126.1 125.7

Std. Dev. 26.93 26.53 27.30 27.19

CV 0.2010 0.2000 0.2034 0.2033

Quartile 75% 102.3 104.3 105.1 104.8

* Observed UQR means upper quartile range of annual maximum rainfall series obtained from Seoul meteorological observatory. Simulated UQR means generated upper quartile range data from MCS., Quantile estimation performed method of moments (MOM), method of maximum likelihood (ML), and method of probability weighted moments (PWM).

ݡᔢ⦹⃽ᮁᩎ᮹ᮁప⊂ᖒᖒŝෝၵ┶ᮝಽᙹ᭥-ᮁపšĥłᖁ

ᮥ᯲ᖒ⦽đŝFigure 5ᨱᕽᅕ۵ၵ᪡zᯕĥ⫮⪮ᙹ᭥ᨱɝᱲ⦹Ñ ӹ ᯕෝ ᔢ⫭⦹۵ ⪮ᙹ۵ ၽᔾ⦹ḡ ᦫᦹᮝ໑, ᩍᱥ⯩ Łᙹ᭥ᨱ

ݡ⦽ᇩ⪶ᝅᖒ(uncertainty)ᯕ᳕ᰍ⧉ᮥ⪶ᯙ⧁ᙹᯩᨕḡᗮᱢᯙ

༉ܩ░ยᮥ☖⦽ᙹྙᯱഭ᮹⪶∊ᯕ᫵Ǎࡽ݅. ᬑᯕ⃽ᰆᬵƱḡᱱ ᨱᕽ⩥ᰍʭḡš⊂ࡽ↽Łᙹ᭥۵EL.18.42mᯕ໑, ᯕভ᮹↽ݡ

ᮁᗮᮡ4.08m/sᯕ݅. ੱ⦽, 2010֥ʭḡ᮹ᯱഭෝၵ┶ᮝಽ}ၽࡽ

ᙹ᭥-ᮁపšĥłᖁ᜾ᮡx á ÔÖíÒÒÞo à ÎÓíÎÏÎÕÖß^{ÎíÓÏÖÐÏÔ},ãÎÓíÏÑ

; ¡ ; ÎÕíÑÏäᯕ໑, š⊂ᯱഭ᪡ łᖁ᜾ŝ᮹ đᱶĥᙹ(«^Ï)۵ 0.9463ᮝಽ ᇥᕾࡹᨩ݅(Table 2)

4. ᇥᕾđŝ

4.1 MCS ࡦଭէր

MCSᨱ᮹⦽vᬑᯱഭ᮹༉᮹ၽᔾႊჶᨱ঑௝, ݡᔢ⦹⃽ᮁᩎ ᮹⪮ᙹపᇡ⦹aaᰆⓍíၽᔾ⦹۵ᯥĥḡᗮʑe(2᜽e)ᨱݡ⦹

ᩍ᭥⨹ࠥ⧕ᕾᨱᔍᬊࡹ۵ᄡᙹ᮹ᝅ⊂⊹᪡༉᮹ࡽđŝ᮹ɚݡ⊹

ᙹྙప ၽᔾᮥ ᭥⦹ᩍ ᔢ᭥ 75% ༉᮹ၽᔾ vᙹపᮥ ᱢᬊ⦹ᩍ

☖ĥᱢ✚ᖒ⊹ෝᇥᕾ⦹ᩡ݅(Table 3). š⊂ᯱഭ᪡༉᮹ၽᔾᯱഭ

᮹UQR (Upper Quartile Range) vᙹపsᮥእƱ⦽đŝ⠪Ɂŝ

ᇥᔑ, ⢽ᵡ⠙₉॒᮹ʑⅩ☖ĥపᮡ༉᮹ၽᔾᯱഭ᪡Ñ᮹ᯝ⊹⦹۵

sᮥᅕᩍᵝŁᯩᮝӹ, ↽ݡ⊹᮹Ğᬑš⊂ᯱഭᨱእ⦹ᩍ༉᮹ၽᔾ

ᯱഭabๅ}ᄡᙹ⇵ᱶႊჶᄥಽ22.6%~25.1%ʭḡⓍíӹ┡ӹ

ᔢ᭥ 75% ༉᮹ၽᔾ vᙹపᨱ ݡ⦹ᩍ MCSᨱ ᮹⦽ ༉᮹ ၽᔾ

ႊჶᯕɚݡ⊹ᙹྙప⠪aᨱᮁญ⦹íᱢᬊࢁᙹᯩᮭᮥ⪶ᯙ⧁

ᙹᯩ݅. ݅ᮭFigure 5۵༉ູ✙ჶ(MOM; method of moments)ŝ

↽ᬑࠥჶ(ML; method of maximum likelihood), əญŁ⪶ශa ᵲ༉ູ✙ჶ(PWM; method of probability weighted moments)ᨱ

᮹⦽ ༉᮹ၽᔾᯱഭ᪡ ᔢ᭥ 75% ༉᮹ၽᔾ vᙹప᮹ ⦹⦽ĥ s

ᖅᱶ᮹ ʑᵡᯕ ࡹ۵ Quartile 75%sᮥ ӹ┡ԕᨩ݅.

ᮁᩎ᮹ᮁ⇽ŝᱶᮡ☁ḡᯕᬊŝᖁ⧪ᙹྙᔍᔢ॒ᨱ঑௝ݍ௝ḡ ۵ๅᬑᅖᰂ⦽᧲ᔢᮥு໑, ᮁᩎ᮹vᬑ-ᮁ⇽šĥaእᖁ⩶ᖒᮥ

ԕ⡍⦹Łᯩᨕᕽᮁᩎ᮹ᮁ⇽᮹ᱶ⪶⦽ᩩ⊂ᮡๅᬑᨕಅᬕྙᱽᯕ

݅. ঑௝ᕽᅙᩑǍᨱᕽ۵ᱥᖙĥᱢᮝಽձญᔍᬊ⦹Łᯩᮝ໑,

ࠥ᜽ᮁᩎ᮹ᬑᙹၰ᪅ᙹ⃹ญ᜽ᜅ▽᮹ᅕ݅ᱶ⪶⦽⧕ᕾŝᝁ഑ᖒ

(7)

(a) Model Gcalibration (b) Model Gverification

(c) Model Gcalibration (d) Model Gverification

Fig. 6. Model calibration and verification for Model I (Runoff) and Model G(Runoff+Extran)

ᯩ۵đŝෝʑݡ⧁ᙹᯩ۵U.S. EPA᮹SWMM (Storm Water Management Model)ᮥᔍᬊ⦹ᩍࠥ᜽⦹⃽ᙹĥᨱᕽ᮹⪮ᙹᮁ⇽

᮹ ᩩ⊂ᱶࠥෝ ׳ᯕŁᯱ ⦹ᩡ݅.

