Re-Analysis of Clark Model Based on Drainage Structure of Basin

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Received June 17, 2013/ revised July 18, 2013/ accepted August 21, 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)

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵Ǥ͸Ǥʹʹͷͷ ǤǤǤ

⇮⟖ጪ⸮Ἲ#Ꮾ⇖⳺Ḛ#㬚#Clark ⁦㯓ⴖ#⵪㬲⛛

ࢮঃ෮ȵ׌சశȵ୨ܛ֝ȵ୨ւ৤

Park, Sang Hyun*, Kim, Joo Cheol**, Jeong, Dong Kug***, Jung, Kwan Sue****

Re-Analysis of Clark Model Based on Drainage Structure of Basin

ABSTRACT

This study presents the width function-based Clark model. To this end, rescaled width function with distinction between hillslope and channel velocity is used as time-area curve and then it is routed through linear storage within the framework of not finite difference scheme used in original Clark model but analytical expression of linear storage routing. There are three parameters focused in this study: storage coefficient, hillslope velocity and channel velocity. SCE-UA, one of the popular global optimization methods, is applied to estimate them. The shapes of resulting IUHs from this study are evaluated in terms of the three statistical moments of hydrologic response functions: mean, variance and the third moment about the center of IUH. The correlation coefficients to the three statistical moments simulated in this study against these of observed hydrographs were estimated at 0.995 for the mean, 0.993 for the variance and 0.983 for the third moment about the center of IUH. The shape of resulting IUHs from this study give rise to satisfactory simulation results in terms of the mean and variance. But the third moment about the center of IUH tend to be overestimated. Clark model proposed in this study is superior to the one only taking into account mean and variance of IUH with respect to skewness, peak discharge and peak time of runoff hydrograph. From this result it is confirmed that the method suggested in this study is useful tool to reflect the heterogeneity of drainage path and hydrodynamic parameters. The variation of statistical moments of IUH are mainly influenced by storage coefficient and in turn the effect of channel velocity is greater than the one of hillslope velocity. Therefore storage coefficient and channel velocity are the crucial factors in shaping the form of IUH and should be considered carefully to apply Clark model proposed in this study.

Key words : Width function, SCE-UA, Storage coefficient, Hillslope velocity, Channel velocity

Ⅹಾ

ᅙᩑǍᨱᕽ۵ᮁᩎ᮹႑ᙹǍ᳑ෝᖅ໦⧁ᙹᯩ۵⡎⧉ᙹʑၹ᮹Clark ༉⩶ᮥᱽᦩ⦹ᩡ݅. ᜽e-໕ᱢłᖁᮝಽ۵ḡ⢽໕ŝ⦹⃽ᨱݡ⦹ᩍ}ᄥ ᱢᯙ࠺ᙹᩎ⦺ᱢ✚ᖒᮥᱢᬊ⦽ᰍ᳑ᱶࡽ⡎⧉ᙹෝᯕᬊ⦹ᩡ݅. ᖁ⩶ᱡᙹḡ⇵ᱢ᮹Ğᬑʑ᳕᮹Clark ༉⩶ŝzᯕ₉ᇥ⪵ࡽ⩶┽aᦥܩ௝⧕

ᕾ᜾ᮥᱢᬊ⦹ᩍᙹ⧪⦹ᩡ݅. ᅙᩑǍᨱᕽŁಅ⦽ᵝ᫵⦽ๅ}ᄡᙹॅಽ۵ḡ⢽໕⠪Ɂᯕᘂᗮࠥၰ⦹⃽⠪Ɂᯕᘂᗮࠥ᪡ᱡඹᔢᙹෝॅᙹᯩ݅.

ᝅᱽๅ}ᄡᙹ᮹⇵ᱶŝᱶᨱ۵ᱥᩎ↽ᱢ⪵ʑჶᵲ᮹⦹ӹᯙSCE-UA ʑჶᮥᱢᬊ⦹ᩡ݅. ੱ⦽Clark ༉⩶ᮝಽᇡ░ᮁࠥࡽᙽe݉᭥ࠥ᮹⩶

ᔢᮡᬱᱱᨱݡ⦽1₉༉ູ✙᪡໕ᱢᵲᝍᨱݡ⦽2, 3₉༉ູ✙ಽǍᇥ⦹ᩍ⠪a⦹ᩡ݅. š⊂ᙹྙᔍᔢ᮹☖ĥ༉ູ✙ॅŝᅙᩑǍᨱᕽ⇵ᱶࡽ☖

ĥ༉ູ✙ॅ᮹ᔢšĥᙹ۵1₉༉ູ✙᮹Ğᬑ0.995, 2₉༉ູ✙۵0.993, 3₉༉ູ✙۵0.983ಽᔑᱶࡹᨩ݅. ⠪Ɂŝᇥᔑᨱݡ⧕ᕽ۵⇵ᱶsŝ

š⊂sᯕݡℕಽᯝ⊹⦹۵Ğ⨆ᮥᅕᩍᵝᨩ݅. ə్ӹ⇵ᱶࡽ3₉༉ູ✙ᨱݡ⦽đŝ۵݅ᗭŝݡ⠪aࡹ۵Ğ⨆ᮥӹ┡ԕᨩ݅. ᱽᦩࡽClark

༉⩶ᮡᙽe݉᭥ࠥ᮹⩶ᔢᮥ⠪ɁŝᇥᔑอᮥŁಅ⦹ᩍᱢᬊ⦽ႊჶᅕ݅ᙹྙłᖁ᮹᪽łၰ℉ࢱ᳭⢽᮹༉᮹᪡šಉࡽ⦽ĥᱱᮥ}ᖁ⦹ᩡ݅.

սėॡ

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ᯕ్⦽đŝಽᇡ░ᅙᩑǍᨱᕽᱽ᜽⦽ႊჶುᮡ႑ᙹĞಽ᮹ᯕḩᖒŝ࠺ᱢๅ}ᄡᙹॅ᮹ᩢ⨆ᮥᱢᱩ⦹íၹᩢ⧁ᙹᯩᮭᮥ⪶ᯙ⧁ᙹᯩᨩ݅.

ᅙᩑǍᨱᕽŁಅ⦽༉ູ✙ॅ᮹ᄡ࠺ᖒᮡᵝಽᱡඹᔢᙹ᮹ᩢ⨆ᯕⓍíӹ┡ӹŁᯩᮝ໑, ḡ⢽໕⠪Ɂᯕᘂᗮࠥᅕ݅۵⦹⃽⠪ɁᯕᘂᗮࠥaⓍí

ᩢ⨆ᮥၙ⊹۵äᮥ⪶ᯙ⧁ᙹᯩᨩ݅. ᯕಽᇡ░ᱡඹᔢᙹ᪡⦹⃽⠪ɁᯕᘂᗮࠥaClark ༉⩶ᮝಽᇡ░ᮁࠥࡹ۵ᙽe݉᭥ࠥ᮹⩶ᔢᮥđᱶ⦹۵ ߑḡ႑ᱢᯙᩎ⧁ᮥ⦹۵äᮝಽ⪶ᯙࡹᨩ݅. ঑௝ᕽࢱๅ}ᄡᙹ۵༉⩶᮹ᱢᬊŝᱶᨱᕽᵲ᫵⦹íŁಅࡹᨕ᧝⧁äᮝಽ❱݉ࡽ݅.

áᔪᨕ⡎⧉ᙹ, SCE-UA, ᱡඹᔢᙹ, ḡ⢽໕⠪Ɂᯕᘂᗮࠥ, ⦹⃽⠪Ɂᯕᘂᗮࠥ

1. ᕽು

Nash(1959)ᨱ᮹⦹ᩍ༉ູ✙ჶᯕᱽ᜽ࡽᯕ௹ᙽe݉᭥ࠥ᮹

☖ĥ⦺ᱢ༉ູ✙۵vᬑ-ᮁ⇽᮲ݖŝᱶᮥ⧕ᕾ⦹ʑ᭥⦽ᵝ᫵⦽

✚ᖒๅ}ᄡᙹಽᯕᬊࡹᨕ᪵݅. Rinaldo et al.(1991)ᮡStrahler᮹

₉ᙹჶ⊺ᮥʑၹᮝಽᮁᩎԕ႑ᙹĞಽ᮹ᯕḩᖒ(heterogeneity)ᨱ

ݡ⦽ᇥᕾᮥ☖⦹ᩍᙽe݉᭥ࠥ᮹2₉༉ູ✙(ᇥᔑ)ᨱݡ⦽ℕĥᱢ ᯙᱲɝႊჶᮥᱽ᜽⦹ᩡ݅. ᯕ⬥GIS᮹ၽᱥŝ⧉̹ᯕॅᮡĊᯱෝ

ʑၹᮝಽ ⦽ ႑ᙹǍ᳑᮹ ᯕḩᖒŝ đ⧊⦹ᩍ ᙽe݉᭥ࠥ᮹ 2₉

༉ູ✙ෝ ᱶప⪵⧁ ᙹ ᯩ۵ }ֱᮝಽ ၽᱥ⦹ᩡ݅(Di Lazzaro, 2009).

Botter and Rinaldo(2003)۵Ċᯱෝʑၹᮝಽ⦽ᙹ⊹ᝅ⨹ᮥ

႑Ğᮝಽḡ⢽໕ᮁ࠺ŝ⦹⃽ᮁ࠺᮹ᔢ⪙᯲ᬊᯕᙽe݉᭥ࠥ᮹᪽

łࠥ(skewness) ⪚ᮡ3₉༉ູ✙᮹Ñ࠺ᮥḡ႑⦹۵ᵝ᫵⦽✚ᖒᯕ

ࢁᙹᯩᮭᮥḡᱢ⦽ၵᯩ݅. ✚⯩ᯕॅᮡᯱᩑᮁᩎ᮹⡎⧉ᙹ(width function)a᧲ᯱ᮹ᔢ⪙᯲ᬊᨱ঑௝᪽łࠥaᩎᱥࡽ⩶┽᮹᮲ݖ

⧉ᙹಽ ᄡ⪵⦹۵ ŝᱶᮥ ᩩ᜽⦽ ၵ ᯩ۵ߑ, ᅙ ᩑǍ۵ ᯕ ᱱᨱ

ᵝ༊⦹ᩍ⇽ၽ⦹íࡹᨩ݅. ᷪᅙᩑǍᨱᕽࠥḡ⢽໕ᮁ࠺ŝ⦹⃽ᮁ

࠺᮹ᔢ⪙᯲ᬊᨱ঑ෙ ᙽe݉᭥ࠥ᮹☖ĥ⦺ᱢ༉ູ✙ॅᨱݡ⦽

ྜྷญᱢᱲɝᮥᙹ⧪⧁ᙹᯩ۵༉⩶ᮥᱽᦩ⦹Łᯱ⦹۵äᯕ݅.

