Application of the Width Function Instantaneous Unit Hydrograph: A Case Study of Cheongmi River

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** ᕽᬙݡ⦺Ʊ Ŗŝݡ⦺ Õᖅ⪹ĞŖ⦺ᇡ ၶᔍŝᱶ ([email protected])

Received February 14 2013, Revised March 20 2013, Accepted April 30 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͵͵ǤͶǤͳͶʹͷ

ǤǤǤ

㦫㬦⟖#ᢦⳂᦂ≓ⴂ#ⴲⱧ㬚#㉫↶㉚#⟖⃶ኟ⛞#♮ⷓ

ছ૳଀ȵࢮஜ෴ȵଲܛথȵ׌ઽૈ

Seo, Yongwon, Park, Junehyeong, Rhee, Dong Sop, Kim, Young-Oh****

Application of the Width Function Instantaneous Unit Hydrograph:

A Case Study of Cheongmi River

ABSTRACT

This paper examines the applicability of the Width Function Instantaneous Unit Hydrograph (WFIUH) with a case study of Cheongmi River in South Korea. The parameter values of WFIUH can be physically determined compared to the lumped hydrologic models, which are typically accompanied by parameter estimation procedures with gage records. Assuming uniformly distributed rainfall, the hydrographs obtained with the WFIUH show good agreement with observed data and also the results from HEC-1. A simple investigation of the effect from the rainstorm movement with the WFIUH demonstrates the ability of the proposed model and the need to consider the rainstorm movement effect on the resulting hydrographs for prediction purposes.

Key words : Instantaneous unit hydrograph, Rainstorm movement, Width function

Ⅹಾ

ᅙᩑǍᨱᕽ۵⡎⧉ᙹ(width function)ᨱʑⅩ⦽݉᭥ࠥჶ(WFIUH)ᮥᯕᬊ⦹۵ᙹྙłᖁᔑᱶႊჶᨱݡ⦹ᩍᗭ}⦹Łᝅᱽᮁᩎ(ℎၙ⃽)ᨱ

ᱢᬊ⦹ᩍəᱢᬊᖒᮥá☁⦹ᩡ݅. ʑ᳕Ḳᵲ⩶༉⩶ŝእƱ⦹ᩍWFIUH۵ๅ}ᄡᙹෝྜྷญᱢᮝಽđᱶ⧁ᙹᯩ۵✚Ḷᯕᯩᮝ໑ᵡᇥ⡍⩶༉

⩶ᮝಽᮁᩎ✚ᖒၰvᬑ᮹᜽Ŗeᱢᄡ࠺ᖒᮥᙹྙłᖁᔑᱶᨱၹᩢ⧁ᙹᯩ۵ᰆᱱᯕᯩ݅. ŖeᱢᮝಽɁ॒⦽vᬑෝaᱶ⦹ᩍℎၙ⃽ᮁᩎᨱ

ᱢᬊ⦽đŝš⊂⊹᪡᯹ᯝ⊹⦹۵äᮥ᦭ᙹᯩᨩᮝ໑ჵᬊ༉⩶ᯙHEC-1᪡እƱ⦹ᩍᮁᔍ⦽đŝෝᅕᯕ۵äᮝಽӹ┡ԍ݅. ੱ⦽ᯕ࠺vᬑ ᨱݡ⦽e݉⦽á☁ᔍಡෝ☖⧕WFIUHෝᯕᬊ⦹ᩍvᬑᯕ࠺ᯕᙹྙłᖁ᮹༉᧲ŝ℉ࢱᮁపᨱၙ⊹۵ᩢ⨆ᮥ⠪a⧁ᙹᯩ۵äᮥᅕᩡ݅.

áᔪᨕ ݉᭥ࠥჶ, ᯕ࠺vᬑ, ⡎⧉ᙹ

1. ᕽು

ḡɩʭḡ ฯᮡ ᩑǍᯱॅᯕ ⦹⃽฾ ᩑđǍ᳑(topology)ෝ ʑၹᮝಽ ⦽ ᙹྙ᮲ݖ(hydrologic response)ᨱ ݡ⦽ ᩑǍෝ ⧕᪵ᮭᨱࠥ

ᇩǍ⦹Ł ǎԕ ᱢᬊᔍಡ۵ ऽྙ äᯕ ⩥ᝅᯕ݅. ᯕ᪡ šಉ⦹ᩍ ᮁᩎ᮹ Ǎ᳑ᱢ ✚ᖒᨱ ݡ⦽ ᮁᩎ᮹ ၹ᮲ᮥ ᩑǍ⦽ ℌ ჩṙ ᔍಡಽᕽ

GIUH(Geomorphologic Instantaneous Unit Hydrograph)(Rodriquez-Iturbe and Valdes, 1979; Gupta et al., 1980) ෝॅᙹᯩ݅.

GIUH۵ ᙽe݉᭥vᬑa ᮁᩎᨱ ᵝ᯦ࡹᨩᮥ ভ ᮁᩎ ⇽Ǎᨱᕽ ࠥݍ᜽e᮹ ᇥ⡍a ⦹⃽ ᩑđǍ᳑᪡ zᮡ ᮁᩎ᮹ ḡ⩶⦺ᱢ ✚ᖒŝ

᳑ࠥĥᙹ᪡ zᮡ ⮱෥᮹ ᙹญ⦺ᱢ ✚ᖒᮥ ၹᩢ⧉ᮥ ᅕᩍᵡ݅(Franchini᪡ O’Connell, 1996).

սėॡ

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GIUH ႊჶᮡ ⦹⃽᮹ ₉ᙹ᪡ ḡ⩶⦺ᱢ ᇥᔑᮥ Łಅ⦹۵ߑ, ᯕ۵ᔢඹ⦹⃽᮹}ᙹಽb⦹⃽ॅ᮹₉ᙹෝๅĉᯕॅᮥᇥඹ⦹۵