30ᯝ⪙ᬑᔍᔢŝ2003֥7ᬵ22ᯝ⪙ᬑᔍᔢᮥᖁ┾⦹ᩡ݅(Kim et al. 2005). ᯝၹᱢᮝಽ vᬑ-ᮁ⇽ ༉⩶᮹ ᱢ⧊ᖒᮥ ⠪a⦹ʑ

᭥⦽ฯᮡ☖ĥᱢᱢ⧊ࠥʑᵡᯕᱽᦩࡹᨩᮝӹᱢ⧊ࠥʑᵡᅕ݅۵

༉᮹ ၽᔾࡽ sŝ ⊂ᱶࡽ s ᔍᯕ᮹ ᇩᯝ⊹ᨱ ޵ ᵲᱱᮥ ࢱŁ

ᯩ݅. š⊂ŝ ༉᮹᮹ ☖ĥᱢ ⠪a ᙹ݉ᮝಽ ྕ₉ᬱ ĥᙹᯙ Eq.

(9)᪡ zᮡ ༉⩶ ⬉ᮉᖒ ĥᙹ (CME: coefficient of model efficiency)᪡Eq. (10)ⴇ(12)ŝzᮡྕ₉ᬱĥᙹಽᕽ℉ࢱᮁప᮹

%᪅₉(PEP: percent error of peak)᪡ᮁ⇽ᬊᱢ᮹%᪅₉(PEV:

percent error of volume) ၰ℉ࢱᮁపၽᔾ᜽e(Tp)᮹%᪅₉

(PETP: percent error of time of peak)ෝᱢᬊ⦹ᩍ༉⩶᮹ᱢ⧊ᖒ

ᮥ⠪a⦹ᩡ݅. ༉⩶⬉ᮉᖒĥᙹ۵☖ĥᱢʑᵡᮝಽ⠙᮹ෝᵥᯝ

ᙹᯩ۵ྕ₉ᬱĥᙹᯕ໑༉᮹ࡽᙹྙłᖁᯕᝅ⊂ᙹྙłᖁŝ᯹

ᯝ⊹⧁ᙹಾ1ᨱaʭᬭḡ۵ᖒḩᯕᯩ݅. ᯕʑᵡᮡྕ₉ᬱ᧲ᮝಽ ᕽ ᯱഭ᮹ }ᙹᨱ šĥᨧᯕ ᱩݡᱢ ⠪aʑᵡᯕ ࢁ ᙹ ᯩ݅.

¦ á ć_×^Ï

×Ïà ^Ï

(9)

ᩍʑᕽ, ^Ïá_{Ƈ á Î}

ā

^ƌ ^ãƏ^×^{à Ə}^Ƒ^ä^Ƈ^Ï^ᯕŁ^×^Ï^á

ā

_{Ƈ á Î}^ƌ ^ãƏ^×^{à ćƏä}^Ƈ^Ï^ᯕ݅. ^Ï^۵

ᝅ⊂⊹᪡ᩩ⊂⊹ᔍᯕ᮹ᇩᯝ⊹ḡ⢽(unconformity index)ᯕŁ,

_×^Ï۵ ᝅ⊂ᮁప᮹ Ⅹʑᇥᔑᮥ ӹ┡ԕ໑, Ə_×۵ ᝅ⊂ᮁపᮥƏ_Ƒ۵

༉᮹ ᮁప, ćƏ۵ š⊂ᮁప᮹ ⠪Ɂᮥ ᮹ၙ⦽݅.

©© á ćƏ_Ǝ×

Ə_ƎƑà Ə_Ǝ×

Z Î×× (%) (10)

©¯ á ć¯_×

¯_Ɓà ¯_×

Z Î×× (%) (11)

(8)

Table 4. Statistical evaluation and model calibration and verification of runoff model

Applied models Rainfall event (2001/07/30) Rainfall event (2003/07/22)

Remark CME PEP (%) PEV (%) PETP (%) CME PEP (%) PEV (%) PETP (%)

Model  0.96 0.36 19.70 12.86 0.77 3.01 - 17.08 -8.33 Cal.

Model  0.96 0.27 4.29 4.29 0.85 -0.84 -2.01 -4.17 Ver.

* Model : Kinematic Wave Model, Model : Kinematic Wave+Dynamic Wave Model, Cal: Model Calibration, Ver: Model Verification

(a) Calibration (July, 12, 2006) (b) Verification (July, 16, 2006) Fig. 7. Calibration and verification of flood events

©© á ć_Ǝ×

ƎƁà _Ǝ×

Z Î×× (%) (12)

ᩍʑᕽ, ƏƎƑ᪡ƏƎ×۵ ᩩ⊂ ၰ ᝅ⊂ ℉ࢱᮁపᯕŁ¯Ɓ᪡¯×۵

ᩩ⊂ၰᝅ⊂ᮁ⇽ᬊᱢᯕ໑_ƎƁ᪡_Ǝ×۵ᩩ⊂ၰᝅ⊂℉ࢱᮁప᮹

ၽᔾ᜽eᯕ݅. vᬑ-ᮁ⇽༉᮹᮹ᱢ⧊ᖒᮥ⠪a⦹ʑ᭥⧕ᕽFigure 6ᨱ ᝅ⊂⊹᪡ ༉᮹ đŝෝ ࠥ᜽ᱢᮝಽ ᇥᕾ⦹ᩡ݅. ݅ᮭ Table 4᮹☖ĥᱢḡ⢽ᨱᕽᅕ۵ၵ᪡zᯕᩑĥ༉⩶(Model II:ⷚRunoff+

Extran)ᯕ݉ᯝ༉⩶(Model I: Runoff)ᮥᱢᬊ⦹ᩡᮥভᅕ݅℉ࢱ

ᮁప᮹ ၽᔾ᜽e, ℉ࢱᮁపᨱᕽ እƱᱢ ᬑᙹ⦽ đŝෝ ᅕᩡ݅.

SWMM᮹Model IIෝ☖⦹ᩍ༉᮹⦽đŝ۵༉⩶⬉ᮉᖒĥᙹa

Ñ᮹1ᨱaʾíᔑᱶࡹᨕᙹྙłᖁ᮹ᩩ⊂ᐱอᦥܩ௝℉ࢱ᜽eŝ

℉ࢱᮁప᮹ ༉᮹ᨱᕽࠥ ᬑᙹ⦽ äᮝಽ ᇥᕾࡹᨩ݅.

ݡᔢ⦹⃽⦹ࠥ᮹⪮ᙹ᭥⇵ᱢᮥ᭥⦹ᩍᯝ₉ᬱᨱթḡႊᱶ᜾ᮥ

ʑᅙᮝಽ⦹ᩍᨱթḡᗱᝅᮡษₑŝ݉໕ᙹ⇶/⪶ᰆᨱ᮹⧕Ǎ⦹۵

ႊჶᮥᔍᬊ⦹ᩡ݅. ⦽݉໕ᨱᕽ݅ᮭ݉໕ʭḡ᮹ᙹ໕᳦݉໕ࠥ۵

ၙḡ᮹ ᙹ᭥ෝ ᔑᱶ⦹ʑ ᭥⦽ ⢽ᵡ⇶₉ĥᔑჶ(standard step method)ᮝಽ ᔢඹᇡ᪡ ⦹ඹᇡ ݉໕ᨱ ݡ⧕ ၹᅖᱢᮝಽ ᨱթḡ

ႊᱶ᜾ᮥ ⣣ᮝಽ៉ ᨜ᮥ ᙹ ᯩᮝ໑, ݅ᮭ Eq. (13)ᮡ ⦽݉໕᮹

ᙹ᭥ෝaᱶ⧕ᕽ݅ᮭ݉໕᮹ᙹ᭥ෝᨱթḡႊᱶ᜾ᮝಽǍ⦹۵༉

⩶᮹ ⪮ᙹ᭥ ⇵ᱢĥᔑ᜾ᯕ݅.