ᅙᩑǍᨱᕽ۵ᯕ్⦽ᱽၹᔍ⧎ᮥᱢᬊ⧁ᙹᯩ۵ࠥǍಽClark

༉⩶ᮥ ᖁᱶ⦹ᩡ݅.

Clark ༉⩶ᮡǎԕᨱᕽࠥฯᮡᱢᬊŝᩑǍaᙹ⧪ࡹŁᯩᮝӹ

ݡᇡᇥๅ}ᄡᙹ⇵ᱶŝĞ⨹᜾}ၽᨱḲᵲࡹᨕᯩ݅(Yoo, 2009).

Yoon and Hong(1995)۵ᮁᩎ⠪Ɂᮁᗮᮥᔑᱶ⦹ᩍ᜽e-໕ᱢł ᖁᮥe݉⯩Ǎᖒ⧁ᙹᯩ۵ႊჶᮥ}ၽ⦹ᩡŁ, ๅ}ᄡᙹෝၙĥ⊂

ᮁᩎᨱᕽ ᛞí ᔑᱶ⧁ ᙹ ᯩࠥಾ ݉ᙽ ⫭ȡ᜾ᮥ ᮁࠥ⦹ᩡ݅.

Seong(1999)ᮡ᜽e-໕ᱢłᖁᮥ⧕ᕾᱢᯙႊჶᮝಽᮁࠥ⦹ᩡᮝ ໑ࠥݍ᜽eᮡḡ⩶⦺ᱢᯱʑᔢᔍᖒ, ᱡඹᔢᙹ۵ᮁᩎᨱݡ⦽᜽e

✚ᖒ᮹ᔢᔍᖒŖ᜾ᮥᯕᬊ⦹ᩍ⇵ᱶ⦹ᩡ݅. Jeong and Bae(2003) ۵᜽e-໕ᱢłᖁᮥGIS ʑჶᮥᯕᬊ⦹ᩍᔑᱶ⧁ᙹᯩ۵ႊჶᮥ

ᱽᦩ⦹ᩡŁ ᮁ⇽⧕ᕾᨱ ၙ⊹۵ ᩢ⨆ᮥ á☁⦹ᩡ݅. Yoon et al.(2005)ᮡᩢ⨆ಆᯕ׳ᮡᮁᩎ᮹✚ᖒᯙᯱෝᯕᬊ⦽Clark ⧊ᖒ

݉᭥ࠥ᮹ๅ}ᄡᙹ᮹⫭ȡ᜾ᮥᮁࠥ⦹ᩡ݅. Lee et. al.(2009)ᮡ

Ŗeᱢᮝಽᇥ⡍ࡽvᬑᯱഭ᮹༉᮹ʑ܆ᮥ⇵a⦽Modified Clark

ႊჶᮥᯕᬊ⦹ᩍ, Ⓧญʦႊჶᨱ᮹⧕Ŗeᇥ⡍ࡽvᬑෝ∊ᵝݱ

ᮁᩎᨱᱢᬊ⦹ᩡ݅. ᯕᩑǍᨱᕽᱢᬊࡽModified Clark ႊჶᮡ

Ċᯱᄥᮁ⦹Ñญෝᔑᱶ⦹Łᮁᩎ⇽Ǎʭḡ᮹ࠥݍ᜽eᮡĊᯱᄥಽ

Łᮁ⦹íᔑᱶࡽ݅. ə్ӹĊᯱᄥࠥݍ᜽eᔑᱶᮥ᭥⦽ᮁᗮᮡ

ᮁᩎᱥℕෝ࠺ᯝ⦹íaᱶ⦹ᩍᱢᬊ⦹íࡽ݅. Yoo and Shin (2010)ᮡNash ᙽe݉᭥ࠥ᮹Ǎ᳑ෝᯕᬊ⦹ᩍᮁᩎ᮹ᱡඹᔢᙹ᪡

ࠥݍ᜽eᮥ⇵ᱶ⦹۵Ğ⨹ᱢᯙႊჶᮥᱽ᜽⦹ᩡ݅. ᯕ్⦽ᩑǍॅ

ᮡ ᝅྕᨱᕽ ⬉ᮉᱢᯕŁ ᝁ഑ᖒ ᯩ۵ Clark ༉⩶᮹ ᱢᬊ ॒ᮥ

᭥⦹ᩍၹऽ᜽⦥᫵⦹ḡอ, Clark ༉⩶ᮥᯕᬊ⦹ᩍᱶ⪶⦽vᬑ-ᮁ

⇽⧕ᕾᮥ᭥⧕ᕽ۵༉⩶ᨱݡ⦽ɝᅙᱢᯙᯕ⧕aၹऽ᜽⦥᫵⦹݅.

ᯕ్⦽ vᬑ-ᮁ⇽ ⩥ᔢ᮹ ᅙḩᱢᯙ ✚ᖒᨱ ᱲɝ⦹ʑ ᭥⧕ᕽ۵

Clark ༉⩶᮹ᯕುᱢɝÑᯙᙽe݉᭥ࠥ᮹⩶ᔢᨱݡ⦽ᱶపᱢᯙ

⠪aaᖁ⧪ࡹᨕ᧝⧁äᮝಽ❱݉ࡽ݅. ⦹ḡอᯕᨱݡ⦽ǎԕ

ᩑǍᔍಡ۵ ₟ᦥᅕʑa ᨕಅᬕ ᝅᱶᨱ ᯩ݅.

Park et. al.(2013)ᮡ⡎⧉ᙹෝʑၹᮝಽ᜽e-໕ᱢłᖁᮥǍᖒ

⦹Ł, ༉ູ✙ჶ᮹ᬱญᨱ঑௝ࠥݍ᜽eŝᱡඹᔢᙹෝᔑᱶ⧁ᙹ

ᯩ۵ႊჶುᮥᱽ᜽⦹ᩡ݅. ੱ⦽ᙽe݉᭥ࠥ᮹⩶ᔢᮥᱶపᱢᮝಽ

ĥప⦹۵šĥ᜾ᮥᱽ᜽⦽ၵᯩ݅. ə్ӹPark et. al.(2013)ᯕ

ᱽᦩ⦽ႊჶᮡᙽe݉᭥ࠥ᮹⩶ᔢᮥ⠪Ɂŝ ᇥᔑอᮥŁಅ⦹ᩍ

ᱢᬊ⦽äᯕŁ, đŝಽᙹྙłᖁ᮹᪽łࡹ۵ᱶࠥ᪡℉ࢱᮁపᯕ

ݡℕಽ ŝᗭ⠪a ࡹ۵ ⦽ĥᱱᮥ ᅕᩍᵝᨩ݅.

঑௝ᕽᅙᩑǍᨱᕽ۵ᮁᩎ᮹႑ᙹǍ᳑ෝᖅ໦⧁ᙹᯩ۵⡎

⧉ᙹʑၹ᮹Clark ༉⩶ᮥᱽᦩ⦹Ł, ᜽e-໕ᱢłᖁᮝಽ۵ḡ⢽໕ ŝ⦹⃽ᨱݡ⦹ᩍ}ᄥᱢᯙ࠺ᙹᩎ⦺ᱢ✚ᖒᮥᱢᬊ⦽ᰍ᳑ᱶࡽ

⡎⧉ᙹෝᯕᬊ⦹Łᯱ⦽݅. ੱ⦽ᖁ⩶ᱡᙹḡ⇵ᱢ᮹Ğᬑʑ᳕᮹

Clark ༉⩶ŝzᯕ₉ᇥ⪵ࡽ⩶┽aᦥܩ௝⧕ᕾ᜾ᮥᱢᬊ⦹ᩍ

ᙹ⧪⦹Łᯱ⦽݅. ᅙᩑǍᨱᕽᱽᦩࡽ༉⩶ᮥʑၹᮝಽᙽe݉᭥ࠥ

᮹⩶ᔢᮥᱶపᱢᮝಽĥప⧁ᙹᯩ۵šĥ᜾ᮥᱽ᜽⦹Łᯱ⦽݅.

ᯕෝၵ┶ᮝಽᅙᩑǍ۵vᬑ-ᮁ⇽⩥ᔢ᮹ᅙḩᱢᯙ✚ᖒᨱᱲɝ⧁

ᙹ ᯩ۵ ⧊ญᱢᯙ ᙹ݉ᮥ ᱽŖ⧁ ᙹ ᯩᮥ äᮝಽ ʑݡࡽ݅.

2. ᯕುᱢ႑Ğ

2.1 Clark ࡦ෴ଭվਐฃ

Clark(1945)ᮡ᜽e-໕ᱢłᖁᮥᖁ⩶ᱡᙹḡᨱ⇵ᱢ⦹ᩍᙽe

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݉᭥ࠥ᮹ }ֱᮥ ᱽ᜽⦹ᩡŁ, ᯝၹ᜾ᮡ ᜽e-໕ᱢłᖁƕÞƒß᪡

Eq. (1)ŝzᮡᖁ⩶ᱡᙹḡƄÞƒß᮹⫭ᖁᱢᇥ(convolution) ⩶┽ಽ

Eq. (2)᪡ zᯕ ӹ┡ԝ ᙹ ᯩ݅.

ƄÞƒß á ć¤Î ƃ^{à ć}^¤^ƒ, _{× ï ƒ ï t} (1)

ƆÞƒß áõ_×^ƒƕÞŉßƄÞƒà ŉßƂŉ (2)

ᩍʑᕽƆÞƒß۵Clark᮹ᙽe݉᭥ࠥ᪡¤۵ᱡඹᔢᙹᯕ݅. Clark

༉⩶᮹ๅ}ᄡᙹ۵ࠥݍ᜽e(time of concentration) _Ɓ᪡¤ಽ

bbᖁ⩶ᙹಽĥᩕ᮹ʑᱡ᜽e(base time)ŝᖁ⩶ᱡᙹḡ᮹⠪Ɂℕ ඹ᜽eᮝಽ ⧕ᕾࡹᨕ ḥ݅.