äᯕ݅(Strahler, 1957). ᯕ᪡ݡ᳑ᱢᮝಽ⦹⃽฾ᮝಽᇡ░Ḣᱲ

᨜ᮥᙹᯩ۵⡎⧉ᙹ(width function)ෝᯕᬊ, ⦹⃽฾᮹᭥ᔢ⦺ᱢ

✚ᖒᮥÑญ᮹eఖ⦽⧉ᙹ⩶┽ಽӹ┡ԕᨕ(Moussa, 2008a, b) ᯕෝᮁ⇽ĥᔑᨱᯕᬊ⦹۵ႊჶࠥᯩ݅. ᮁᩎ᮹ᙹྙၹ᮲ᮡ⡎⧉ᙹ

᪡ ၡᱲ⦹íšಉᯕ ᯩᮝӹ(Gupta᪡ Waymire, 1983), ᯕ్⦽

ၹ᮲ᨱݡ⦽ᱶᅕ۵bḡඹॅᮥə൚ᮝಽྗᮥĞᬑ, ᷪGIUH᪡

zᮡႊჶᮥᯕᬊ⧁Ğᬑᔢᝅ⧁ᙹᯩ݅(TroutmanŝKarlinger, 1985). ঑௝ᕽ ⡎⧉ᙹෝ ݉᭥ᮁపࠥ }ֱᨱ ᱢᬊ⦽WFIUH(the Width Function Instantaneous Unit Hydrograph) ᮹Ğᬑ, ⦹⃽฾

ᩑđǍ᳑᮹✚ᖒᮥ₉ᙹಽӹ┡ԕʑᅕ݅⡎⧉ᙹ᮹⩶┽ಽəݡಽ

ᯕᬊ⧉ᮝಽ៉GIUHᅕ݅ᔢݚ⯩eఖ⧕ḥ݅(Di Lazzaro, 2009).

Mesa᪡Mifflin(1986)ŝNaden(1992)۵⡎⧉ᙹ᪡⪮ᙹ❭᮹ᯕ ᘂ⪶ᔑႊᱶ᜾ᮥđ⧊⦹ᩍᮁᩎၹ᮲ᨱݡ⦽ᙹญᱢᯙᇥᔑᮥ⪮ᙹ

❭ᱥ❭ᗮࠥ᪡᳦ႊ⨆⪶ᔑĥᙹಽӹ┡ԕᨩ݅. ᯕভ⧕᮹ๅ}ᄡᙹ

ॅᮡᄥࠥ᮹⇵ᱶᱩ₉ᨧᯕ⦹⃽Ğᔍ, ݉໕⩶ᔢ॒ᮝಽᇡ░ྜྷญᱢ ᮝಽđᱶࡽ݅(Franchini᪡O’Connell, 1996). Ḳᵲ⩶ᙹྙ༉⩶

(Lumped hydrologic model) ŝ እƱ⦹ᩍ WFIUH۵ ᵡᇥ⡍⩶

༉⩶(Semi-distributed model)ᯕ௝Ł⧁ᙹᯩ݅. ᵡᇥ⡍⩶༉⩶

᮹✚ᖒᔢ౩ᯕ޵vᬑ᪡zᮡvᬑ᮹᜽Ŗeᱢᇥ⡍ෝŁಅ⧁

ᙹᯩᮝ໑⋉⚍ప॒᮹ĥᔑੱ⦽Ċᯱ݉᭥ಽᙹ⧪ᯕa܆⦹݅.

Ḳᵲ⩶ᙹྙ༉⩶᮹ĥᙹॅᯕ༉⩶ᮥǍᖒ⧁ভษ݅ĥᙹ⇵ᱶ᮹

ŝᱶᯕ⦥᫵⦽äŝእƱ⦹ᩍWFIUH᮹ĥᙹॅᮡྜྷญᱢᮝಽ

đᱶࡽ݅۵ᰆᱱᯕᯩ݅. ੱ⦽ə⦥᫵ᯱഭ᮹⊂໕ᨱᕽ᪥ᱥᇥ⡍⩶

༉⩶(Fully-distributed model)ᨱእ⦹ᩍᱢᬊᖒᯕ୑ᨕӽvᱱᯕ

ᯩ݅.

ǎԕᨱᕽ۵GIUHaLee᪡Park(1987)ᨱ᮹⧕ᗭ}ࡽᯕ⬥,

݅᧲⦹íᱢᬊࡹᨕ᪅Łᯩ݅(Ahn ॒, 2002; Heo᪡Lee, 2002;

Kim ॒, 2003; Choi ॒, 2006; Ham ॒, 2008; Choi ॒, 2010;

Joo ॒, 2011). ᯕᨱၹ⧕əᰆᱱၰᯕುᱢᯙ݉ᙽᖒᨱࠥᇩǍ⦹Ł

WFIUHᨱݡ⧕ᕽ۵ǎԕᨱᕽᩑǍaḥ⧪ࡽᔍಡaᱢ݅. Choi

॒(2010)ŝKim ॒(2011)ᮡၙĥ⊂ᮁᩎᨱ᮹ᱢᬊᮥ᭥⦹ᩍ⡎⧉ᙹ

ෝᯕᬊ⦽⧊ᖒ݉᭥ࠥʑჶᮥᱽ᜽⦹ᩡᮝӹ༉ࢱDi Lazzaro(2009) ᮹ᱲɝႊ᜾ᮥ঑௝ᮁᩎ᮲ݖ᮹࠺ᙹᩎ⦺ᱢᇥᔑ(hydrodynamic dispersion)ᮥŁಅ⦹ḡᦫᦹᮝ໑✚⯩Ɂ॒vᬑෝaᱶ⦽݉᭥ࠥ

᮹ᔾᖒᨱᵲᱱᮥࢱᨩ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵࠺ᙹᩎ⦺ᱢᇥᔑᮥ

Łಅ⦽WFIUHෝᝅᱽᮁᩎᯙℎၙ⃽ᮁᩎᨱᱢᬊ⦹Ł, əđŝෝ

š⊂⊹᪡እƱ⦹ᩍ༉⩶᮹ᱢᬊᖒᮥá☁⦹ᩡᮝ໑, vᬑ᮹ᯕ࠺

ၰ᜽Ŗeᇥ⡍ෝŁಅ⧁ᙹᯩ۵ᵡ⣝⡍༉⩶ᮝಽᕽ᮹⪽ᬊa܆ᖒ ᨱ ᵲᱱᮥ ࢱŁᯱ ⦹ᩡ݅.