²Ïâ ³_Ïâ ķ_ÏćÏƅ

¯_Ï^Ï

á ²_Îâ ³_Îâ ķ_ÎćÏƅ

¯_Î^Ï

â Ɔ_ƃ (13)

ᩍʑᕽ, ³۵ʑᵡ໕(datum)ᮝಽᇡ░⦹⃽ၵ݆ʭḡ᮹Ñญᯕ໑,

²۵Ǎe݉໕ᙹ᭥, ¯۵Ǎe᧲݉ᨱᕽ᮹⠪Ɂᮁᗮ, ķ۵Ǎe

᧲݉ᨱᕽ᮹ᨱթḡᅕᱶĥᙹ, ƅ۵ᵲಆaᗮࠥ,Ɔƃ۵ᨱթḡᗱᝅᙹ ࢱᯕ݅. ᨱթḡᗱᝅᙹࢱᨱ ݡ⦽ ႊᱶ᜾ᮡ Eq. (14)᪡ z݅.

Ɯ

ƚ

_ć

Ïƅ ķ_Ï¯_Ï^Ï

à ćÏƅ ķ_Î¯_Î^Ïƛ

Ɲ

ƞ

(14) ᩍʑᕽ, ¥ᮡᮁపaᵲǍeÑญ, ^ć¬Ƅ۵Ǎe᮹⠪ɁษₑĞᔍ,

۵݉໕⪶ݡၰ⇶ᗭᨱ᮹⦽ᗱᝅĥᙹᯕ݅. ᙹ᭥۵᭥ࢱႊᱶ᜾ᮥ

ၹᅖ⦹ᩍ⧕ෝĥᔑ⧉ᮝಽ៉᨜ᮥᙹᯩᮝ໑ĥᔑŝᱶᮡᔢඹ݉໕ ᮹ᙹ᭥ෝaᱶ(ᔍඹǍeᨱᕽ۵⦹ඹ݉໕ᙹ᭥aᱶ)⦹ᩍ, aᱶᙹ

᭥ᨱݡ⦹ᩍ☖ᙹ܆(K)ŝᗮࠥᙹࢱෝǍ⦹Ł, ᯕsᮥᯕᬊ⦹ᩍ ć¬_Ƅෝᔑ⇽⦽᭥᮹Eq. (14)ᮥᯕᬊ⦹ᩍƆ_ƃෝǍ⦹໑, Eq. (13)ᨱ ᮹⦽ᔢඹ݉໕᮹ᙹ᭥᪡aᱶ⦽ᙹ᭥aᔢݡ᪅₉ჵ᭥ԕಽᙹಕ⧁

ভʭḡ ⇶₉ᱢᮝಽ ၹᅖ ĥᔑ⦽݅.

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Table 5. Model calibration and verification results from two extreme rainfall events Rainfall

Events

Observed Data Simulated

RMSE Steady Flow Unsteady Flow Note

ª_Ǝ (m³/s) ¡_Ǝ (EL.m) ¯_Ƌ (m/s) ¡_Ǝ (EL.m) ¯_Ƌ (m/s) ¡_Ǝ (EL.m) ¯_Ƌ (m/s) ¡_Ǝ (m) ¯_Ƌ (m/s)

July, 12, 2006 344.37 18.65 3.27 19.18 3.01 18.62 3.16 0.020 0.012 Cal.

July, 16, 2006 338.12 18.72 3.02 19.08 2.99 18.70 2.98 0.014 0.002 Ver.

*ª_Ǝ: Peak Discharge, ¡_Ǝ: Peak Water Surface, ¯_Ƌ: Average Velocity, RMSE: Root Mean Square Error, Cal: Calibration, Ver: Verification

MCS đŝ༉᮹ၽᔾࡽḡᱱᄥ⪮ᙹపᮥᔢඹ݉Ğĥ᳑Õᮝಽ

⦹Ł⦹ඹ݉Ğĥ᳑Õᮡ॒ඹᙹᝍ(normal depth)ᮝಽ⦹ᩍ⪮ᙹ᭥

ෝᔑᱶ⦹ᩡ݅(Yoon, 2012). ݅ᮭFigure 7ᮡ2006֥7ᬵ12ᯝ

⪙ᬑᔍᔢᨱݡ⦽⪮ᙹ᭥š⊂sᨱݡ⦽ᱶᔢඹ⧕ᕾŝᇡᱶඹ⧕ᕾ ᮹ᅕᱶ(calibration)ŝá᷾(verification)đŝෝӹ┡ԕᨩ݅. š⊂

ᙹ᭥ᨱݡ⦽ᇥᕾđŝᱶᔢᇡ॒ඹ⧕ᕾđŝ۵᧞eⓍíӹ᪅໑, ᝅᱽ⪮ᙹᔍᔢᮡ⪮ᙹ❭᮹qᙁ⬉ŝಽᯙ⦹ᩍᱥℕᱢᮝಽᇡᱶඹ

⧕ᕾđŝ᪡ᮁᔍ⦽᧲ᔢᮥӹ┡ԕŁᯩ݅. ᙹญ⦺ᱢ⪮ᙹ⇵ᱢ༉⩶

ᮥ☖⦽⪮ᙹ᭥⇵ᱢđŝʑ᳕᮹ᱶᔢඹ(steady flow) ⧕ᕾ༉⩶ᅕ

݅ᇡᱶඹ(unsteady flow) ⧕ᕾ༉⩶ᨱᕽ24% ᯲íᔑᱶࡹᨩᮝӹ, ᇡᱶඹ⧕ᕾ༉⩶ᮥ☖⦽ᙹญ⦺ᱢ⪮ᙹ⇵ᱢᨱ᮹⦽ĥᔑᙹ᭥(h)a

ᝅᱽ ⪮ᙹ᭥᳑Õᮥ ᅕ݅ ᬑᙹ⦹í ၹᩢ⦹Ł ᯩᮭᮥ ⪶ᯙ⧁ ᙹ

ᯩᨩ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵MCSᨱ᮹⦽Łᙹ᭥༉᮹ၽᔾᮥ

᭥⦹ᩍ ᇡᱶඹ ⧕ᕾᨱ ᮹⦽ ⪮ᙹ᭥ ⇵ᱢsᮥ ᔍᬊ⦹ᩡ݅.