2.2 Clark ࡦ෴ଭധծࡦࡖൈ

Eq. (2)ಽᱶ᮹ࡹ۵ᙽe݉᭥ࠥ᮹ᵝ᫵⦽☖ĥ༉ູ✙ॅᮡ༉ູ

✙ჶ᮹ ᬱญಽᇡ░ ݅ᮭŝ zᯕ ᮁࠥ⧁ ᙹ ᯩ݅(Dooge, 1973;

Singh, 1988).

¦ÎÞƆß á ćƒáõ_×^Ɓ^{ƒƕÞƒßƂƒâ¤}⁽³⁾

¦_Ï^łÞƆß á ň_ƒ^Ïáõ_×^Ɓ^{Þƒà ćƒß}^Ï^{ƕÞƒßƂƒâ¤}^Ï⁽⁴⁾

¦_Ð^łÞƆß áõ_×^Ɓ^{Þƒà ćƒß}^Ð^{ƕÞƒßƂƒâÏ¤}^Ð⁽⁵⁾

ᩍʑᕽ¦ÎÞƆß۵ᬱᱱᨱݡ⦽ᙽe݉᭥ࠥƆÞƒß᮹1₉༉ູ✙ᯕ Ł¦ÏłÞƆß, _¦_Ð^łÞƆßᮡ bb ໕ᱢ ᵲᝍᨱ ݡ⦽ƆÞƒß᮹ 2, 3₉

༉ູ✙ᯕ݅. Lienhard(1964)᮹☖ĥྜྷญ⦺ᱢᱲɝჶᨱ঑௝ᙽe

݉᭥ࠥ۵ྕ᯲᭥⇵⇽⦽vᬑ᯦ᯱ᮹ᮁᩎԕᮁ⦹᜽e(travel time)᮹

⪶ශၡࠥ⧉ᙹ᪡⧊࠺ᯥᯕ໦᜽ᱢᮝಽ᯦᷾ࡽၵᯩ݅(Rodriguez- Iturbe and Valdes, 1979). ᯕᨱ঑௝¦ÎÞƆß,_¦_Ï^łÞƆß۵bbᮁ⦹᜽

e᮹ ⠪Ɂ(ćƒ)ŝᇥᔑ(ňƒÏ)᮹᮹ၙෝaḡíࡹŁ¦ÐłÞƆß۵ᮁ⦹᜽

e ᇥ⡍᮹ ᪽łᮥ ᱶప⪵⦹í ࡽ݅.

3. ᮁᩎԕ႑ᙹĞಽ᮹ᯕḩᖒᮥŁಅ⦽Clark ༉⩶᮹ᱽᦩ

3.1 ࡦ෴ଭ֜ন

Park et. al.(2013)ᯕᱽ᜽⦽ŝᱶᮥʑၹᮝಽᮁᩎԕ႑ᙹĞಽ

ෝ ḡ⢽໕ŝ ⦹⃽ᮝಽ Ǎᇥ⦹໕, ᜽e-໕ᱢłᖁᮡ ᰍ᳑ᱶࡽ ⡎

⧉ᙹಽᇡ░ᔑᱶࢁᙹᯩ݅. ᯥ᮹᮹Ƈḡᱱᨱᕽᮁᩎ⇽Ǎᱱʭḡ

ⅾᮁ⦹᜽eᮡᬕ࠺⦺ᱢ✚ᖒᯙḡ⢽໕⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɔ)᪡⦹⃽

⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɓ)ෝ ᱢᬊ⦹ᩍ Eq. (6)ŝ zᯕ ⢽⩥⧁ ᙹ ᯩ݅.

ੱ⦽ᰍ᳑ᱶࡽ⡎⧉ᙹƕÞƒß۵Eq. (7)ŝzᯕӹ┡ԝᙹᯩ݅.

ƒƇá ććƓ_Ɔ

¥_Ɔ_Ƈ â ććƓ_Ɓ

¥_Ɓ_Ƈ

(6)

ƕÞƒß á ƕĖ

Ęė^ć^¥^ćƓ^Ɔ^Ɔ^Ƈ^{â ć}^¥^ćƓ^Ɓ^Ɓ^Ƈ^ę^ěĚ ⁽⁷⁾

ᩍʑᕽ¥_Ɔ_Ƈ᪡¥_Ɓ_Ƈ۵Ƈḡᱱᨱᕽᮁᩎ᮹⇽Ǎḡᱱʭḡḡ⢽໕ŝ

⦹⃽Ğಽʙᯕෝ᮹ၙ⦽݅. ੱ⦽ᵝ᫵⦽☖ĥ༉ູ✙ॅᮡEqs. (3)~

(5)᮹༉ູ✙ჶ᮹ᬱญಽᇡ░݅ᮭŝzᯕᮁࠥ⧁ᙹᯩ݅. ᯕäᮡ

ᮁᩎ᮹ḡ⩶✚ᖒŝᩑđ⦹Łᬕ࠺⦺ᱢ✚ᖒᄡ⪵ᨱ঑௝ᙽe݉᭥

ࠥ⩶ᔢᮥ⧊ญᱢᮝಽ⠪a⧁ᙹᯩ۵ᙹ݉ᯕࢁᙹᯩᮭᮥ᮹ၙ⦽݅.

¦ÎÞƆß áĖ

Ęė^ć^ć^¥^ćƓ^Ɔ^Ɔ^{â ć}^ćƓ^ć^¥^Ɓ^Ɓ^ę^ěĚ^â¤ ⁽⁸⁾

¦ÏłÞƆß á ƙ

Ɯƚ^{â ć}^ć^ć^Ɠ^Î^Ɔ^Ï^ćƓ^åƆ^ććƓ^ƌ^ÎƁ^ā^{Ƈ á Î}^ƌ ^Þ^¥^Ɔ^Ƈ^{à ć}^¥^Ɔ^ß^Ï^æ^{â ć}^ć^Ɠ^Î^Ɓ^Ï^å^ć^ƌ^Î^{Ƈ á Î}^ā^ƌ ^Þ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓ^ß^Ï^æ

Ï å^ć^ƌ^Î^ā^{Ƈ á Î}^ƌ ^Þ^¥^Ɔ^Ƈ^{à ć}^¥^Ɔ^ßÞ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓ^ßæ

ƛ

Ɲƞ^â¤^Ï

(9)

¦_Ð^łÞƆß á ƙ

Ɯƚ^{â ć}^{â ć}^ć^ć^Ɠ^Î^Ɔ^Ð^ć^Ɠ^ć^Ɠ^å^Ɔ^Ï^Ɔ^Ð^Ð^ć^ć^Ɠ^ć^Ɠ^ƌ^Î^Ɓ^Ɓ^Ï^ā^{Ƈ á Î}^å^å^ƌ^ć^ƌ^ć^Î^ƌ^Î^Þ^¥^ā^{Ƈ á Î}^ā^{Ƈ á Î}^ƌ^ƌ^Ɔ^Ƈ^Þ^{à ć}^Þ^¥^¥^¥^Ɔ^Ɔ^Ƈ^Ƈ^Ɔ^{à ć}^{à ć}^ß^Ð^¥^æ^¥^{â ć}^Ɔ^Ɔ^ß^ßÞ^Ï^ć^Ɠ^Þ^Î^¥^Ɓ^Ð^¥^Ɓ^å^Ɓ^Ƈ^Ƈ^{à ć}^ć^{à ć}^ƌ^Î^¥^{Ƈ á Î}^¥^ā^Ɓ^ƌ^Ɓ^ß^ß^Ï^Þ^æ^æ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓ^ß^Ð^æ^ƛ^Ɲƞ^âÏ¤^Ð

(10)

ᩍʑᕽ^ć¥Ɔ᪡^ć¥Ɓ۵⠪Ɂḡ⢽໕Ğಽʙᯕ᪡⠪Ɂ⦹⃽Ğಽʙᯕෝ

ӹ┡ԙ݅. Eqs. (9) and (10)ᮥᱢᬊ⦹໕, ᪽łᮡEq. (11)ŝzᯕ

ᱶప⪵ ᜽┍ ᙹ ᯩ݅.

á ć¦ÏłÞƆß^ÐîÏ

¦_Ð^łÞƆß

(11)

(4)

Fig. 1. Direct Runoff of Clark Model in This Study ᅙᩑǍᨱᕽ۵ᮁᩎԕ႑ᙹǍ᳑᮹ᯕḩᖒᮥŁಅ⦹ʑ᭥⧕ᕽ

݅ᮭŝzᯕClark ༉⩶ᮥᰍǍᖒ⦹ᩡ݅. อ᧞ᮁᩎᱥၹᨱÙℱ

ƒƂ᮹ḡᗮ᜽e࠺ᦩ݉᭥ᮁ⬉vᬑ᮹ၽᔾ⦹໕, ᰍ᳑ᱶࡽ⡎⧉ᙹ

ƕÞƒßᨱᕽᯥ᮹᮹᜽eeĊƒ_Ɓᨱݡ⦽⩶ᔢᯕḢᔍb⩶(rectangular) ᯕŁ ᯕෝᖁ⩶ᱡᙹḡ᮹᮲ݖ⧉ᙹƄÞƒßᨱ⇵ᱢ⧁Ğᬑᯥ᮹᮹᜽e eĊƒ_Ɓ᮹⡎⧉ᙹಽᇡ░ᮁࠥࡹ۵ḡᗮ᜽e݉᭥ࠥ®Þƒß(Duration Unit Hydrograph, DUH)۵݅ᮭŝzᯕӹ┡ԝᙹᯩ݅(Cheng, 1982)

®Þƒß á ćƒ_ƁÎ ƙƒ_Ƃ

Ɯƚ^^^^ ^å^â¤^â¤^{à ¤â¤}₍₁₂₎^{ƒà ¤â¤}^Þ^Þ^{à ć}^{à ć}^{ƒà ƒ}^{ƒà ƒ}^Þ^¤^¤^{à ć}^Þ^{à ć}^Ƃ^Ɓ^{ƒà ƒ}^ßæ^ßæ^¤^ƒ^âƓ^{à Ɠ}^¤^Ƃ^ßæ^{à ƒ}^ƒ^{à Ɠ}^ƒ^Ƃ^Ɓ^âƒ^Þƒß^Ɓ^ßæ^Ɓ^ƒ^Ƃ^Þƒß^å^Þƒß^{ƒà ƒ}^å^å^{ƒà ƒ}^{ƒà ƒ}^Ɓ^{à ¤}^Ƃ^Ƃ^{à ƒ}^{à ¤}^^Ɓ^^ ^ƛ^Ɲƞ

ᩍʑᕽƓƋÞƒßᮡƒ < Ƌ ĞᬑƓƋÞƒß á ÎᯕŁƒ ï Ƌ ĞᬑƓƋÞƒß á ×ᮝಽᱶ᮹ࡹ۵ĥ݉⧉ᙹ(step function)ෝӹ┡ԙ݅. ᰍ᳑ᱶࡽ

⡎⧉ᙹƕÞƒßᨱ᮹⦽ḡᗮ᜽e݉᭥ࠥ۵Eq. (12)ᨱƕÞƒß᮹᜽ee Ċᄥaᵲ⊹ॅᮥŒ⦹Ł᜽eeĊƒ_Ɓอⓝ᷾a᜽┅໑ḡℕ᜽┉݅.