2. WFIUH (Instantaneous Unit Hydrograph based on the Width Function)

ᮁᗮᯕᯝᱶ⦹݅Łaᱶ⧩ᮥভ, Ñญෝ᜽eᮝಽᄡ⪹⧉ᮝಽ៉

WF ۵ᯕᔑ⪵ࡽ݉᭥ࠥಽᛞíᄡ⪹⧁ ᙹᯩ݅. ə్ӹᩍʑᕽ

⦹⃽᮹ᱡᙹᬊపŝࠥݍ᜽e᮹ᄡ࠺ᖒᮡྕ᜽ࡽ݅. ᝅᱽ⦹⃽฾ᮡ

ʙᯕ ĢƖ ᮹b}ࠦพᱢᯙ݉᭥⦹⃽ॅ᮹ᩑđಽᅝᙹᯩᮝ໑, bbᮡ⊂໕ᮁ᯦ᯕᯩᮥäᯕŁ, Ñญ Ɩ ᨱ᭥⊹⦽ᮁᩎ⇽Ǎಽ

ᩑđࡽ݅. Van de Nes(1973)ᮡḩప-ᬕ࠺పᅕ᳕ႊᱶ᜾ᮥʑၹᮝ ಽ ⦹ᩍ ᦥ௹᮹ ⪮ᙹ❭᮹ ᯕᘂ⪶ᔑ ႊᱶ᜾ᮥ ᱽᦩ⦹ᩡ݅.

ć Şª á ć Şƒ ŞƖ

^Ï

Ş

^Ï

ª à Ɓć Şª ŞƖ (1)

ᩍʑᕽĞĥ᳑Õᮡ ªÞ×ìƒß á ĺÞƒß , _{ªÞƖì×ß á ×} , əญŁ ªÞtìƒß á × ᯕ໑, ª ۵ ᮁ⇽ప(⽎/s), ۵ ⪶ᔑĥᙹ(⽊/s), Ɓ ۵ ᬕ࠺❭

ᱥ❭ᗮࠥ(m/s), ƒ ۵᜽e(s), əญŁ Ɩ ۵⦹ࠥᔢ݉ᮝಽᇡ░᮹Ñญ (m)ᯕ݅. Franchini᪡O’Connell(1996)ᮡWFIUH᮹ᱢᬊᮥ᭥

⧕ᯱᩑ⦹⃽ᨱݡ⦹ᩍŲ⡎Ḣᔍb⩶⦹⃽݉໕ᮥaᱶ, ⪶ᔑĥᙹ

᪡ ᬕ࠺❭ ᱥ❭ᗮࠥ Ɓ ෝ ᦥ௹᪡ zᯕ ᱽ᜽⦹ᩡ݅.

Ɓ á ƉƔì Ɖ j ÎíÒ ⁽²⁾

j ć Ï¬ ª á ć

×

Ï¬

×

Ɨ

_×

Ɣ á ć Ï¬

×

ƔƗ

_×

á ć Ð¬

×

ƁƗ

_×

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ᩍʑᕽ Ɣ ۵ᮁᗮ(m/s), ª ۵ᮁప(⽎/s), ¬

_×

۵⦹⃽Ğᔍ(mm

^-1

), Ɨ

_×

۵ ⦹⃽݉໕᮹ ʫᯕ(m), ۵ ⦹⃽݉໕᮹ թእ(m)ᯕ݅.

ĥᙹಽᱢᬊࡹ۵ ᪡ Ɓ ෝᔢᙹಽࢱŁ, ᜾(1)ŝᔢඹᯥ⟥ᜅ

Ğĥ᳑Õᮝಽᇡ░ᦥ௹᪡zᮡ⧕ෝ᨜ᮥᙹᯩ݅(Van de Nes, 1973; Naden, 1992; Franchini᪡O’Connell, 1996; Da Ros᪡

Borga, 1997).

ƓÞƖìƒß á ć ö ^ć Ñņƒ

^Ð

Ɩ ƙ

Ɯ ƚ _{à ć}

Ñƒ ÞĢƖ à Ɓƒß

^Ï

ƛ

Ɲ ƞ ₍₄₎

ᩍʑᕽ ƓÞƖìƒß ۵⪮ᙹ❭ᨱݡ⦽ᯕᘂ⪶ᔑႊᱶ᜾᮹݉᭥ᯥ⟥ᜅ

ၹ᮲(unit impulse response)ᯕ݅. ঑௝ᕽ⡎⧉ᙹෝʑၹᮝಽ⦹۵

ᮁᩎ᮹݉᭥ࠥ(WFIUH)ෝ݅ᮭŝzᯕӹ┡ԝᙹᯩ݅(Da Ros and Borga, 1997).

ƆÞƒß á

õ_×^t

°ÞƖßƓÞƖìƒßƂƖ (5)

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Fig. 1. The Cheongmi River Basin

Fig. 2. Reconstructed river networks of River Cheongmi with a grid size of 2 km

ᩍʑᕽ °ÞƖß ۵ᱶȽ⪵⦽⡎⧉ᙹᯕ݅. ᯕᱶȽ⪵⦽⡎⧉ᙹ᮹

sᮡᮁᩎၹ᮲᮹᯦ಆ⊹ಽᕽvᬑaᮁᩎ⇽Ǎಽᇡ░x᪡x+dxᔍᯕ ᮹ Ǎeᨱ ਉᨕḩ ⪶ශŝ z݅Ł ⧁ ᙹ ᯩ݅. ᜾ 5ෝ ᯕᔑ⪵⦽

⩶┽ಽ ⢽⩥⦹໕ ݅ᮭ᜾ŝ z݅.

ƆÞƒß á ā

_{Ƈ á Î}^ƌ

^ć _ö ć Ñņƒ

^Ð

ƇĢƖ °ÞƇĢƖß ƙ

Ɯ ƚ _{à ć}

Ñƒ ÞƇĢƖ à Ɓƒß

^Ï

ƛ

Ɲ ƞ _ĢƖ ₍₆₎

ᩍʑᕽ W۵ ⡎⧉ᙹಽᕽ ݅ᮭŝ zᯕ ᱶ᮹ࡽ݅.

°ÞƖß á §åƂÞƖßæ (7)

ᩍʑᕽ⡎⧉ᙹW۵ᵝᨕḥÑญxᨱݡ⧕ə᪡ᯝ⊹⦹۵Ċᯱ᮹

ᙹ᪡z݅. ᮁᩎᨱɁ॒⦽vᬑaᦥܭ᜽eᄥvᬑ᮹Ŗeᇥ⡍ෝ

Łಅ⧁Ğᬑ᜾(6)ᮡ݉᭥ࠥ(IUH)aᦥܭb᜽e݉᭥ᄥၹ᮲⧉ᙹ (response function)ᮝಽ ᱶ᮹ࡽ݅.