ᝅ⊂⪙ᬑᔍᔢᨱ ݡ⦽ ᰆᬵƱ ḡᱱ᮹ ᙹ᭥, ᮁప š⊂ᯱഭෝ

ၵ┶ᮝಽᵝ᫵ḡᱱᨱݡ⦽⪮ᙹపᮥᔑᱶ⦹ᩡᮝ໑, ༉⩶᮹ᔢඹ݉

Ğĥ᳑Õᮝಽᱢᬊ⦹ᩡ݅. ੱ⦽ᰆᬵƱḡᱱ᮹ᝅ⊂ࡽᙹ᭥ᯱഭෝ

⦹ඹ݉Ğĥ᳑Õᮝಽᱢᬊ⦹ᩍᱶᔢᇡ॒ඹၰᇡᱶඹ⧕ᕾᮥᝅ᜽⦹

ᩡ݅. ᝅ⊂(observed)ᙹ᭥᪡ᇡᱶඹ⧕ᕾᨱ᮹⦽༉᮹(simulated) ᙹ᭥᮹ እƱෝ᭥⦹ᩍ☖ĥᱢႊჶᮝಽRMSE (root mean square error)ෝᔍᬊ⦹ᩡ݅. ᝅ⊂ᙹ᭥ᯱഭෝ☁ݡಽ⪙ᬑᔍᔢᮥ⇵⇽⦹

4.3 ৤଍-କ߆ւծմটଭऄคਓܑंজ

ᙹ᭥-ᮁపšĥłᖁ᮹ᇩ⪶ᝅࠥ۵Ⓧíྕ᯲᭥᪅₉(random error),ĥ☖᪅₉(systematic error), ᬑᩑ᪅₉(mistakes, spurious error)aᯩ݅. ᩍʑᕽ, ྕ᯲᭥᪅₉۵ᅕ☖ᝅ⨹᪅₉ಽeᵝࡹ໑

š⊂⊹ॅᮡʑ⫭᮹ჶ⊺ᨱ঑௝⠪Ɂᮥ঑௝ᇥ⡍ࡹŁᱶȽᇥ⡍

(normal distribution)ෝᯕ്݅. ᯕäॅᮡᙹྙš⊂ᨱᯩᨕᕽaᰆ

ᵲ᫵⦽᪅₉ಽᩍĉḥ݅. ੱ⦽, ĥ☖᪅₉۵ʑʑӹᰆ⊹aƱℕࡹḡ

ᦫ۵⦽⊂ᱶs᮹ᙹෝ۹ಅᕽ۵qᗭࡹḡᦫ۵᪅₉ᯕ݅. ᙹྙš⊂

ᨱᯩᨕᕽĥ☖᪅₉۵ʑᵡ⃺, ʑᵡᱱ, ᮁᗮĥ, əญŁᙹ᭥ʑಾĥ ᨱ᳕ᰍ⦽݅. ᯕ᪅₉۵ᯝၹᱢᮝಽ᯲ḡอĞᬑᨱ঑௝ᕽ۵ə

ᩢ⨆ᯕᙹ᭥-ᮁపšĥᨱʭḡ᪅₉ෝᮁၽ⦹íࡽ݅. ੱ⦽ᇡᱶ⪶⦽

ʑᵡᱱᮡ᯲ᮡs᮹ᮁపᯝĞᬑᭉᨕ᮹ษ൉ᇡᇥᨱᯩᨕᕽᙹ᭥

⊂ᱶᨱᝍb⦽᪅₉ෝᮁၽ⦽݅. ษḡสᮝಽᬑᩑ᪅₉۵⊂ᱶᮥ

ᙹ⧪⦹۵š⊂ᬱ॒ᨱ᮹⧕ᕽၽᔾ⦹۵᪅₉ಽ☖ĥᱢᮝಽᇥᕾᯕ

ᇩa܆⦽᪅₉ᯕ݅. ə్အಽš⊂⊹ᵲᨱᕽᯕ్⦽᪅₉aၽᔾ⦹

ᩡᮥ Ğᬑᨱ۵ ᱽ᫙⧕᧝อ ⦽݅. ᙹ᭥-ᮁపšĥ۵ ⦹⃽᮹ ᵝ᫵

ḡᱱᨱᕽᙹ᭥᪡ᮁపᮥ࠺᜽ᨱ⊂ᱶ⦹ᩍᯕॅ᮹šĥෝ᜾ᮝಽ

ӹ┡ԙäᯕ݅. ᙹ᭥-ᮁపšĥ᮹ᇩ⪶ᝅࠥ۵ᙹ᭥-ᮁపšĥᨱ᮹⧕

ĥᔑࡽᮁపᯕᝅ⊂ᮁపŝ᮹₉ᯕᨱᕽၽᔾ⦹۵ᇩ⪶ᝅࠥ(¬ƋƐ)᪡

ᙹ᭥-ᮁపšĥłᖁᨱ ݡ⦽ ᝅ⊂ ᮁప᮹ ⢽ᵡ᪅₉(¬_ƃ)ᨱ ᮹⧕ᕽ

ĥᔑࢁᙹᯩ݅(Ministry of Land, Infrastructure and Transport, 2007). ᙹ᭥-ᮁపšĥ᮹ ⢽ᵡ᪅₉¬_ƃ۵ ݅ᮭ Eq. (15)᪡ z݅

(ISO 1100-2, 1998).

¬_ƃá

å

^ć

^ā

^{Þªà ª}^{§ à Ï} ^Ɓ^ß^Ï

æ

^ÎîÏ⁽¹⁵⁾

ᩍʑᕽ,ª۵⊂ᱶᮁపᯕ໑,ªƁ۵ᙹ᭥-ᮁపšĥಽĥᔑࡽᮁప ᯕŁ, §ᮡᱥℕᮁప⊂ᱶ}ᙹᯕ݅. ⠪Ɂᨱݡ⦽ᇩ⪶ᝅࠥ(Ï¬_ƋƐ) ۵ ݅ᮭ Eq. (16)ᨱ ᮹⧕ᕽ ĥᔑࡽ݅.

Ï¬ƋƐá

X ƒ¬_ƃ

å

^ć^§^{Î â ć}

_ā

ãÞ¡à Ƙß à ćÞ¡ à Ƙßä^Ï

æ

^ÎîÏ^{Z Î×× Ü}⁽¹⁶⁾

ᩍʑᕽ, ƒ۵ᙹ᭥-ᮁపšĥᨱᕽᯱഭⓍʑᨱ঑ෙáᱶ☖ĥపᯕ݅.