ᯕ⬥࠺ᯝ⦽᜽e⇶ᨱݡ⦽᳦Ñsॅᮥ٥ᱢ⦹໕ᰍ᳑ᱶࡽ⡎⧉ᙹ

ƕÞƒßᨱ᮹⦽ḡᗮ᜽e݉᭥ࠥෝᔑᱶ⧁ᙹᯩ݅. ḡᗮ᜽e݉᭥ࠥa

ᔑᱶࡹ໕bḡᗮ᜽eᄥᮁ⬉ᬑపᮝಽᯙ⦽Ḣᱲᮁ⇽ᙹྙłᖁᮡ

݉᭥ࠥ᪡᮹⫭ᖁᱢᇥᩑᔑᨱ᮹⧕ĥᔑࢁᙹᯩ݅. Fig. 1ᮡᯕᔢ᮹

ŝᱶᮥ☖⦹ᩍᮁᩎ⇽ǍᨱᕽḢᱲᮁ⇽పᮥᔑᱶ⦹۵ŝᱶᮥӹ┡

ԙäᯕ݅. ᅙŝᱶᮡ⥥ಽə௹ၮᨙᨕᯙFORTRANᮥᯕᬊ⦹ᩍ

Ǎᖒ⦹ᩡ݅. Clark ༉⩶ᨱ᮹⦽vᬑ-ᮁ⇽༉᮹۵Eq. (13)ŝzᯕ

₉ᇥ⪵ࡽᖁ⩶ᱡᙹḡ⇵ᱢᮥᱢᬊ⦹۵äᯕᯝၹᱢᯕ݅. ə్ӹ

ᯕෝᱢᬊ⦹໕ᙹ⦺ᱢᮝಽ⢽⩥ᯕa܆⦽ᙽe݉᭥ࠥ᮹↽ݡᰆᱱ ᯙ⧕ᕾᱢᯙ⠪a۵ᨕಖíࡽ݅. ᯕᨱၹ⧕ᅙᩑǍᨱᕽᱽᦩࡽ

Clark ༉⩶ᮡ Eqs. (8)~(10)ᮥ ᯕᬊ⦹ᩍ ᙽe݉᭥ࠥ᮹ ⩶ᔢᨱ

ݡ⦽ ⧕ᕾᱢ ⠪aa a܆⧕ ḥ݅.

¨_Ƈá ƙƜƚ_ć

¤â×íÒĢƒĢƒ ƛ

Ɯƚ_{Î à ć}

¤â×íÒĢƒĢƒ ƛ

ᩍʑᕽ¨_Ƈ۵Ƈ᜽ᱱ᮹Ḣᱲᮁ⇽ప,¤ᮡᱡඹᔢᙹ,Ģƒ۵᜽ee Ċ, ¢۵Ƈà ÎŝƇ ᜽eeĊᨱ ݡ⦽ ⠪Ɂᮁ᯦పᮥ ӹ┡ԙ݅.

3.2 ࠻Թ࣡৤ଭॺ୨

ᅙᩑǍᨱᕽᱽᦩࡽClark ༉⩶ᮥᱢᬊ⦹ʑ᭥⧕ᕽ۵ḡ⢽໕ŝ

⦹⃽᮹ ⠪Ɂᯕᘂᗮࠥෝ ӹ┡ԕ۵ćƓ_Ɔ, ćƓ_Ɓ᪡ ᖁ⩶ᱡᙹḡ ⇵ᱢᮥ

᭥⦽ᱡඹᔢᙹ¤ᮥ⦥᫵ಽ⦽݅. อ᧞⪙ᬑᔍᔢᨱݡ⦽š⊂ᯱഭa

ᵝᨕḩĞᬑๅ}ᄡᙹॅᮡEqs. (8)~(10)ᮥᯕᬊ⦹ᩍᔑᱶࢁᙹ

ᯩ݅. ə్ӹ3₉ᩑพႊᱶ᜾ᯙEqs. (8)~(10)ᮡćƓ_Ɔ, _ćƓ_Ɓ᪡¤ᮥ

⧕ᕾᱢᮝಽᮁࠥ⦹ʑᨱᨕಅᬡᯕ঑ෙ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵

SCE-UA ↽ᱢ⪵ʑჶᮥᯕᬊ⦹ᩍš⊂ᯱഭಽᇡ░Ḣᱲᔑᱶ⦹Ł

ᯱ⦽݅. SCE-UA ↽ᱢ⪵ʑჶᮡDuan et al.(1992)ᨱ᮹⧕}ၽࡹ

ᨩᮝ໑, ᯕ ʑჶᮡ ᵝᨕḥ ༊ᱢ⧉ᙹᨱ ݡ⧕ ༉⩶᮹ ๅ}ᄡᙹෝ

⬉ŝᱢᮝಽ ⇵ᱶ⧁ ᙹ ᯩ۵ äᮝಽ ᦭ಅᲙ ᯩ݅(Eckardt and Arnold, 2001; Lee and Kang, 2001; Lee, 2006).

4. ᱢᬊᔍಡ

4.1 ۩ঃକલր৤ࢂॷঃࢫ஺෴൉ন଴ୀॺ୨

ᅙᩑǍ᮹ᱢᬊᮡFig. 2᪡zᯕɩvᙹĥᯙᅕℎ⃽ᨱ᭥⊹⦽

ʑݡ᪡ᔑĥᙹ᭥ǎᮥ⇽Ǎḡᱱᮝಽ⦹۵ᮁᩎᮥݡᔢᮝಽ⦹ᩡ

݅. ੱ⦽ᙹྙᔍᔢᮡInternational Hydrologic Programme(IHP) Research Paper(2001~2005)᪡Water Management Information System(http://www.wamis.go.kr)ᨱᕽᱽŖ⦹۵ᙹ᭥ᯱഭෝAnnual Hydrological Report on Korea(2007, 2009, 2010)᪡ 2011֥

Hydrological Survey Report(2012)᮹ᙹ᭥-ᮁపłᖁ᜾ᨱᱢᬊ⦹

ᩍᖁᱶ⦹ᩡ݅. ᅙᩑǍᨱᕽ໕ᱢ⠪Ɂvᬑపᮡ❑ᖝჶᮥᱢᬊ⦹ᩡ

Ł, ʑᱡᮁ⇽ᇥญ۵ᙹ⠪Ḣᖁᇥญჶᮥᔍᬊ⦹ᩡᮝ໑ᙹ⠪Ḣᖁᇥ

(5)

Fig. 2. Target Basin of This Study

Table 1. The Outline of Storm Events

Watershed Event Runoff rate _ª_Ǝ(Ƌ^ÐîƑ) ƒ_Ǝ(hr)¿

Gidae

2007-07-01 0.53 209.7 5

2009-07-12 0.35 160.6 7

2011-07-25 0.47 251.5 5

2011-08-03 0.39 86.2 6

Sangye

2000-06-26 0.24 284.5 9

2001-06-30 0.23 75.3 11

2004-08-18 0.22 139.0 12

2007-07-10 0.58 226.7 14

Table 2. Geomorphological Statistics of Each Target Basin

Water-shed Area() Channel Hillslope

Co-variance() Total variance() Mean(m) Variance() Mean(m) Variance()

Gidae 354.14 17,104 62,831,300 375 152,181 -339,719 62,258,725

Sangye 485.21 30,027 158,953,000 373 148,836 -190,788 158,711,391

Water-shed

3rd moment()

ćƌÎ_{Ƈ á Î}ā^ƌ Þ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓß^Ð ćƌÎ_{Ƈ á Î}ā^ƌ Þ^¥^Ɔ^Ƈ^{à ć}^¥^Ɔß^Ð ^A ^B ^¦^Ð^ł^Þ¥ß

Gidae 103,755,833,344 122,648,656 -86,362,440 -86,362,240 103,360,307,200

Sangye -713,747,398,656 116,987,856 8,245,073 7,846,858 -713,582,116,864

ญჶ᮹ᱢᬊᯕᨕಅᬕĞᬑᨱ۵ᙹྙłᖁ᮹qᙹᇡෝၹݡᙹḡᨱ

ࠥ᜽⦹ᩍqᙹᇡĞᔍaɪᄡ⦹۵ᱱᮥ᳦ᱱᮝಽ⦹۵ᵝḡ⦹ᙹ

qᙹłᖁ(master depletion point)ᨱᱢᬊ⦹ᩡ݅. ੱ⦽ᮁ⬉ᬑప

ᇥญႊჶᮡᙹྙłᖁ᮹ᔢ᜚᜽ᱱᯕᱥʭḡ᮹vᬑపᮡⅩʑᗱᝅಽ

≉⦹Ł, ə⬥᮹ᗱᝅపᮡᯝᱶᗱᝅᮉಽaᱶ⦹۵Ⅹʑᗱᝅ-ᯝᱶᗱ ᝅჶᮥᱢᬊ⦹ᩡ݅. ᯕᔢ᮹ŝᱶᮥ☖⦹ᩍᖁᱶࡽᗭᮁᩎᄥᙹྙᔍ ᔢॅᮡ Table 1ŝ z݅.