ƐÞŉì ƒß á ā

_{Ƈ á Î}^ƌ

^ć _ö ć Ñņŉ

^Ð

ƇĢƖ °

«

ÞƇĢƖì ƒß ƙ

Ɯ ƚ _{à ć}

Ñŉ ÞƇĢƖ à Ɓŉß

^Ï

ƛ

Ɲ ƞ _ĢƖ

(8)

ᩍʑᕽ W

R

ᮡ ݉᭥ᮁ⬉vᬑa ᦥܭ ᯥ᮹᮹ Ŗeᇥ⡍ෝ aḥ

vᬑ᪡đ⧊⦹ᩍᱶ᮹ࡹ۵⡎⧉ᙹಽᕽb᜽et ษ݅݅ᮭŝzᯕ

ᱶ᮹ࡽ݅.

°

_«

ÞƖìƒß á ā

_Ƈìƈ

^«

^Ƈƈ

^ÞƖìƒß ⁽⁹⁾

ᩍʑᕽR

ij

(x,t)۵dt᮹᜽eeĊ࠺ᦩĊᯱ(i, j)ᨱਉᨕḥvᬑపᯕ

݅. ᜾9۵đŝᱢᮝಽ႑ᙹ฾ᮥ঑௝ᮁᩎ⇽Ǎಽᇡ░᮹Ñญᨱ

঑௝ᱶ᮹ࡽᮁᩎӺ⦹vᬑప᮹⧊ᮥ᮹ၙ⦽݅. ᮁᩎ⇽Ǎᨱᕽ᮹

ᙹྙłᖁᮡ᜽eᄥಽᔑᱶࡽၹ᮲⧉ᙹ(᜾8)᮹٥ᱢ⧊ŝz݅. ᯕ

ভၹ᮲⧉ᙹ᮹ๅ}ᄡᙹc᪡D۵vᬑvࠥᨱࠦพᱢᯕ௝aᱶ⦽݅.

3. ᱢᬊᮁᩎ

WFIUH᮹ᱢᬊᮁᩎᮝಽ⦽vᱽ1ḡඹᯙǎa⦹⃽ℎၙ⃽ᮥ

ݡᔢᮁᩎᮝಽ⦹ᩡ݅(Figure 1). ℎၙ⃽᮹ᮁᩎ໕ᱢᮡ595.13 ⽋,

ᮁಽᩑᰆᮡ60.69kmᮝಽᇢ࠺ႊ⨆ᮝಽᮁ⦹⦽݅. ᮁᩎ᮹⠪ɁŁ

ࠥ۵EL. 142.23m, ⠪ɁᮁᩎĞᔍ۵15.46%᪡z݅. ᦿᕽᨙɪ⦽

ၵ᪡zᯕᵡᇥ⡍༉⩶ᯙWFIUH᮹༉ुĥᔑᮡĊᯱ݉᭥ಽᯕ൉

ᨕḥ݅. ⮱෥᮹ႊ⨆ᮡ࠺ᕽԉᇢ᮹օႊ⨆ᮝಽᖅᱶ⦹ᩡ݅. Figure 2ᮡℎၙ⃽᮹⦹⃽฾ᮥ16×21᮹Ċᯱ฾(ĊᯱⓍʑ2km)ᨱᰍǍᖒ

⦽äᯕ݅. Figure 3ᮡFigure 2᪡zᯕᰍǍᖒࡽℎၙ⃽᮹⦹⃽฾

ࠥಽᇡ░⇵⇽ࡽ⡎⧉ᙹෝӹ┡ԙäᯕ݅. ᩍʑᕽ⡎⧉ᙹ᮹sᮡ

ᵝᨕḥÑญᨱ⧕ݚ⦹۵Ċᯱᙹ᪡z݅. ᯕჩᩑǍᨱᕽ᮹⡎⧉ᙹ۵

ʑ᳕⡎⧉ᙹᨱݡ⦽ᱶ᮹᪡݅ᗭ₉ᯕaᯩᮥᙹᯩ݅(Lashermes᪡

Foufoula-Georgiou, 2007). ə్ӹʑᅙᱢᮝಽ⡎⧉ᙹ۵Ñญ-໕ ᱢ ⧉ᙹෝ ӹ┡ԕအಽ(Lee᪡ Delleur, 1976; Moussa, 2008a) ᅙᩑǍᨱᕽᔍᬊ⦽⡎⧉ᙹ۵}ֱᱢᮝಽ┡ݚ⦹݅Ł⧁ᙹᯩ݅.

ᮁ⇽łᖁᮥࠥݍ᜽e᮹⪶ශ⧉ᙹ௝Ł⧁Ğᬑ, ⇽Ǎḡᱱᮝಽᇡ░

᮹Ñญෝӹ┡ԕ۵⡎⧉ᙹ۵ᮁ⇽łᖁᨱݡ⦽Ḣᱲᱢᯙ⧕ᕾᯕ௝

⧁ᙹᯩ݅. ᷪ, ࠺ᯝ⦽ᮁᗮᮥaᱶ⦹ᩡᮥভ⡎⧉ᙹ۵ၵಽᙹྙł ᖁᮝಽ⊹⪹ࢁᙹᯩ݅. Figure 4۵Ċᯱ݉᭥ಽᔑᱶ⦽ᮁ⇽łᖁḡᙹ (Curve Number) ᯕ݅. ᮁ⬉ᬑపᮡSCS ᮁ⇽łᖁḡᙹჶ(AMC-III)

ᮥ ᯕᬊ⦹ᩍFigure 4᮹ᮁ⇽łᖁḡᙹෝᯕᬊ⦹ᩍĊᯱ݉᭥ಽ

(4)

Fig. 3. The width function of River Cheongmi obtained from the reconstructed river networks on a lattice

Fig. 4. Curve number (CN) obtained on a lattice for each grid

Fig. 5. The flood celerity and the diffusion coefficient as functions of water depths

Table 1. Information of the Cheongmi gage station

River Station Location

Observation Started Reference(EL.m)

Location Longitude Latitude

Cheongmi Cheongmi (T/M) Wonbu-ri, Jeomdong-myun, Yeoju-gun 129-18-41 35-32-59 Jan 1, 1985 51.066 (51.146)*

*Reference for 1998-2000

ᔑᱶ⦹ᩡᮝ໑݉᭥᜽eᄥಽᔑᱶࡽŖeᇥ⡍ෝaḥᮁ⬉ᬑపᮥ

ᯕᬊᔩಽᯕᱶ᮹ࡽ⡎⧉ᙹ(᜾9) ၰၹ᮲⧉ᙹ(᜾8)ෝᔑᱶ⦹ᩡ݅.