ᬑᯕ⃽ᰆᬵƱḡᱱ᮹⊂ᱶᨱݡ⦽⢽ᵡ᪅₉(¬_ƃ)۵0.056ᮝಽ

ᇥᕾࡹᨩᮝ໑ ᯕ۵ ⠪Ɂᱢᮝಽ ⊂ᱶ⊹᮹ 95%۵ 5.6%᮹ Ḣᖁ

ჵ᭥ԕᨱ⡍⧉ࡽ݅۵äᮥ᮹ၙ⦽݅. ݅ᮭFigure 8ᮡš⊂ᙹ᭥-ᮁ

పᯱഭ᮹ྕ᯲᭥ᇩ⪶ᝅࠥᇥᕾđŝᯕ݅. ੱ⦽, Table 6ᮡᯥ᮹

ᙹ᭥Þ¡ à Ƙßᨱݡ⦽ª_Ɓ᮹}ᄥsᨱݡ⦽ྕ᯲᭥ᇩ⪶ᝅᖒ (_Ï¬_ƋƐ_Ö) đŝෝ ӹ┡ԕᨩᮝ໑, ĥᔑ đŝෝ ၵ┶ᮝಽ ᯲ᖒࡽ

Rating Curveᨱݡ⦽ᝁ഑ᖒᮥ⠪a⦹ʑ᭥⧉ᯕ݅. ĥᔑđŝᬑᯕ

⃽ḡᱱ᮹ᮁప⊂ᱶᖒŝ۵⠪ɁX ÎíÑÐ%, ↽ݡX ÑíÏÔ%᮹ᇩ⪶

ᝅᖒᯕ ᯩ۵ äᮝಽ ᇥᕾࡹᨩ݅.

(10)

Fig. 8. Results for random uncertainty of observed discharge data

Table 6. Random uncertainty of observed discharge data

Obs.

Data

¡ àƘ (m)

ª (^Ðî)

ª_Ɓ

(^Ðî) ^ª =_{Ɨ ª}_Ɓ =_Ɨ_Ɓ ^{ÞƗà Ɨ}^Ɓ^ß

Ï

(m) Ï¬_ƋƐ

(%) 1 0.68 38.08 43.25 3.64 3.77 0.02 1.22 2 0.52 13.79 27.86 2.62 3.33 0.49 1.50 3 0.27 3.87 9.50 1.35 2.25 0.81 2.45 4 0.15 1.46 3.61 0.38 1.28 0.82 3.40 5 1.08 48.64 92.26 3.88 4.52 0.41 1.09

108 1.07 103.26 90.86 4.64 4.51 0.02 1.09 109 0.82 76.33 58.77 4.34 4.07 0.07 1.10

(a) Logarithmic method (b) Stevens method

Fig. 9. Extension of Rating Curve from logarithmic and stevens method

4.4 ৤଍-କ߆ւծմটଭ઴ୋ

ᙹ᭥-ᮁపšĥłᖁᮡᮁప⊂ᱶᖒŝ᮹ᙹ᭥ჵ᭥ၷᨱᕽ۵ᱢᬊ

ࢁᙹᨧ݅. ə్ӹš⊂ࡽᙹ᭥ჵ᭥ၷ᮹ᮁప⇵ᱶᯕ⦥᫵⦽

Ğᬑ, ᙹ᭥-ᮁపšĥłᖁ᮹᫙ᔞᯕ⦥᫵⦹݅. ᯝၹᱢᮝಽ⪮ᙹ᜽᪡

zᮡŁᙹ᭥ᨱᕽ۵዁ෙᮁᗮ, ⓑᙹᝍၰᇡᮁྜྷ॒ᮝಽᯙ⦹ᩍ

ᮁప⊂ᱶᯕᨕಖÑӹᇩa܆⦹Ł᭥⨹⦹݅. ੱ⦽Łᙹ᭥ෝ⊂ᱶ⧁

อ⦽⪙ᬑᔍᔢᯕၽᔾ⦹ḡᦫᦹᮥĞᬑᨱ۵᫙ᔞᮥ☖⦹ᩍᙹ᭥-ᮁ

పšĥłᖁᮥᩑᰆ⧕᧝⦽݅(MOLIT, 2007). ᅙᩑǍᨱᕽ۵ᯝၹ ᱢᮝಽฯᯕᔍᬊ⦹Łᯩ۵ᱥݡᙹḡჶ(logarithmic method)ŝ

Stevens (1907)ႊჶᮥᱢᬊ⦹ᩍŁᙹ᭥ᨱݡ⦽ᙹ᭥-ᮁపšĥłᖁ

ᮥ ᩑᰆ⦹ᩡ݅.

š⊂ࡽᙹ᭥᪡ᮁపᮥᱥݡᙹḡᨱࠥ᜽⦹໕Figure 9(a)᪡zᮡ

Ḣᖁᮝಽӹ┡ӹ໑, ᯕಽᇡ░ᯥ᮹ᙹ᭥ᨱݡ⦽ᮁపᮥᱢᬊ⧁ᙹ

ᯩ݅. ݅ᮭFigure 9۵ᱥݡᙹḡ᪡Stevens ႊჶᮥᱢᬊ⦽đŝෝ

ӹ┡ԕŁᯩ݅. ᯕ᪡zᮡ᫙ᔞᮡᵲȽ༉᪡ݡȽ༉ᮁపᨱݡ⧕ᕽ

⦹ࠥ☖ᱽᯙĞᬑᨱᱢ⧊⦹ӹ↽Ł⊂ᱶᮁప᮹1.5႑ᯕᔢᨱݡ⧕ᕽ ۵᫙ᔞ⧕ᕽ۵ᦩࡽ݅(MOLIT, 2007). Figure 9ᨱᕽᅕ۵ၵ᪡

zᯕ, ᬑᯕ⃽ ᮁᩎ᮹ ᮁప ⊂ᱶ đŝಽᇡ░ ĥᔑ⦽ ᱥݡᙹḡჶ

ၰStevensႊჶᨱ᮹⦽ᙹ᭥-ᮁపšĥłᖁ᮹ᩑᰆ᮹Ğᬑݡℕᱢ ᮝಽᙹ᭥ᨱእ⦹ᩍᮁపᯕŝݡᔑᱶࡹ۵äᮝಽӹ┡ӹŁᙹ᭥ᨱ

ݡ⦽Rating Curve ᩑᰆᨱᱢᬊ⦹ʑᨱ۵݅ᗭᝁ഑ᖒᯕਉᨕḡ۵

äᮝಽ ᇥᕾࡽ݅.

4.5 MCS઩ଭ෉ճ৤଍Rating Curve ઴ୋ

ᙹ᭥-ᮁపšĥłᖁᮡḡᗮᱢᯙ⦹⃽༉ܩ░ย(monitoring)ᮥ

☖⧕ᕽ}ၽ/ᅕ᪥ࡹᨕᲙ᧝⦹ӹᦥḢʭḡǎԕ⦹⃽᮹Ğᬑᙹྙš

⊂ᯱഭa ∊ᇥ⦹ḡ ᦫᮝ໑ᯝᇡ Ǎ⇶ᯕ ࡹᨕᯩ݅Ł ⦹޵௝ࠥ

Łᙹ᭥ᨱݡ⦽ᯱഭa⪶ᅕࡹḡ༜⦽Ğᬑaݡᇡᇥᯕ݅. ঑௝ᕽ

ᅙᩑǍᨱᕽ۵ᮁ⇽ᇥᕾ᮹ᝁ഑ࠥෝ⨆ᔢ᜽┅Ł Łᙹ᭥ᨱݡ⦽

ᙹྙᯱഭ᮹⪶∊ᮥ᭥⦹ᩍ᭥⨹ࠥʑၹMCSෝ☖⦽Łᙹ᭥Rating Curveෝ ᩑᰆ⦹۵ ႊჶᮥ }ၽ⦹ᩡ݅. ↽ᱢ᮹ ⪶ශᇥ⡍⩶ᮝಽ

ᖁᱶࡽGumbelᇥ⡍⩶᮹Ƚ༉ๅ}ᄡᙹ(scale parameter)᪡᭥⊹

ๅ}ᄡᙹ(location parameter)ᨱbbӽᙹ[0, 1]ෝᱢᬊ⦹ᩍ݅ᙹ ᮹vᬑపǑ(300 set, 500 set, 800 set, 1000 set)ᮥ༉᮹ၽᔾ⦹ᩡ

(11)

Table 7. Stochastic evaluation of observed and simulated outflow data

Data H Q CC

(Q_obs vs. Q_cal)

RMSE (Q_obsvs. Q_cal)

Max Min Max Min

Observations 18.42 16.24 344.37 0.87 0.957265 18.1565

MCS Sim.