ᅙᩑǍᨱᕽḡ⩶ᇥᕾᮥ᭥⧕ᔍᬊࡽᙹ⊹Łࠥ༉⩶(DEM)ᮡ

1/25,000 ᙹ⊹ḡࠥಽᇡ░ᔢᬊS/WᯙArc Infoෝᯕᬊ⦹ᩍ20 m×20 m᮹Ċᯱ฾ᮝಽǍᖒ⦹ᩡ݅. ੱ⦽DEMᮥᯕᬊ⦹ᩍ⮱෥ႊ

⨆ࠥෝᔾᖒ⦹ŁArc/Info᮹FLOWLENGTH ⧉ᙹෝᔍᬊ⦹ᩍ

bĊᯱᄥḡ⢽໕ŝ⦹⃽᮹Ğಽʙᯕෝĥᔑ⦹ᩡ݅. ᯕෝၵ┶ᮝಽ

༉ູ✙ ჶ᮹ ᬱญᨱ ঑௝ ᔑᱶࡽ b᳦ ḡ⩶✚ᖒᯙᯱॅᮡ Table 2᪡z݅. ᩍʑᕽA۵_ć_ƌ^Îā_{Ƈ á Î}^ƌ ^Þ^¥^Ɔ^Ƈ^{à ć}^¥^Ɔ^ß^Ï^Þ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓ^ß^{, B}^۵^ćƌÎā_{Ƈ á Î}^ƌ

Þ^¥^Ɔ^Ƈ^{à ć}^¥^ƆßÞ^¥^Ɓ^Ƈ^{à ć}^¥^Ɓß^Ï^ᯕŁ^¦^Ð^ł^Þ¥ßᮡᮁ⦹Ñญ᮹໕ᱢᵲᝍᨱݡ

⦽ 3₉ ༉ູ✙ෝ ᮹ၙ⦽݅.

4.2 ඒ෌৤ࠜଲ૳෉ਏԩ-࡟ୡմটଭ֜ন

ᅙᩑǍᨱᕽᱽᦩࡽClark ༉⩶ᮥᱢᬊ⦹ʑ᭥⦹ᩍ᜽e-໕ᱢł ᖁᮡᦿᕽᱽ᜽⦽Eq. (7)ᮥᯕᬊ⦹ᩍǍᖒ⦹ᩡ݅. Figs. 3~4۵

ᮁᩎᱥℕ⠪ɁᮁᗮćƓᮥÎ îಽaᱶ⦹Ł⦹⃽⠪Ɂᯕᘂᗮࠥ

(ćƓ_Ɓ)᮹ḡ⢽໕⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɔ)ᨱݡ⦽እᯙrá ćƓ_ƁîćƓ_Ɔᮥ1~100 ᮝಽᄡ⪵᜽┅໑Ǎᖒ⦽ᰍ᳑ᱶࡽ⡎⧉ᙹෝӹ┡ԙ݅. ๅ}ᄡᙹॅ

ᵲᨱᱡඹᔢᙹ¤۵0, ḡ⢽໕⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɔ)᪡⦹⃽⠪Ɂᯕᘂ ᗮࠥ(ćƓ_Ɓ)۵Eq. (8)ෝᯕᬊ⦹ᩍđᱶ⦹ᩡ݅. ੱ⦽⡎⧉ᙹ᮹⩶ᔢᮥ

ӹ┡ԕ۵b᳦༉ູ✙ॅᮡEqs. (8)~(10)ᮥᯕᬊ⦹ᩍᔑᱶ⦹ᩡ݅.

ᩍʑᕽᱡඹᔢᙹ¤a0ᯙäᮡᱥ⩶ᱢᯙ᜽e-໕ᱢłᖁ᮹ᩎ⧁ᯙ

ḡℕ⬉ŝ(translation effect)ෝᖅ໦⦹۵äᯕ݅. Figs. 3~4ෝᔕ

⠕ᅕ໕r=1ᯙĞᬑ۵ḡ⢽໕ŝ⦹⃽⠪ɁᯕᘂᗮࠥabbÎ î

ಽ ࠺ᯝ⦹í ᱢᬊࡽ äᮝಽ, ᯕ۵ ᮁᩎ ԕ ႑ᙹĞಽ᮹ ࠺ᯝ⦽

✚ᖒᨱ᮹⦹ᩍḡℕ⬉ŝᨱݡ⦽༉᮹aᯕ൉ᨕḡŁᯩᮭᮥӹ┡ԙ

݅. ੱ⦽ᬕ࠺⦺ᱢ✚ᖒᯕᄡ⧉ᨱ঑௝႑ᙹǍ᳑᮹ᯕḩᖒভྙᨱ

ᰍ᳑ᱶࡽ⡎⧉ᙹ(᜽e-໕ᱢłᖁ) ⩶ᔢᯕᄡ⪵⦹Łᯩᮭᮥ⪶ᯙ⧁

ᙹ ᯩ݅.

(6)

Fig. 3. Rescaling Width Function of Gidae Watershed According to r=^ć_Ɠ_ƁîćƓ_Ɔ;ćƓá Îí× î

Fig. 4. Rescaling Width Function of Sangye Watershed According to r=ćƓ_ƁîćƓ_Ɔ;ćƓá Îí× î

Table 3. Estimation of Clark Method Parameters, Dynamic Parameter and Moment by Observed Event and Estimated SCE-UA Optimization

Water-shed Event

Parameters Moment

¤(hr) _Ɓ(hr) (m/s) (m/s) Observation SCE-UA Optimization

¦_ÎÞƆß(ƆƐ) _¦_Ï^łÞƆß(ƆƐ^Ï) ¦_Ð^łÞƆß(ƆƐ^Ð) ¦_ÎÞƆß(ƆƐ) _¦_Ï^łÞƆß(ƆƐ^Ï) ¦_Ð^łÞƆß(ƆƐ^Ð)

Gidae

2007-07-01 6.06 5.98 0.243 3.067 7.92 32.05 227.66 8.04 37.33 444.66

2009-07-12 10.12 6.21 0.238 2.911 12.85 106.76 1312.37 12.19 103.04 2070.66 2011-07-25 8.36 3.62 0.459 4.057 10.50 82.76 1170.03 9.75 70.13 1166.51 2011-08-03 11.25 7.07 0.214 2.459 14.50 133.39 1900.62 13.66 127.41 2844.23

Average 8.94 5.72 0.289 3.124 11.44 88.74 1152.67 10.83 80.56 2145.89

Sangye

2000-06-26 8.85 9.89 0.167 2.836 12.11 61.62 583.02 12.41 80.16 1385.24 2001-06-30 6.33 16.81 0.096 1.700 12.30 37.20 205.97 12.32 45.40 507.51 2004-08-18 15.50 8.21 0.245 2.676 20.40 271.21 5841.81 19.04 242.14 7448.57 2007-07-10 12.90 14.93 0.121 1.656 19.75 196.69 4091.00 18.79 171.44 4288.45 Average 10.90 12.46 0.157 2.217 16.14 141.68 2680.45 15.32 121.58 2585.75

4.3 ୠࠑঃ৤૕ܑۜਏԩࢫ൉নକুଭॺ୨

ᱽᦩࡽClark ༉⩶ᮥʑၹᮝಽḢᱲᮁ⇽పᮥᔑᱶ⦹ʑ᭥⧕ᕽ۵

ᱡඹᔢᙹ᪡ࠥݍ᜽eᯕ⇵ᱶࡹᨕ᧝⦽݅. ✚⯩ᮁᩎᮥḡ⢽໕ŝ

⦹⃽ᮝಽǍᇥ⦹ᩡʑভྙᨱࠥݍ᜽e᮹ᔑᱶᮥ᭥⧕ᕽ۵ḡ⢽໕

⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɔ)᪡⦹⃽⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɓ)۵ၹऽ᜽đᱶࡹᨕ᧝

⦽݅. ᯕෝ᭥⦹ᩍᅙᩑǍᨱᕽ۵SCE-UA ↽ᱢ⪵ʑჶᮥᯕᬊ⦹ᩍ

š⊂ᯱഭಽᇡ░ๅ}ᄡᙹॅᮥḢᱲ⇵ᱶ⦹ᩡ݅. ↽ᱢ⪵ʑჶᮥ

ᱢᬊ⧁ভๅ}ᄡᙹॅ᮹Ğĥ᳑ÕᮡPark et. al.(2013)ᯕᱽ᜽⦽

ᩑǍđŝ᪡Bhattacharya et. al.(2012)᮹ᩑǍᨱᕽᔑᱶࡽๅ}ᄡ ᙹॅᮥá☁⦹ᩡŁ, ᯕᨱ঑௝⇵ᱶࢁᙹᯩ۵a܆ჵ᭥ෝŁಅ⦹ᩍ

đᱶ⦹ᩡ݅. ᱡඹᔢᙹ᮹Ğĥ᳑Õᮡ0.0 hrŝ30.0 hr, Ⅹʑ᳑Õᮡ

15.0 hrᮥ ᱢᬊ⦹Ł ḡ⢽໕ ⠪Ɂᯕᘂᗮࠥ(ćƓ_Ɔ) Ğĥ᳑Õᮡ 0.0

î᪡1.0 î,Ⅹʑ᳑Õᮡ0.5 î əญŁ⦹⃽⠪Ɂᯕᘂᗮࠥ

(ćƓ_Ɓ)Ğĥ᳑Õᮡ0.0 î᪡5.0 î,Ⅹʑ᳑Õᮡ2.5 îෝ

ᱢᬊ⦹ᩡ݅. ੱ⦽༊ᱢ⧉ᙹ۵š⊂ࡽḢᱲᮁ⇽ᙹྙłᖁŝ༉᮹ࡽ

Ḣᱲᮁ⇽ᙹྙłᖁ᮹⠪ɁᱽŒɝ᪅₉(Root Mean Square Error;