Ų⡎Ḣᔍb⩶݉໕ᮥaᱶ⧁Ğᬑ⦹ࠥĞᔍaๅ}ᄡᙹᔑᱶᨱ

aᰆⓑᩢ⨆ᮥၙ⊽݅. ᅙᩑǍᨱᕽ۵ℎၙ⃽ᱥǍe⦹ࠥ᮹⠪ɁĞ ᔍ(1/1140)ᮥᯕᬊ⦹ᩡᮝ໑ᯕᨱ঑ෙᮁᗮၰ⪮ᙹ❭ᱥ❭ᗮࠥ

əญŁ ⪶ᔑĥᙹෝ ᙹᝍᨱ ݡ⦽ ⧉ᙹಽ ӹ┡ԙ đŝ۵ Figure

5᪡z݅. ℎၙ⃽ᮁᩎᨱݡ⦽WFIUH᮹ĥᙹ⇵ᱶđŝⅩʑᙹᝍᮥ

1.0m ԕ᫙ಽaᱶ⧁Ğᬑ, ⪮ᙹ❭᮹ᱥ❭ᗮࠥc۵1.25m/s, ⪶ᔑĥ ᙹD۵4.5×10

³

⽊/sಽđᱶ⧁ᙹᯩ݅(Figure 5). ᯕ۵Franchini᪡

O’Connell(1996) ᯕᱽ᜽⦽ᯱᩑ⦹⃽᮹⪮ᙹ❭ᱥ❭ᗮࠥ(10

⁰

) ၰ

⪶ᔑĥᙹ(10

³

)᮹ჵ᭥᪡ᯝ⊹⦹۵đŝᯕ݅. ĊᯱⓍʑᨱݡ⦽༉⩶

᮹ ၝqࠥ ᇥᕾᮡ ᅙ ᩑǍ᮹ ݡᔢᨱᕽ ᱽ᫙⦹ᩡ݅.

4. š⊂⊹ၰʑ᳕༉⩶(HEC-1)ŝ᮹እƱ

WFIUH ᮹ᱢᬊᖒᮥá☁⦹ʑ᭥⦹ᩍℎၙᙹ᭥š⊂ᗭ᮹ᝅ⊂

⪮ᙹపᮥáᱶᨱᔍᬊ⦹ᩡ݅(Table 1). WFIUHᨱݡ⦽እƱá☁

ෝ᭥⦽ᯱഭಽჵᬊ༉⩶ᯙHEC-1ᮥᯕᬊ⦽Ḳᵲ⩶༉⩶᮹đŝࠥ

ᯕᬊ⦹ᩡ݅.

Figure 6 ŝ7ᮡbb2009֥7ᬵ12ᯝ, 2010֥9ᬵ10ᯝ᮹

ࢱvᬑᔍᔢᨱݡ⦽ᙹྙłᖁᮥᔑᱶ⦽äᯕ݅. ᯕĞᬑvᬑ۵

ᮁᩎᨱŖeᱢᮝಽɁ॒(uniform)⦹íᇥ⡍ࡹᨕԕญ۵äᮝಽ

aᱶ⦹ᩡ݅. əฝᨱӹ┡ӽၵ᪡zᯕWFIUHෝᯕᬊ⦹ᩍᔑᱶ⦽

ᙹྙłᖁᯕš⊂⊹ၰʑ᳕Ḳᵲ⩶༉⩶(HEC-1)ᮥᯕᬊ⦽đŝ (Ministry of Construction and Maritime Affaires(ᯕ⦹MCMA), 2011) ᪡᯹ᯝ⊹⧉ᮥ᦭ᙹᯩ݅. ✚⯩ᙹྙłᖁᨱᯩᨕ℉ࢱᮁప᮹

Ⓧʑ᪡℉ࢱᮁప᮹ၽᔾ᜽eᨱᯩᨕʑ᳕HEC-1༉⩶ŝእƱ⧁อ

(5)

Fig. 6. The hydrograph obtained from the WFIUH compared with the observation for a rainstorm event (12 Jan 2009)

Fig. 7. The hydrograph obtained from the WFIUH compared with the observation for a rainstorm event (10 Sep 2010)

Table 2. Parameter estimation of the Clark IUH (MCMA, 2011)

Subbasin Area

(km

²

)

tc(hour) k(hour)

Initial Optimized Initial Optimized

Outlet 27.32 1.55 2.05 2.44 2.97

Geumgok 17.03 1.13 1.63 1.72 2.24

Geumgok (before) 34.17 1.43 1.93 1.90 2.42

Seolsung 37.79 1.23 1.73 1.43 1.95

Seolsung (before) 11.81 0.73 1.23 1.07 1.60

Ogap 30.54 0.85 1.35 1.14 1.66

Ogap (before) 37.04 1.44 1.94 2.03 2.56

Eung 103.02 2.09 2.89 2.47 3.49

Eung (before) 33.48 1.38 1.88 1.56 2.09

Seokwon 51.60 1.57 2.07 1.73 2.26

Seokwon (before) 40.64 1.42 1.92 1.72 2.24

Juksan 54.20 1.57 2.07 1.88 2.40

Juksan (before) 116.48 2.66 3.31 2.98 4.50

⦹໑ʑᱡᮁపᮥᇥญ(ᙹ⠪Ḣᖁᇥญჶ)⦽š⊂ᮁపŝእƱ⧕ᕽࠥ

ᳬᮡđŝෝᅕᩍᵝŁᯩ݅. ᩍʑᕽʑ᳕HEC-1༉⩶ᮡ༉ࢱ13}

᮹ᗭᮁᩎᮝಽǍᖒࡹᨕᯩᮝ໑ᮁᩎ⇵ᱢჶᮝಽ۵Clark ݉᭥ࠥჶ

ᮥ ⦹ࠥ⇵ᱢʑჶᮝಽ۵ Muskingum ႊჶᮥ ᯕᬊ⦽ đŝᯕ݅

(MCMA, 2011). 2000 ֥ 7ᬵ 22ᯝ, 2002֥ 8ᬵ 6ᯝ, 2004֥

7ᬵ15ᯝ, 2006֥7ᬵ28ᯝ॒ʑ᪶4}š⊂ᮁపၰvᬑᔍᔢᮥ

ᯕᬊ⦹ᩍbᗭᮁᩎᄥಽ↽ᱢ⪵ࡽHEC-1 ༉⩶Clark ݉᭥ࠥჶ᮹

ๅ}ᄡᙹ(ᱡඹᔢᙹ ၰ ࠥݍ᜽e)۵ Table 2᪡ z݅.