300 set 20.29 16.04 511.79 11.31 0.998235 5.7278

500 set 20.29 16.04 511.79 11.31 0.998086 6.0285

800 set 20.46 16.04 541.35 11.31 0.998149 5.8300

1000 set 20.46 15.87 541.35 6.05 0.998162 5.7719

* CC = Þ

ā

^Þª^ƍƀƑ^ÞƇßàª^ƁſƊ^ÞƇßßîƌ^ß^à^Þ

ā

^ª^ƍƀƑ^ÞƇßîƌ^ß^Z^Þ

ā

^ª^ƁſƊ^ÞƇßîƌ^ß^î^ö^ć^¬^Î^Z¬^Ï^,

RMSE = ö^ć

ā

^Þ^ª^ƍƀƑ^{à ª}^ƁſƊ^ß^Ï^îƌ, Where n is a number of data, ª_ƍƀƑ means observed discharge data, and ª_ƁſƊ means simulated discharge data.

(a) (b)

(c) (d)

Fig. 10. Observed and simulated Rating Curves: (a) 300 set, (b) 500 set, (c) 800 set and (d) 1000 set

݅. ᔢʑ༉᮹ၽᔾࡽvᬑపᮥၵ┶ᮝಽHuff-2ᇥ᭥ᇥ⡍ᨱ⧕ݚ⦹

۵᜽eᇥ⡍vᬑపᮥᔾᖒ⦹ᩡᮝ໑, ᯕෝݡᔢ⦹⃽ᮁᩎᨱ↽ᱢ⪵

ࡽvᬑ-ᮁ⇽༉⩶ᯙSWMMᨱᱢᬊ⦹ᩍᮁ⇽ᇥᕾᮥᝅ᜽⦹ᩡ݅.

ᇥᕾࡽᮁ⇽đŝෝ⪮ᙹ᭥⇵ᱢ༉⩶ᨱᱢᬊ⦹ᩍbb᮹⬂݉໕ (cross section) ᭥⊹ᨱᕽ⪮ᙹ᭥⇵ᱶᮥᝅ᜽⦹ᩡᮝ໑, ĥᔑࡽᙹ᭥

᪡ ᮁప đŝෝ ၵ┶ᮝಽ Łᙹ᭥ Rating Curveෝ ᯲ᖒ⦹ᩡ݅.

݅ᮭTable 7ᮡš⊂ᙹ᭥-ᮁపᯱഭŝMCSᨱ᮹⦹ᩍ༉᮹ၽᔾࡽ

ᙹ᭥-ᮁపᯱഭ᮹đŝෝእƱ⦹ᩍӹ┡ԕᨩ݅. š⊂ᙹ᭥᮹Ğᬑ

↽ݡE.L.18.42mಽӹ┡ԍᮝ໑, ĥᔑࡽᙹ᭥-ᮁపšĥłᖁŝ᮹

ᔢšĥᙹ۵ 0.957265ಽ, RMSE۵ 18.1565ಽ ӹ┡ԍ݅. ੱ⦽

MCSᨱ᮹⦹ᩍ༉᮹ၽᔾࡽᙹ᭥۵1000set ༉᮹ၽᔾ⦽đŝ↽ݡ

E.L.20.46mಽӹ┡ԍᮝ໑, ĥᔑࡽᙹ᭥-ᮁపšĥłᖁŝ᮹ᔢš ĥᙹ۵ 99.8%ಽ, RMSE۵ 5.7719ಽ ӹ┡ԍ݅.

ᱢᬊݡᔢ⦹⃽ᮁᩎ⦹ඹᇡᰆᬵƱḡᱱ᮹ⅾ11}֥(2000ⴇ

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Table 8. Development of high water level Rating Curves

Data Rating Curve Equation STDEV _«^Ï

Observations x á ÔÖíÒÒÞo à ÎÓíÎÏÎÕÖß^{ÎíÓÏÖÐÏÔ} ÞÎÓíÏÑ ; ¡ ; ÎÕíÑÏß 20.6754 0.9463

MCS Simulated Data

300 set x á ÐÕíÑÐÞo à ÎÒíÒÖÕÏÑß^{ÎíÔÎÏÔÐÖ} ÞÎÓí×Ñ ; ¡ ; Ï×íÏÖß 5.7374 0.9965 500 set x á Ñ×íÏÐÞo à ÎÒíÓÏÕ×Õß^{ÎíÓÕÒÐÏ×} ÞÎÓí×Ñ ; ¡ ; Ï×íÏÖß 6.0345 0.9962 800 set x á ÐÖíÏÓÞo à ÎÒíÓÎÐ×Öß^{ÎíÔ×ÎÔÒÎ} ÞÎÓí×Ñ ; ¡ ; Ï×íÑÓß 5.8337 0.9963 1000 set x á ÐÕíÓ×Þo à ÎÒíÓ×ÎÏÔß^{ÎíÔÎÎÒÎÓ} ÞÎÒíÕÔ ; ¡ ; Ï×íÑÓß 5.7807 0.9963

Fig. 11. Rainfall-Stage-Discharge curve developed by MCS technique considering the critical duration 2010֥) ᮁపš⊂ᯱഭෝၵ┶ᮝಽᙹ᭥-ᮁపšĥłᖁᮥ᯲ᖒ⦹ᩡ