RMSE)ෝ↽ᗭ⪵⦹۵äᮝಽᖅᱶ⦹ᩡ݅. ᩍʑᕽᵝ᮹⧁ᱱᮡ

⦹⃽⠪Ɂᯕᘂᗮࠥ᮹ḡ⢽໕⠪Ɂᯕᘂᗮࠥᨱݡ⦽እᯙrᯕ1ᅕ݅

᯲ᮡĞᬑaၽᔾ⦹۵ḡᩍᇡෝ⪶ᯙ⧁⦥᫵aᯩ݅. rᯕ1ᅕ݅

᯲ᮡ Ğᬑ۵ ḡ⢽໕⠪Ɂᯕᘂᗮࠥa ⦹⃽⠪Ɂᯕᘂᗮࠥᅕ݅ ⓕ

ভ ӹ┡ӹ۵ äᮝಽ, ᯕ۵ ྜྷญᱢᮝಽ ┡ݚᖒᯕ đᩍࡽ äᮥ

᮹ၙ⦽݅. ᯕෝၵ┶ᮝಽ⇵ᱶࡽๅ}ᄡᙹॅ, š⊂ᯱഭಽᇡ░

ᔑᱶࡽ༉ູ✙ॅŝEqs. (8)~(11)ᮥᯕᬊ⦹ᩍᔑᱶࡽ༉ູ✙ॅᮡ

Table 3ŝz݅. ᩍʑᕽࠥݍ᜽eᮡĞಽʙᯕᄥಽḡ⢽໕⠪Ɂᯕ ᘂᗮࠥ᪡⦹⃽⠪Ɂᯕᘂᗮࠥෝᱢᬊ⧩ᮥভaᰆʕᮁ⦹᜽eᮥ

᮹ၙ⦽݅. ੱ⦽ᔑᱶࡽݡᔢᮁᩎᄥๅ}ᄡᙹॅ᮹⠪Ɂsᮡ⇵⬥

ᅙᩑǍᨱᕽᱽᦩࡽClark ༉⩶ᨱݡ⦽ๅ}ᄡᙹॅᄡ⪵ᨱ঑ෙ

༉ູ✙ॅ᮹Ñ࠺✚ᖒᮥ⪶ᯙ⦹ʑ᭥⦽ʑᵡsᮝಽᔍᬊ⦹Łᯱ

⦽݅. š⊂ᙹྙᔍᔢ᮹☖ĥ༉ູ✙ॅŝ༉᮹ࡽ☖ĥ༉ູ✙ॅᮡ

ᔢšĥᙹ(«)ᮡ0.995, 2₉༉ູ✙(ᇥᔑ)ᮡ0.993, 3₉༉ູ✙۵

0.983ಽᔑᱶࡹᨩ݅. ⇵ᱶsŝš⊂sᨱݡ⦽☖ĥ༉ູ✙ॅ᮹

(7)

Fig. 5. Scatter Diagram of _¦_ÎÞƆß

Fig. 6. Scatter Diagram of ¦_Ï^łÞƆß

Fig. 7. Scatter Diagram of _¦_Ð^łÞƆß

Fig. 8. Comparison of Observed and Simulated Runoff Hydrographs in the Gidae Watershed(2009.07.12)

Fig. 9. Comparison of Observed and Simulated Runoff Hydrographs in the Sangye Watershed(2000.06.26)

ᔢšĥᙹ۵ݡℕಽ᧲⪙⦽đŝෝӹ┡ԕᨩ݅. ੱ⦽⠪Ɂŝᇥᔑ ᨱݡ⧕ᕽ۵⇵ᱶsŝš⊂sᯕݡℕಽᯝ⊹⦹۵Ğ⨆ᮥᅕᩍᵝ ᨩ݅. ə్ӹ3₉༉ູ✙ᨱݡ⦽đŝ۵ᅙᩑǍᨱᕽᱽ᜽⦽šĥ

᜾ᯕ݅ᗭŝݡ⠪aࡹ۵Ğ⨆ᮥӹ┡ԕᨩ݅. ⨆⬥޵ฯᮡᙹྙᔍ ᔢ᮹ ᇥᕾ ੱ۵ ݡᔢᮁᩎ᮹ ⪶ᰆᮥ ☖⦹ᩍ ᝍࠥ ᯩ۵ ᇥᕾᮥ

ᙹ⧪⦹Ł, bᔍᔢ᮹Ⅹʑ᜽ᱱᨱᕽݡᔢᮁᩎ᮹ᖁ⧪⧉ᙹ᳑Õᨱ

঑ෙ☁᧲Ŗɚ᮹⡍⪵ࠥၰᯕᨱ঑ෙᮁ⇽ᩎ᮹ᄡ⪵ෝŁಅ⦹ᩍ

႑ᙹǍ᳑᮹⠪aෝᙹ⧪⦽݅໕᮹ၙᯩ۵đŝෝ⪶ᯙ⧁ᙹᯩᮥ

äᮝಽ ❱݉ࡽ݅.

4.4 ୡ૳নՑഠ

ᱢᬊᖒᮥá☁⦹ʑ᭥⦹ᩍTable 3ŝzᯕ⇵ᱶࡽๅ}ᄡᙹॅᮥ

༉⩶ᨱ ᯦ಆ⦹ᩍ Ḣᱲᮁ⇽పᮥ ᔑᱶ⦹ᩡŁ, ə đŝෝ Figs. 8 and 9᪡zᯕࠥ᜽⦹ᩡ݅. ᩍʑᕽMoment Method Ḣᱲᮁ⇽ᙹྙ

łᖁᮡ ᅙ ᩑǍᨱᕽ ᱽᦩ⦽ ႊჶŝ᮹ ᔢݡᱢᯙ ᬑᙹᖒ እƱෝ

᭥⦹ᩍPark et. al.(2013)ᯕᱽᦩ⦽ႊჶᮥ࠺ᯝ⦽ᔍᔢᨱᱢᬊ⦽

đŝෝӹ┡ԙäᯕ݅. ੱ⦽ᱶపᱢᮝಽእƱ⦹ʑ᭥⧕℉ࢱᮁపŝ

℉ࢱ᜽e, š⊂ࡽ℉ࢱᮁపᨱݡ⦽ᔢݡ᪅₉᪡℉ࢱၽᔾ᜽eᨱ

ݡ⦽ᔢݡ᪅₉, ⠪ɁᱽŒɝ᪅₉(Root Mean Square Error; RMSE) ၰ⬉ᮉĥᙹE(Efficiency Coefficient)ෝTable 4᪡zᯕᔑᱶ⦹ᩡ

(8)

Table 4. The Relative Err., RMSE and the Efficiency Coefficient

ª_Ǝ(_Ƌ^ÐîƑ) _Ǝ(hr)

Water-shed Event Obs. Sim. Relative error(%) Obs. Sim. Relative error(%) RMSE Efficiency Coefficient

Gidae

2007-07-01 209.7 208.1 0.8 5 5 0.0 4.7 0.99

2009-07-12 160.6 151.4 5.7 7 7 0.0 6.9 0.97

2011-07-25 251.5 241.7 3.9 5 5 0.0 8.4 0.98

2011-08-03 86.2 74.3 13.8 6 6 0.0 3.8 0.96

Sangye

2000-06-26 284.5 266 6.5 9 9 0.0 11.3 0.98

2001-06-30 75.3 67.4 10.5 11 11 0.0 4.1 0.96

2004-08-18 139.0 128.9 7.3 12 12 0.0 5.9 0.97

2007-07-10 226.7 219.1 3.4 14 14 0.0 7.3 0.99

Fig. 10. Comparison of Observed and Verified Runoff Hydrographs in the Sangye Watershed(2008.07.23)

݅. ᩍʑᨱᕽ⬉ᮉĥᙹ௡༉᮹ࡽḢᱲᮁ⇽ᙹྙłᖁ᮹ᰍ⩥ᱶࠥෝ

⠪a⦹ʑ᭥⦹ᩍNash and Sutcliffe(1970)ᨱ᮹⦹ᩍᱽᦩࡽđᱶ ĥᙹ᪡ᮁᔍ⦽⩶┽᮹ḡ⢽ಽᕽ1ᨱaʭᬙᙹಾᬑᙹ⦽ᰍ⩥ᱶࠥෝ

᮹ၙ⦽݅. ℉ࢱᮁపᨱ ݡ⦽ ᔢݡ᪅₉۵ ʑݡ 0.8~13.8%, ᔑĥ

3.4~10.5%᮹ჵ᭥ෝӹ┡ԕᨩ݅. ੱ⦽℉ࢱ᜽eᨱݡ⦽ᔢݡ᪅₉ ۵š⊂sŝᯝ⊹⧉ᮥ⪶ᯙ⦹ᩡ݅. ⠪ɁᱽŒɝ᪅₉۵ʑݡ3.8~8.4, ᔑĥ7.3~11.3᮹ჵ᭥ෝᅕᩍᵝᨩ݅. ⬉ᮉĥᙹ۵ݡᔢᮁᩎᨱݡ⦹

ᩍ0.96 ᯕᔢ᮹ᙹ⊹ෝᅕᯕŁᯩ݅. ᯕᔢ᮹đŝෝá☁⦹ᩍᅕ໕

ᱥℕᱢᮝಽ ༉᮹đŝa š⊂sᨱ ᱲɝ⦹Ł ᯩ݅. ੱ⦽ Figs. 8 and 9ෝᔕ⠕ᅕ໕, Park et. al.(2013)ᯕᱽᦩ⦽ႊჶᮝಽ༉᮹ࡽ

đŝᅕ݅ ᅙ ᩑǍᨱᕽ ᱽᦩࡽ ༉⩶᮹ đŝa }ᖁࡹŁ ᯩᮭᮥ

ӹ┡ԕŁᯩ݅. ə్ӹ℉ࢱᮁపᨱݡ⧕ᕽ۵HEC-1ᮥᯕᬊ⦹ᩍ

༉᮹ࡽđŝaš⊂sᨱ޵aʭᬕᙹ⊹ෝᅕᯕŁᯩ݅. ⦹ḡอ

ᅙᩑǍᨱᕽᰍ⧕ᕾࡽClark ༉⩶ࠥš⊂sᨱᕽⓍíჸᨕӹḡ

ᦫ۵ äᮝಽ ❱݉ࡽ݅. ᮁᩎᮥ ḡ⢽໕ŝ ⦹⃽ᮝಽ Ǎᇥ(ᮁᩎ᮹

႑ᙹǍ᳑Łಅ)⦹ᩍᰍ⧕ᕾ⦽⊂໕ᮡ⦹ӹ᮹࠺ᯝ⦽ᮁᗮᮝಽaᱶ

⦹ᩍ༉᮹ࡹ۵ʑ᳕᮹Clark ༉⩶ᨱእ⧕ᝅᱽᮁ⇽༉᮹ᨱᯩᨕ

޵ ྜྷญᱢᯙ ✚ᖒᮥ ၹᩢ⦽ ᩑǍ đŝಽ ❱݉ࡽ݅.