5. vᬑᯕ࠺᮹ᩢ⨆⠪a

vᬑᯕ࠺᮹ᙹྙłᖁᨱݡ⦽ᩢ⨆ᮡฯᮡᩑǍಽၾ⩡ḥၵᯩ݅

(Singh, 1997; Seo, 2012). ᯝၹᱢᮝಽ⦹ඹႊ⨆ᮝಽᯕ࠺⦹۵

ĞᬑᮁᩎᨱŖeᱢᮝಽɁ॒⦽vᬑ᪡እƱ⦹ᩍᙹྙłᖁᮡ܇í

ӹ┡ӹ۵ɪĊ⦽ᙹྙłᖁ᮹ᔢ᜚ŝ℉ࢱᮁప᮹᷾aෝ✚Ḷᮝಽ

⦽݅. ၹݡಽvᬑaᔢඹႊ⨆ᮝಽᯕ࠺⦹۵Ğᬑᙹྙłᖁ᮹ᔢ᜚

ᯕᯝ⁮ӹ┡ӹӹəʑᬙʑ۵᪥อ⦹໑℉ࢱᮁప᯲ࠥíӹ┡ӽ݅.

ᯕ᪡zᯕvᬑᯕ࠺ᨱ঑ෙvᬑ᮹᜽Ŗeᱢᄡ࠺ᮡᙹྙłᖁ᮹

⩶ᔢᨱฯᮡᩢ⨆ᮥၙ⊹အಽᩩ⊂᮹༊ᱢᮝಽᙹྙłᖁᮥᔑᱶ⧁

Ğᬑᯕᨱݡ⦽Łಅaၹऽ᜽⦥᫵⦹݅. ᵡᇥ⡍༉⩶ᮝಽᕽWFIUH ᮹ ✚Ḷ ᵲ ⦹ӹ۵ vᬑ᮹ ᜽Ŗeᱢᄡ࠺ᖒᨱ ݡ⦽ ᙹྙłᖁᮥ

ᔑᱶ⧁ᙹᯩ݅۵äᯕ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵ᮁᩎᨱԕฑⅾvᬑ పᯕᯝᱶ⧁Ğᬑᯕ࠺vᬑ᮹ʙᯕȽ༉᪡ᯕ࠺ᗮࠥᨱ঑ෙᩢ⨆ᮥ

á☁⦹ࠥಾ⦹ᩡ݅. Figure 8ᮡᯕ࠺vᬑ᮹ႊ⨆ᨱ঑௝ᱶ᮹ࡹ۵

ᯕ࠺vᬑ᮹ʙᯕȽ༉(L

s

) ᪡ᯕ࠺ᗮࠥ(v

s

) ෝᅕᩍᵝŁᯩ݅. ᩍʑᕽ

vᬑ᮹ʙᯕȽ༉(L

s

)۵vᬑḥ⧪ႊ⨆ᮝಽᯕ࠺vᬑ᮹ʙᯕಽᱶ᮹

(6)

Fig. 9. The variation of hydrographs at the outlet of the watershed depending on the storm movement: (a) Ls = 2km, vs = 0.55m/sec; (b) Ls = 4km, vs = 1.1m/sec; (c) Ls = 8km, vs = 2.2m/sec

Fig. 8. The length scale (Ls) and the speed (vs) depending on the direction of rainstorm movements

ࡹ໑, ᯕভvᬑ᮹ḥ⧪ႊ⨆ᨱḢbႊ⨆, ᷪ, ⬂ႊ⨆ʙᯕȽ༉۵

ᮁᩎ᮹ʙᯕȽ༉ᅕ݅⧎ᔢⓍÑӹzᮡäᮝಽaᱶ⦽݅. ᯕ࠺vᬑ ᮹ჵ᭥ԕᨱᕽvᬑ᮹vᬑvࠥ۵ᯝᱶ⦹໑, ঑௝ᕽḡᱱᨱԕฑ

vᬑపᮡ ḡᱱ vᬑ ḡᗮ᜽eᨱ እಡ⦽݅.