ᮝ໑, ᯕෝᱥݡᙹḡჶၰStevensႊჶ᮹Łᙹ᭥ᩑᰆđŝ᪡MCS ᨱ᮹⦽༉᮹ၽᔾႊჶᮝಽࠥ᜽⦹⃽ᮁᩎ᮹Łᙹ᭥Rating Curve

ෝ᯲ᖒ⦹ᩍእƱ⦹ᩡ݅(Figure 10). ᬑᯕ⃽ᮁᩎᰆᬵƱḡᱱ᮹

ᝅ⊂⪮ᙹపᨱݡ⦽⪮ᙹ᭥łᖁ᜾᮹ᔑᱶđŝᝅ⊂ᯱഭ᪡ᙹ᭥-ᮁ

పłᖁ᜾ŝ᮹ᔢššĥ۵95.72%ಽᇥᕾࡹᨩŁ, ⢽ᵡ⠙₉۵20.68,

«^Ï۵0.9463ಽᇥᕾࡹᨩ݅. š⊂ᮁపᵲ↽Łᙹ᭥۵2006֥7ᬵ

12ᯝ⪙ᬑᔍᔢᨱᕽၽᔾ⦹ᩡŁ, ᯕভ᮹ᮁపᮡ344.8^Ðî, ↽Ł ᙹ᭥۵EL.18.42mಽᇥᕾࡹᨩŁ, ᯕ⬥᮹Łᙹ᭥š⊂ᮡᯕ൉ᨕḡ ḡᦫᦹ݅. ੱ⦽, MCSᮥ☖⦹ᩍ༉᮹ၽᔾ⦽ᮁపᨱݡ⦽⪮ᙹ᭥

⇵ᱢđŝ۵ᮁ⇽ᯱഭෝ300set, 500set, 800set ၰ1,000set ༉᮹⦽

đŝ۵༉ࢱእ᜘⦹íӹ┡ԍᮝ໑, bb᮹ᙹ᭥-ᮁపłᖁ᜾ᮡ݅ᮭ

Table 8ᨱᱶญ⦹ᩡ݅. ༉᮹ၽᔾࡽᯱഭ᪡ĥᔑ᜾ŝ᮹ᔢššĥ۵

99.80ⴇ99.82 %ಽ׳ᮡᔢšᖒᮥᅕᩡᮝ໑, ⢽ᵡ⠙₉(STDEV)۵

5.74ⴇ6.03, «^Ï۵0.9962ⴇ0.9965ಽᇥᕾࡹᨩ݅. đŝෝၵ┶ᮝ ಽᇥᕾ⧕ᅝভ, ʑ}ၽࡽš⊂ᯱഭ᮹ᙹ᭥-ᮁపłᖁ᜾ᮡᮁప⊂

ᱶᨱᯩᨕš⊂᪅₉᪡޵ᇩᨕŁᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥԕ⡍⦹Ł

ᯩ݅Ł⧁ᙹᯩ݅. ੱ⦽ᱥݡᙹḡჶŝStevensႊჶᮡ⦹⃽ᮁᩎ

Ƚ༉ᨱእ⦹ᩍᙹ᭥ᨱ঑ෙ⪮ᙹపᯕթྕŝݡᔑᱶࡹ۵ྙᱽᱱᯕ

ᯩ۵äᮝಽᇥᕾࡹᨩ݅. ⦹ḡอ, ɩ⫭}ၽࡽMCSᨱ᮹⦽༉᮹ၽ ᔾᮁపᨱݡ⦽Łᙹ᭥Rating Curve ᩑᰆႊჶᮡᮁᩎ᮹ๅ}ᄡᙹ

↽ᱢ⪵ࡽvᬑ-ᮁ⇽༉⩶ŝ⪮ᙹ᭥⇵ᱢ༉⩶ᮥᩑĥ⦹ᩍᔍᬊ⦹ᩍ, ᅕ݅ᝁ഑ᖒᯩ۵Łᙹ᭥Rating Curve᮹ᩑᰆŝ޵ᇩᨕࠥ᜽⦹⃽

ᮁᩎ᮹Łᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥqᗭ᜽┅۵⬉ŝaᯩ۵äᮝಽ

ᇥᕾࡽ݅.

ੱ⦽, ᅙᩑǍᨱᕽ۵MCSෝ☖⦽ᱽႊ᮹᭥⨹ࠥෝᔑᱶ⦹ᩡᮝ ໑, Łᙹ᭥᮹ᙹ᭥-ᮁపšĥłᖁ᮹ᩑᰆŝəᨱ঑ෙvᬑ-ᙹ᭥-ᮁ

పłᖁᮥ }ၽ⦹ᩡ݅(Figure 11). ᇥᕾđŝ, ḡᗮ᜽e 1᜽eŝ

3᜽eᨱݡ⦽ᱽႊ᮹ᬵඹ᭥⨹ࠥ۵8.0×10^-3ŝ1.8×10^-2ᯕ໑, ᱽႊ

ᬵඹa܆vᙹపᮡ1᜽e114.27mm, 3᜽e180.45mmಽӹ┡ԍ

݅. ᱽႊ᮹ᬵඹ᭥⨹ࠥaaᰆ׳ᮡḡᗮ᜽eᮡᯥĥḡᗮ᜽eᯙ

2᜽eᮝಽᇥᕾࡹᨩᮝ໑, ᬵඹ᭥⨹ࠥ۵1.9×10^-2, ᱽႊᬵඹa܆

vᙹపᮡ143.33mmಽӹ┡ԍ݅. ᬑᯕ⃽ŝzᮡḡႊ2ɪ⦹⃽(ᵲ ᗭ⦹⃽)ᮡࠥݍ᜽eᯕ݉᜽e(1ⴇ3᜽e)ᨱᇩŝ⦹໑, ᵲᗭ⦹⃽᮹

(13)

ĞᬑᰆʑeᨱÙ⊽vᬑᵲᨱᕽࠥ1ⴇ3᜽eᱶࠥ᮹℉ࢱvᬑᨱ

᮹⧕ᕽ℉ࢱᮁ⇽ᯕၽᔾ⧁ᙹᯩ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵ᬑᯕ⃽

ᮁᩎ᮹ࠥݍ᜽eᮥqᦩ⦹ᩍ3᜽eᯕ⦹ᨱݡ⧕ᕽvᬑ-ᙹ᭥šĥ łᖁᮥࠥ⇽⦹ᩡᮝ໑, ʑ᳕᮹ᙹ᭥-ᮁపšĥłᖁŝᱲ༊⦹ᩍvᬑ -ᙹ᭥-ᮁపšĥłᖁᮥ}ၽ⦹ᩡ݅. ᅙᩑǍ᮹ᖒŝ۵⪮ᙹᩩĞᅕ

᜽ᜅ▽ Ǎ⇶ ॒ ⬉ᮉᱢᯙ ⦹⃽ႊᰍĥ⫮ ᙹพᨱ ʑᩍ⧁ äᮝಽ

ᔍഭࡽ݅.

5. đು

ᅙᩑǍᨱᕽ۵ࠥ᜽⦹⃽ᮁᩎᮥݡᔢᮝಽMCSෝ☖⦽ᱢᱶᇥ⡍

⩶᮹ᯥĥḡᗮ᜽eᨱݡ⦹ᩍvᬑෝ༉᮹ၽᔾ᜽┕ᮝಽ↽ᱢ⪵ࡽ

vᬑ-ᮁ⇽༉⩶ᮥ☖⦽ᮁ⇽༉᮹ෝᝅ᜽⦹Ł, ᯕෝ⪮ᙹ᭥⇵ᱢ༉⩶

ŝᩑĥ⦹ᩍŁᙹ᭥Rating Curveෝ᯲ᖒ⦹۵ႊჶᮥᱽᦩ⦹ᩡᮝ ໑, ݅ᮭŝ zᮡ đುᮥ ࠥ⇽⦹ᩡ݅.