ᯕ్⦽đŝಽᇡ░ᅙᩑǍᨱᕽᱽ᜽⦽ႊჶುᮡ႑ᙹĞಽ᮹

ᯕḩᖒŝ࠺ᱢๅ}ᄡᙹॅ᮹ᩢ⨆ᮥ ᱢᱩ⦹íၹᩢ⧁ᙹᯩᮭᮥ

⪶ᯙ⧁ᙹᯩᨩ݅. ੱ⦽ᙽe݉᭥ࠥ᮹᪽łࠥ(skewness) ⪚ᮡ3₉

༉ູ✙᮹Ñ࠺ᮡᅙᩑǍᨱᕽᱽᦩࡽ༉⩶ᮥʑၹᮝಽᱢᱩ⦹í

⠪a⧁ ᙹ ᯩᮭᮥ ᦭ ᙹ ᯩᨩ݅.

4.5 ൉নକুրୠࠑঃ৤઩ݗࠛClark ০ԩۚ଍ܑ෴ঃ

ଭՋܛ൉নंজ

ᅙᩑǍᨱᕽᱽᦩࡽClark ༉⩶᮹ᵝ᫵ๅ}ᄡᙹ۵ḡ⢽໕⠪Ɂ ᯕᘂᗮࠥၰ⦹⃽⠪Ɂᯕᘂᗮࠥಽݡᄥࡹ۵✚ᖒᮁᗮŝᱡඹᔢᙹᯕ

݅. ᯕ్⦽ๅ}ᄡᙹॅᨱ঑ෙClark ༉⩶᮹Ñ࠺✚ᖒᮡJeong(1989) ᯕ ᱽ᜽⦽ႊჶŝᮁᔍ⦹íᙹ⧪ࡹᨩ݅. Eqs. (8)~(10)ᮥᯕᬊ⦹ᩍ

ᔑĥ ᮁᩎ᮹ݡ⢽⦹۵ๅ}ᄡᙹॅᮥᄡ⪵᜽┅໕ᕽᙽe݉᭥ࠥ⩶

ᔢ, ᷪ☖ĥ༉ູ✙ॅᨱݡ⦽ᄡ࠺ᖒᮥ⪶ᯙ⦹ᩡ݅. ᔑĥᮁᩎ᮹

ݡ⢽⦹۵ ๅ}ᄡᙹॅᮡ Table 3ŝ zᯕ ᔍᔢᄥಽ ᔑᱶࡽ sᮥ

⠪Ɂ⦹ᩍᯕᬊ⦹ᩡŁ, ʑᵡᮝಽᯕᬊࢁᙹᯩ۵ḡᩍᇡෝ⪶ᯙ⦹ʑ

᭥⧕ᔑᱶࡽݡ⢽ๅ}ᄡᙹॅᮥᝅᱽᙹྙᔍᔢᨱᱢᬊ⦹ᩍFig.

10ŝzᯕá᷾ᮥᝅ᜽⦹ᩡ݅. ᙹྙᔍᔢ᮹ᇡ᳒ᮝಽᝁ഑ᖒᯩ۵

á᷾᮹đŝෝᱽ᜽⦹ʑ۵ၙ⯂⧁ḡ௝ࠥ༉⩶᮹Ñ࠺✚ᖒᇥᕾᮥ

᭥⦽ݡ⢽ๅ}ᄡᙹॅಽᔍᬊࡹʑᨱ۵ݡℕಽ᧲⪙⦽äᮝಽ❱݉

ࡽ݅. Ñ࠺✚ᖒᇥᕾᮡݡ⢽ๅ}ᄡᙹॅᮥʑᵡᮝಽᯝᱶእᮉಽ

qᗭ⪚ᮡ᷾a᜽┅໕ᕽᙹ⧪ࡹᨩ݅. ᩍʑᕽ1₉༉ູ✙۵ᮁᩎᄥ

ʑᵡ ๅ}ᄡᙹॅ᮹ ḡℕ᜽eᮥ ʑၹᮝಽ ྕ₉ᬱ⪵ ⦹ᩡŁ, 2₉

༉ູ✙۵⢽ᵡ⠙₉᮹⠪Ɂ⊹ᨱݡ⦽እᮉᮥ ӹ┡ԕ۵ᄡ࠺ĥᙹ (variation coefficient)᪡3₉༉ູ✙۵Eq. (11)᮹᪽łࠥ(skewness)

ෝ ᯕᬊ⦹ᩡ݅.

Figs. 11~13ᮥၵ┶ᮝಽÑ࠺✚ᖒᇥᕾđŝෝᔕ⠕ᅕ໕, ᱡඹᔢ ᙹᨱ᮹⦽ḡℕ᜽eᄡ࠺ᖒᮥᱽ᫙⦹Łb᳦☖ĥ༉ູ✙᮹ᄡ࠺ᖒ

ᮡእᖁ⩶šĥෝӹ┡ԕᨩ݅. ᯕ్⦽እᖁ⩶šĥ۵Eqs. (8)~(10) ᨱᕽ⪶ᯙ⧁ᙹᯩ݅. እᖁ⩶šĥᨱ঑௝໦⪶⦹íÑ࠺✚ᖒᮥ

(9)

Fig. 11. Behavioral Analysis of Lag Time for Sangye Watershed

Fig. 12. Behavioral Analysis of Coefficient Variation for Sangye Watershed

Fig. 13. Behavioral Analysis of Skewness for Sangye Watershed

Table 5. Estimation of Clark Method Parameters and Dynamic Parameter by Estimated SCE-UA Optimization ; Constant

to Each Watershed

Water-shed Event

Parameters SCE-UA optimization

¤(hr) _Ɓ(hr) (î) (î)

Gidae

2007-07-01 6.07 5.43 0.289 2.950 2009-07-12 10.13 5.54 0.289 2.794 2011-07-25 8.17 4.90 0.289 4.000 2011-08-03 11.26 5.97 0.289 2.330

Sangye

2000-06-26 8.83 10.21 0.157 2.863 2001-06-30 6.44 13.30 0.157 1.603 2004-08-18 15.47 10.18 0.157 2.876 2007-07-10 12.91 13.30 0.157 1.603

❱݉⧁ᙹᨧḡอ, Ğ⨆ᖒᮡFigs. 11~13ᮥၵ┶ᮝಽá☁ࡹᨩ݅.

Fig. 11ᮥᔕ⠕ᅕ໕, ḡℕ᜽eᄡ࠺ᖒᮡᱡඹᔢᙹaݡℕಽⓍí

ӹ┡ӹŁ ᯩ݅. ੱ⦽ḡ⢽໕⠪Ɂᯕᘂᗮࠥᅕ݅⦹⃽⠪Ɂᯕᘂᗮࠥ

aⓍíӹ┡ӹ۵äᮥ⪶ᯙ⧁ᙹᯩ݅. ᱡඹᔢᙹ۵ᖁ⩶ᱢᯙእಡš ĥෝᅕᯕ۵äᯕ✚ᯕ⦽ᱱᯕ݅. ᯕ్⦽ᱡඹᔢᙹᨱݡ⦽ḡℕ᜽e

᮹ᄡ࠺ᖒᮡEq. (8)ᨱᕽ⪶ᯙ⧁ᙹᯩ݅. ḡ⢽໕⠪Ɂᯕᘂᗮࠥ᪡

⦹⃽⠪Ɂᯕᘂᗮࠥaᯥ᮹᮹ᙹಽŁᱶࡽ݅໕ᱡඹᔢᙹ۵ᖁ⩶š ĥෝӹ┡ԙ݅. ᅙᩑǍᨱᕽᱽ᜽ࡽClark ༉⩶ᨱ᮹⦽ᱡඹ⬉ŝ(ᱡ ඹᔢᙹ)۵႑ᙹǍ᳑ၰ࠺ᙹᩎ⦺ᱢ✚ᖒॅŝࠦพᱢᮝಽŁಅࡹŁ

ᯩᮭᮥ⪶ᯙ⧁ᙹᯩ݅. ə్ӹᱡඹᔢᙹᨱࠥᮁᩎԕྜྷ᯦ᯱॅ᮹

⮱෥⩥ᔢᮥԕ⡍⦹Łᯩʑভྙᨱ, อ᧞ᱡඹᔢᙹᯱℕಽอ⧕ᕾࡽ

݅໕vᬑ-ᮁ⇽⩥ᔢ᮹ᅙḩᱢᯙ✚ᖒᨱᱲɝ⦹ʑaᨕಅᬙäᯕ݅.

ᩍ ᱡඹᔢᙹ᮹ ɝᅙᱢᯙ ᮹ၙෝ ❭ᦦ⧕᧝ ⧁ äᮝಽ ❱݉ࡽ݅.

Figs. 12 and 13ᮥᔕ⠕ᅕ໕ᄡ࠺ĥᙹ᪡᪽łࠥ۵ᱡඹᔢᙹ,

⦹⃽⠪Ɂᯕᘂᗮࠥ, ḡ⢽໕⠪Ɂᯕᘂᗮࠥᙽᮝಽӹ┡ԕᨩ݅. ᩍʑ ᕽᵝ༊⧁ᱱᮡᄡ࠺ĥᙹၰ᪽łࠥᨱᕽᱡඹᔢᙹ᪡⦹⃽⠪Ɂᯕᘂ ᗮࠥaᮁᔍ⦽Ñ࠺✚ᖒᮥᅕᩍᵝŁᯩ݅۵äᯕ݅. 2₉༉ູ✙᪡

3₉༉ູ✙۵Eq. (9) ၰEq. (10)ᨱᕽᔢ⪙᯲ᬊ⦹۵✚ᖒᮁᗮॅ᮹

⧎ŝᱡඹᔢᙹಽǍᇥࡹᨕᲙᯩ݅. Table 2᮹ḡ⩶⦺ᱢ☖ĥsᮥ

ᔕ⠕ᅕ໕, ⦹⃽Ğಽʙᯕᨱݡ⦽2, 3₉༉ູ✙aḡ⢽໕Ğಽʙᯕᅕ

݅ḡ႑ᱢᯙsᮥӹ┡ԙ݅. ᯕෝၵ┶ᮝಽᄡ࠺ĥᙹ᪡᪽łࠥ۵

⦹⃽⠪Ɂᯕᘂᗮࠥ᪡ᱡඹᔢᙹaḡ႑ᱢᮝಽʑᩍ⦹Ł, ᯕᨱ঑௝

ᮁᔍ⦽ Ñ࠺ ✚ᖒᮥ ᅕᩍᵝ۵ äᮝಽ ❱݉ࡽ݅.