࠺ᕽԉᇢ4}᮹ႊ⨆ᮝಽᬡḢᯕ۵ᯕ࠺vᬑෝaᱶ⦹ᩍWFIUH

ෝ ᯕᬊ⦹ᩍᮁᩎ⇽Ǎᨱᕽ᮹ᙹྙłᖁᮥᔑᱶ⦹ᩡ݅. Figure 9ᮡ

ḡᱱ݉᭥vᬑvࠥ(1mm/hr)ෝaᱶ⦹ᩡᮥĞᬑvᬑᯕ࠺ᨱ঑ෙ

ℎၙ⃽ᮁᩎ⇽Ǎᨱᕽ᮹ᙹྙłᖁ᮹ᄡ⪵ෝࠥ᜽⦽äᯕ݅. ᦿᕽ

ᨙɪ⦽ݡಽᯕভᮁᩎᨱԕญ۵ⅾvᬑపၰḡᱱvᬑḡᗮ᜽eᮡ

ᯝᱶ⦹ࠥಾ⦹ᩡ݅. ঑௝ᕽvᬑ᮹ʙᯕȽ༉(L

s

)᪡ᯕ࠺ᗮࠥ(v

s

)۵

ᕽಽእಡ⦽݅. ᩩෝॅᨕ2km᮹⡎ᮥw۵ʕு༉᧲(band)᮹

⩶┽ᯝĞᬑ, እƱᱢ۱ฑᗮࠥ(0.55m/sec)ಽ᜽e݉᭥ಽ⦽݉᭥Ċ

ᯱෝ ᯕ࠺⦹۵ äᮝಽ aᱶ⦽݅. อ᧞ vᬑ ʙᯕȽ༉a 4kmᯝ

Ğᬑᯕ࠺ᗮࠥ۵ᯕᨱእಡ⦹ᩍ1.1m/secಽᱶ᮹ࡽ݅. ᦿᕽᨙɪ⦽

ၵ᪡zᯕℎၙ⃽ᮁᩎᮡᇢ࠺ႊ⨆ᮝಽ⦹⃽ᯕᮁ⦹⦹۵ḡ⩶⦺ᱢ

✚ᖒᮥaḡŁᯩ݅. ঑௝ᕽvᬑ᮹ᯕ࠺ႊ⨆ᯕᮁᩎ⇽Ǎෝ⨆⧁

Ğᬑ(eastward, northward) Figure 9᮹đŝᨱӹ┡ӽၵ᪡zᯕ

ᮁᩎᨱŖeᱢᮝಽɁ॒⦽vᬑၰ݅ෙႊ⨆ᮝಽᯕ࠺⦹۵Ğᬑ᪡

እƱ⦹ᩍ℉ࢱᮁపᨱⓑ₉ᯕaӹ┡ӹ۵äᮥ᦭ᙹᯩ݅. ⦹ඹႊ⨆

(Eastward)ಽ ᯕ࠺⦹۵ vᬑᯝ Ğᬑ əಽ ᯙ⧕ ᮁᩎ ⇽Ǎᨱᕽ

ၽᔾ⦹۵ᙹྙłᖁ᮹℉ࢱᮁపᯕᔢඹႊ⨆(Westward)᪡እƱ⦹

ᩍ᧞2.1႑ⓑäᮥ᦭ᙹᯩ݅(Figure 9). ᷪzᮡʙᯕȽ༉᪡

ⅾప᮹ vᬑa ၽᔾ⦹ᩍࠥ ə ᯕ࠺ႊ⨆ᨱ ঑௝ 2႑ ᯕᔢ᮹ ⓑ

₉ᯕaၽᔾ⦽݅۵äᮥ᦭ᙹᯩ݅. ᯕĞᬑᮁᩎᨱv⦹⦽vᬑ᮹

ⅾపၰᮁᩎ᮹ᯥ᮹᮹ḡᱱᨱᕽ᮹vᬑḡᗮ᜽eᮡᯝᱶ⦹݅. ə్

ӹ, vᬑᯕ࠺ᮝಽ᜽Ŗeᱢᄡ࠺ᖒᮝಽᯙ⦹ᩍ⇽Ǎᨱᕽ᮹ᙹྙł

ᖁ᮹ ⩶ᔢᨱ ⓑ ᩢ⨆ᯕ ᯩ݅۵ äᮥ ᦭ ᙹ ᯩ݅.

(7)

Fig. 10. The peak discharge ratio compared with the uniform rainfall as a function of the ratio of the catchment and the rainstorm length scales( Ls/Lc)

Figure 10 ᨱᕽ۵ᯕ࠺vᬑ᮹ʙᯕȽ༉(L

s

) ᨱ঑௝ᯕ࠺vᬑಽ

ᯙ⦽ᮁᩎ⇽Ǎᨱᕽ᮹℉ࢱ⪮ᙹపᮥᮁᩎɁ॒vᬑෝaᱶ⦹ᩡᮥ

Ğᬑ℉ࢱ⪮ᙹపᨱݡ⦽እಽӹ┡ԙäᯕ݅. Figure 10᮹đŝᨱ

ӹ┡ӽၵ᪡zᯕᯕ࠺vᬑ᮹ʙᯕȽ༉a᷾a⧁ᙹಾvᬑᯕ࠺ᮝ ಽ ᯙ⦽ ℉ࢱᮁపᨱ᮹ ᩢ⨆ᯕ ᱱ₉ qᗭ⦹۵ äᮥ ᦭ ᙹ ᯩ݅.

ੱ⦽ᯕ࠺vᬑ᮹ʙᯕȽ༉aᮁᩎ᮹ʙᯕȽ༉᪡aʭᬭḩĞᬑ,

ᮁᩎᨱŖeᱢᮝಽɁ॒⦽vᬑ᪡እƱ⦹ᩍ℉ࢱᮁపᯕᯝ⊹⦹۵

äᮥ᦭ᙹᯩᮝ໑ᯕ۵ᯕ࠺vᬑ᮹ʙᯕȽ༉a⍅ḩĞᬑᮁ⇽ᙹྙ

łᖁᮥʑᵡᮝಽə⬉ŝaᱶḡᔢ┽(stationary)᮹Ɂ॒(uniform)

⦽vᬑ᪡zᦥḥ݅۵Seo ॒(2012)᮹đŝ᪡ᔢ᮲⦹۵äᯕ݅.

Figure 10 ᮹ đŝᨱᕽ ੱ⦽ ᵝ༊⧕᧝⧁ ᱱᮡ ᮁᩎ ⦹ඹႊ⨆

(Eastward᪡Northward)ᮝಽvᬑaᯕ࠺⧁Ğᬑ✚ᱶvᬑʙᯕ Ƚ༉ᨱᕽ℉ࢱᮁపᯕ↽ݡaࡽ݅۵ᱱᯕ݅. ᯕ۵ᮁᩎษ݅vᬑᯕ

࠺ᨱ঑ෙ↽ݡᮁపᯕ ӹ┡ӹ۵Łᮁ⦽ᯕ࠺vᬑ᮹ʙᯕȽ༉ෝ

ᱶ᮹⧁ ᙹᯩ݅۵ äᮥ ᮹ၙ⦹အಽ⨆⬥ ႊᰍᱢ ⊂໕ᨱᕽ✚⯩

Łಅ⧁ᔍ⧎ᯕ௝⧁ᙹᯩ݅. ၹݡಽᯕ࠺vᬑ᮹ḥ⧪ႊ⨆ᯕᔢඹႊ

⨆(Westward᪡Southward)ᯝĞᬑə⬉ŝ۵ᯕ࠺vᬑ᮹Ⓧʑᨱ

঑௝ ݉ᯝ⦹í(monotonically) ᷾a ⪚ᮡ qᗭ⦹۵äᮥ ᦭ ᙹ

ᯩ݅(Figure 10). ੱ⦽ Figure 10ᨱ ӹ┡ӽ ၵ᪡ zᯕ ℎၙ⃽

ᮁᩎᯕ ࠺ᕽ ႊ⨆ᮝಽ ʕ ᰆႊ⩶᮹ ᮁᩎᯕအಽ ԉᇢ ႊ⨆ᮝಽ

ᬡḢᯕ۵vᬑᅕ݅࠺ᕽ ႊ⨆ᮝಽᬡḢᯕ۵vᬑᨱ℉ࢱᮁప᮹

⊂໕ᨱᕽ ޵ ၝq⦽ äᮥ ᦭ ᙹ ᯩ݅. ᯕ్⦽ ᩑǍđŝ۵ Kim

॒(2003)᮹ ᩑǍđŝ᪡ࠥ ᯝ⊹⦹۵ äᯕ݅.