ʑჶᮝಽ ༉᮹ ၽᔾ᜽⍽ Łᙹ᭥ Rating Curveෝ ᯲ᖒ⦹۵

ႊჶᮥᱽᦩ⦹ᩡᮝ໑, ᅕ݅ᝁ഑ᖒᯩ۵ᙹ᭥-ᮁపᯱഭ᮹⪶ᅕ

ෝ☖⦽Łᙹ᭥᮹ᇩ⪶ᝅᖒᮥqᗭ᜽⍽ᙹ᭥-ᮁపšĥłᖁᮥ

ᩑᰆ⦹۵ ႊჶುᮥ ᱽ᜽⦹ᩡ݅.

(2) ݡᔢ⦹⃽ᮁᩎ᮹š⊂ᮁపᯱഭෝၵ┶ᮝಽ}ၽࡽᙹ᭥-ᮁప

šĥłᖁ᜾ᮡx á ÔÖíÒÒÞo à ÎÓíÎÏÎÕÖß^{ÎíÓÏÖÐÏÔ},ãÎÓíÏÑ ; ¡

; ÎÕíÑÏäᯕ໑, š⊂ᯱഭ᪡łᖁ᜾ŝ᮹đᱶĥᙹ(«^Ï)۵0.9463 ᮝಽ ᇥᕾࡹᨩᮝ໑, š⊂⊹᮹⢽ᵡ᪅₉(¬_ƃ)۵0.056ᮝಽ, ྕ᯲

᭥ᇩ⪶ᝅᖒ(Ï¬ƋƐ)ᮡ⠪ɁX ÎíÑÐ%, ↽ݡX ÑíÏÔ%ಽᇥᕾࡹ

ᨩ݅.

(3) ʑ }ၽࡽ š⊂ᯱഭ᮹ ᙹ᭥-ᮁపłᖁ᜾ᮡ ᮁప⊂ᱶᨱ ᯩᨕ

š⊂᪅₉᪡޵ᇩᨕŁᙹ᭥ᨱݡ⦽ᇩ⪶ᝅᖒᮥԕ⡍⦹Łᯩᮭᮥ

⪶ᯙ⧁ᙹᯩᮝ໑, ᱥݡᙹḡჶŝStevensႊჶᨱ᮹⦽Łᙹ᭥

ᩑᰆᮡࠥ᜽⦹⃽ᮁᩎȽ༉ᨱእ⦹ᩍᙹ᭥ᨱ঑ෙ⪮ᙹపᯕ

թྕ ŝݡ ᔑᱶࡹ۵ ྙᱽᱱᯕ ᯩ۵ äᮝಽ ᇥᕾࡹᨩ݅.

(4) ༉᮹ࡽᙹ᭥ၰᮁపᯱഭෝ☖⦹ᩍŁᙹ᭥ᨱݡ⦽ᙹ᭥-ᮁపł ᖁᮥᩑᰆ⦹Łᯕෝʑ᳕᮹ᱥݡᙹḡჶŝStevensႊჶ᮹đŝ Rating Curveᩑᰆႊჶ᮹ᬑᙹᖒᮥ᯦᷾⦹ᩡᮝ໑, Łᙹ᭥ᩑ ᰆŝᮁᩎ᮹ᯥĥḡᗮ᜽eᨱ঑ෙvᬑ-ᙹ᭥-ᮁపłᖁ᮹}ၽ Łᯱ ⦹ᩡ݅.

ᅙᩑǍ᮹ᖒŝ۵MCSᨱ᮹⦽vᬑ᮹༉᮹ၽᔾŝᮁ⇽ᇥᕾ᮹

ᝁ഑ࠥෝ⨆ᔢ᜽┅ŁŁᙹ᭥ᨱݡ⦽ᙹྙᯱഭ᮹⪶∊ᮥʑၹᮝಽ

⪮ᙹ᜽⪮ᙹ⦝⧕ᩩ⊂ၰ᭥⨹᜽ᖅྜྷᨱݡ⦽ݡ₦ᙹพ॒⬉ᮉᱢᯙ

⦹⃽ႊᰍĥ⫮ᙹพᨱʑᩍ⧁äᮝಽᔍഭࡽ݅. ə్ӹ⨆⬥ᅕ݅

ᝁ഑ᖒᯩ۵ đŝ᮹ ࠥ⇽ŝᝅྕ ⪽ᬊᮥ ᭥⧕ᕽ۵࠺ᯝ ᮁᩎ᮹

š⊂ࡽᯱഭෝၵ┶ᮝಽḡᗮᱢᯙá᷾ᯕ⦥᫵⧁äᮝಽ❱݉ࡽ݅.

qᔍ᮹ɡ

ᯕםྙᮡ2012֥ࠥᕽᬙ᜽พݡ⦺ƱƱԕ⦺ᚁᩑǍእᨱ᮹⦹ᩍ

ᩑǍࡹᨩᮝ໑, ᩑǍእ ḡᬱᨱ qᔍෝ ऽพܩ݅.

References

Afshar, A., Rasekh, A. and Afshar, M. H. (2009). “Risk-based optimization of large flood-diversion systems using genetic algorithms.” Engineering Optimization, Vol. 41, No. 3, pp. 259-273.

Apel, H., Thieken, A. H. Merz, B. and Blöschl, G. (2006). “A probabilistic modelling system for assessing flood risks,” Natural Hazards, Vol. 38, No. 1, pp. 79-100.

Bailey, J. F. and Ray, H. A. (1966). “Definition of stage-discharge relation in natural channels by step-backwater analysis.” River Hydraulics, Geological Survey Water-Supply Paper 1869-A, pp. 1-24.

Clarke, R. T. (1999). “Uncertainty in the estimation of mean annual flood due to Rating Curve indefinition.” Journal of Hydrology, Vol. 222, No. 1-4, pp. 185-190.

DeGagne, M. P. J., Douglas, G. G., Hudson, H. R. and Simonovic, S. P. (1996). “A decision support system for the analysis and use of stage-discharge rating curves.” Journal of Hydrology, 184, 225-241.

IOS (International Organization for Standardization) (1998). Deter- mination of the stage-discharge relationship, Measurement of Liquid Flow in Open Channels-Part 2: ISO Standard 1100-2, pp.

133-153.

Lambie, J. C. (1978). “Measurement of flowvelocity area methods.

In: Hershcy RW, (Ed.), Hydrometry: Principles and Practices.”

Wiley, Chichester, Chapter 1.

MOLIT (Ministry of Land, Infrastructure and Transport) (2007).

Streamflow Survey Report in 2006 (in Korean).

Moon, Y. L., Cho, S. J. and Chun, S. Y. (2003). “Nonparametric Kernel Regression model for Rating curve.” Journal of Korea Water Resources Association, Vol. 36, No. 6, pp. 1025-1033 (in Korean).

Moyeeda, R. A. and Clarke, R. T. (2005). “The use of Bayesian methods for fitting rating curves, with case studies.” Advances in Water Resources, Vol. 28, No. 8, pp. 807-818.

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