á☁⦽đŝಽᅙᩑǍᨱᕽᱽ᜽⦽༉⩶ᮡᱡඹᔢᙹ, ⦹⃽⠪Ɂᯕ ᘂᗮࠥaᙽe݉᭥ࠥ᮹⩶ᔢᮥđᱶ⦹۵ߑḡ႑ᱢᯙᩎ⧁ᮥ⦹۵

äᮝಽ ❱݉ࡽ݅. ঑௝ᕽ ࢱ ๅ}ᄡᙹ۵ ༉⩶᮹ ᱢᬊ ŝᱶᨱᕽ

ᵲ᫵⦹í Łಅࡹᨕ᧝ ⧁ äᮝಽ ᔾbࡽ݅.

4.6 Ջܛ൉নէր઩ݗࠛ৤ࢂॷঃଭୡ૳

ᯕᔢ᮹đŝಽᇡ░ḡ⢽໕⠪Ɂᯕᘂᗮࠥ۵ᱡඹᔢᙹ᪡⦹⃽⠪Ɂ ᯕᘂᗮࠥᨱ እ⧕ Clark ༉⩶᮹ ᙽe݉᭥ࠥ ⩶ᔢᨱ ᔢݡᱢᮝಽ

᯲ᮡᩢ⨆ᮥӝ⊹۵äᮥ⪶ᯙ⦹ᩡ݅. ᯕᨱTable 4᮹ݡᔢᮁᩎᄥ

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ḡ⢽໕⠪Ɂᯕᘂᗮࠥ᮹⠪ɁsᮥŁᱶ᜽┉⬥, SCE-UA ↽ᱢ⪵ʑ ჶᮥᱢᬊ⦹ᩍᱡඹᔢᙹ᪡⦹⃽⠪Ɂᯕᘂᗮࠥෝ⇵ᱶ⦹ᩡ݅. ⇵ᱶ

ࡽๅ}ᄡᙹॅ᮹đŝ۵Table 5᪡zᯕӹ┡ԍ݅. ᮁᩎ᮹ᔢ⦹ඹe

ੱ۵Ƚ༉ᨱ঑௝ᱡඹᔢᙹၰࠥݍ᜽e᮹Ğ⨆á☁۵࠺ᯝ᜽e᮹

ᙹྙᔍᔢᮝಽእƱ⦹۵äᯕaᰆᱢ⧊⦹ӹ, ᙹྙᔍᔢ᮹ᇡ᳒ᮝಽ

ᯕ్⦽á☁ෝᙹ⧪⦹۵ߑ⦽ĥᱱᯕၽᔾ⦹ᩡ݅. ⦹ḡอᮁᩎ᮹

⦹ඹႊ⨆ੱ۵ᮁᩎȽ༉a⍅ḱᨱ঑௝ᱡඹᔢᙹၰࠥݍ᜽eᯕ

ʙᨕḡ۵Ğ⨆ᮥ❭ᦦ⧁ᙹᯩᨩ݅. ⨆⬥ᙹྙᔍᔢၰݡᔢᮁᩎ᮹

⪶ᰆᮥၵ┶ᮝಽᩑǍaᙹ⧪ࡹᨕḥ݅໕, ᳡޵᮹ၙᯩ۵ᩑǍđŝ a ࠥ⇽ࢁ äᮝಽ ᔾbࡽ݅.

5. đು

ᅙᩑǍᨱᕽ۵ᮁᩎ᮹႑ᙹǍ᳑ෝᖅ໦⧁ᙹᯩ۵⡎⧉ᙹʑၹ᮹

Clark ༉⩶ᮥᱽᦩ⦹ᩡŁ, ᜽e-໕ᱢłᖁᮝಽ۵ḡ⢽໕ŝ⦹⃽ᨱ

ݡ⦹ᩍ}ᄥᱢᯙ࠺ᙹᩎ⦺ᱢ✚ᖒᮥᱢᬊ⦽ᰍ᳑ᱶࡽ⡎⧉ᙹෝ

ᯕᬊ⦹ᩡ݅. ੱ⦽ᖁ⩶ᱡᙹḡ⇵ᱢ᮹Ğᬑʑ᳕᮹Clark ༉⩶ŝ

zᯕ₉ᇥ⪵ࡽ⩶┽aᦥܩ௝⧕ᕾ᜾ᮥᱢᬊ⦹ᩍᙹ⧪⦹ᩡ݅. ᅙ

ᩑǍᨱᕽᱽᦩࡽ༉⩶ᮥʑၹᮝಽᙽe݉᭥ࠥ᮹⩶ᔢᮥᱶపᱢᮝ ಽĥప⧁ᙹᯩ۵šĥ᜾ᮥᱽ᜽⦹ᩡ݅. ⇵aಽ, ᱽᦩࡽClark

༉⩶᮹ๅ}ᄡᙹॅᮥᄡ⪵᜽┅໕ᕽᙽe݉᭥ࠥ⩶ᔢ, ᷪ☖ĥ༉ູ

✙ॅᨱݡ⦽ᄡ࠺ᖒᮥ⪶ᯙ⦹ᩡ݅. ᯕᔢ᮹đŝෝ᫵᧞⦹໕݅ᮭŝ

z݅.

(1) ᱽᦩࡽClark ༉⩶ᮡᙽe݉᭥ࠥ᮹⩶ᔢᮥ⠪Ɂŝᇥᔑอᮥ

Łಅ⦹ᩍ ᱢᬊ⦽ ႊჶᅕ݅ ᙹྙłᖁ᮹ ᪽ł ၰ ℉ࢱ᳭⢽᮹

༉᮹᪡šಉࡽ⦽ĥᱱᮥ}ᖁ⦹ᩡ݅. ᯕ్⦽đŝಽᇡ░ᅙ

ᩑǍᨱᕽᱽ᜽⦽ႊჶುᮡ႑ᙹĞಽ᮹ᯕḩᖒŝ࠺ᱢๅ}ᄡᙹ

ॅ᮹ᩢ⨆ᮥᱢᱩ⦹íၹᩢ⧁ᙹᯩᮭᮥ⪶ᯙ⧁ᙹᯩᨩ݅.

ੱ⦽ᙽe݉᭥ࠥ᮹᪽łࠥ(skewness) ⪚ᮡ3₉༉ູ✙᮹Ñ࠺

ᮡᅙᩑǍᨱᕽᱽᦩࡽ༉⩶ᮥʑၹᮝಽᱢᱩ⦹í⠪a⧁ᙹ

ᯩᮭᮥ ᦭ ᙹ ᯩᨩ݅.

(2) š⊂ᙹྙᔍᔢ᮹☖ĥ༉ູ✙ॅŝᅙᩑǍᨱᕽ⇵ᱶࡽ☖ĥ༉ູ

✙ॅ᮹ ᔢšĥᙹ۵ 1₉༉ູ✙᮹ Ğᬑ 0.995, 2₉༉ູ✙۵

0.993, 3₉༉ູ✙۵0.983ಽᔑᱶࡹᨩ݅. ⇵ᱶsŝš⊂sᨱ

ݡ⦽☖ĥ༉ູ✙ॅ᮹ᔢšĥᙹ۵ݡℕಽ᧲⪙⦽đŝෝӹ┡ԕ ᨩ݅. ੱ⦽⠪Ɂŝᇥᔑᨱݡ⧕ᕽ۵⇵ᱶsŝš⊂sᯕݡℕಽ

ᯝ⊹⦹۵Ğ⨆ᮥᅕᩍᵝᨩ݅. ə్ӹ⇵ᱶࡽ3₉༉ູ✙ᨱݡ⦽

đŝ۵݅ᗭŝݡ⠪aࡹ۵Ğ⨆ᮥӹ┡ԕᨩ݅. ⨆⬥޵ฯᮡ

ᙹྙᔍᔢ᮹ᇥᕾੱ۵ݡᔢᮁᩎ᮹⪶ᰆᮥ☖⦹ᩍᝍࠥᯩ۵

ᇥᕾᮥᙹ⧪⦹Ł, bᔍᔢ᮹Ⅹʑ᜽ᱱᨱᕽݡᔢᮁᩎ᮹ᖁ⧪⧉

ᙹ᳑Õᨱ঑ෙ☁᧲Ŗɚ᮹⡍⪵ࠥၰᯕᨱ঑ෙᮁ⇽ᩎ᮹ᄡ⪵

ෝŁಅ⦹ᩍ႑ᙹǍ᳑᮹⠪aෝᙹ⧪⦽݅໕᮹ၙᯩ۵đŝෝ

⪶ᯙ⧁ ᙹ ᯩᮥ äᮝಽ ❱݉ࡽ݅.

(3) ᅙ ᩑǍᨱᕽ Łಅ⦽ ༉ູ✙ॅ᮹ ᄡ࠺ᖒᮡ ᵝಽ ᱡඹᔢᙹ᮹

ᩢ⨆ᯕⓍíӹ┡ӹŁᯩᮝ໑, ḡ⢽໕⠪Ɂᯕᘂᗮࠥᅕ݅۵⦹

⃽⠪ɁᯕᘂᗮࠥaⓍíᩢ⨆ᮥၙ⊹۵äᮥ⪶ᯙ⧁ᙹᯩᨩ݅.

(4) ᱡඹᔢᙹ᪡⦹⃽⠪ɁᯕᘂᗮࠥaClark ༉⩶ᮝಽᇡ░ᮁࠥࡹ

۵ ᙽe݉᭥ࠥ᮹ ⩶ᔢᮥ đᱶ⦹۵ߑ ḡ႑ᱢᯙ ᩎ⧁ᮥ ⦹۵

äᮝಽ⪶ᯙࡹᨩ݅. ঑௝ᕽࢱๅ}ᄡᙹ۵༉⩶᮹ᱢᬊŝᱶᨱ ᕽ ᵲ᫵⦹í Łಅࡹᨕ᧝ ⧁ äᮝಽ ❱݉ࡽ݅.

qᔍ᮹ɡ

ᯕםྙᮡ2012⦺֥ࠥ⦽ԉݡ⦺Ʊ⦺ᚁᩑǍ᳑ᖒእḡᬱᨱ᮹⦹

ᩍ ᩑǍࡹᨩᮭ.

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