6. đು

ᅙᩑǍᨱᕽ۵⦹⃽฾᮹ḡ⩶⦺ᱢᯙᩑđᖒᮥᮁᩎ᮹ᙹྙ⦺ᱢ

ၹ᮲ŝᩑĥ⦹۵ᱲɝႊჶ᮹⦹ӹಽWFIUHෝᗭ}⦹ᩡᮝ໑ᝅᱽ

ᮁᩎᨱ ᱢᬊ⦹ᩍ ə ᱢᬊᖒᮥ á᷾⦹ᩡ݅. GIUH᪡ እƱ⦹ᩍ

WFIUH۵ᵡᇥ⡍༉⩶᮹✚ḶᮥaḡŁᯩᮝ໑ᮁᩎ✚ᖒ᮹Ŗeᱢ

ᇥ⡍ၰvᬑ᮹᜽Ŗeᱢᇥ⡍ෝŁಅ⧁ᙹᯩ݅۵ᰆᱱᮥaḡŁ

ᯩ݅. ๅ}ᄡᙹ ⇵ᱶŝᱶᮥ ၹऽ᜽ ⦥᫵ಽ ⦹۵ ʑ᳕᮹ Ḳᵲ⩶

༉⩶ŝእƱ⦹ᩍWFIUH᮹ๅ}ᄡᙹ۵ྜྷญᱢᮝಽđᱶࡹအಽ

ᙹྙᇥᕾၰᱢᬊ᮹ᨥၡ⧉ᮥᅕᰆ⧁ᙹᯩ݅. vᬑ᮹᜽Ŗeᱢ

ᄡ࠺ᖒᮝಽᯙ⦽ᙹྙłᖁ᮹ᩢ⨆ᨱݡ⦽šᝍᯕԁಽ᷾a⦹Ł

ᯩᮭᨱ ঑௝ ᯕෝ ⠪a⦹۵ ႊჶ ᵲ᮹ ⦹ӹಽ ᪥ᱥᇥ⡍༉⩶ᯕ

ᵝ༊ၼŁᯩᮝӹ, ᔢݡᱢᮝಽฯᮡ⦥᫵ᯱഭ, ᮁᩎ✚ᖒ᮹Ŗeᱢ

Ɂḩᖒ॒ᮝಽ ᯙ⦹ᩍ əᱢᬊᖒᨱ۵ ݅ᗭ ᨕಅᬡᯕᯩ۵ äᯕ

ᔍᝅᯕ݅. ᯕ᪡እƱ⦹ᩍWFIUH۵᪥ᱥᇥ⡍༉⩶ŝእƱ⧁Ğᬑ

əๅ}ᄡᙹ᮹eఖ⧉ŝᯕು᮹݉ᙽ⧉ᮝಽᯙ⧕ᔢݡᱢᮝಽᱢᬊ ᖒᯕ ୑ᨕӽ ✚Ḷᮥ aḡŁ ᯩ݅. ঑௝ᕽ ⨆⬥ ౩ᯕ޵ vᬑ ॒

vᬑ᮹᜽Ŗeᱢᱶᅕ≉ाʑᚁ᮹ḥᅕŝ޵ᇩᨕ݅᧲⦽༊ᱢᮝಽ

WFIUH ᮹ ᱢᬊᯕ Ⓧí ʑݡࡽ݅.

qᔍ᮹ɡ

ᅙᩑǍ۵ǎ☁⧕᧲ᇡÕᖅʑᚁ⩢ᝁᔍᨦ᮹ᩑǍእḡᬱ(11ʑᚁ

ᰍӽ⦝⧕ᱡqʑᚁ}ၽ)᮹ᩑǍእḡᬱᨱ᮹⧕ᙹ⧪ࡹᨩ᜖ܩ݅.

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5, pp. 743-754.

Van de Nes, T. J. (1973). Linear analysis of a physically based model of a distributed surface runoff system, The Netherlands:

Wageningen.

Application of the Width Function Instantaneous Unit Hydrograph: A Case Study of Cheongmi River

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)

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ছ૳଀ ȵࢮஜ෴ ȵଲܛথ ȵ׌ઽૈ

Seo, Yongwon*, Park, Junehyeong**, Rhee, Dong Sop***, Kim, Young-Oh****

Application of the Width Function Instantaneous Unit Hydrograph:

A Case Study of Cheongmi River

ABSTRACT

Key words : Instantaneous unit hydrograph, Rainstorm movement, Width function

Ⅹಾ

ᅙᩑǍᨱᕽ۵⡎⧉ᙹ(width function)ᨱʑⅩ⦽݉᭥ࠥჶ(WFIUH)ᮥᯕᬊ⦹۵ᙹྙłᖁᔑᱶႊჶᨱݡ⦹ᩍᗭ}⦹Łᝅᱽᮁᩎ(ℎၙ⃽)ᨱ

ᱢᬊ⦹ᩍəᱢᬊᖒᮥá☁⦹ᩡ݅. ʑ᳕Ḳᵲ⩶༉⩶ŝእƱ⦹ᩍWFIUH۵ๅ}ᄡᙹෝྜྷญᱢᮝಽđᱶ⧁ᙹᯩ۵✚Ḷᯕᯩᮝ໑ᵡᇥ⡍⩶༉

⩶ᮝಽᮁᩎ✚ᖒၰvᬑ᮹᜽Ŗeᱢᄡ࠺ᖒᮥᙹྙłᖁᔑᱶᨱၹᩢ⧁ᙹᯩ۵ᰆᱱᯕᯩ݅. ŖeᱢᮝಽɁ॒⦽vᬑෝaᱶ⦹ᩍℎၙ⃽ᮁᩎᨱ

áᔪᨕ ݉᭥ࠥჶ, ᯕ࠺vᬑ, ⡎⧉ᙹ

1. ᕽು

ḡɩʭḡ ฯᮡ ᩑǍᯱॅᯕ ⦹⃽฾ ᩑđǍ᳑(topology)ෝ ʑၹᮝಽ ⦽ ᙹྙ᮲ݖ(hydrologic response)ᨱ ݡ⦽ ᩑǍෝ ⧕᪵ᮭᨱࠥ

ᇩǍ⦹Ł ǎԕ ᱢᬊᔍಡ۵ ऽྙ äᯕ ⩥ᝅᯕ݅. ᯕ᪡ šಉ⦹ᩍ ᮁᩎ᮹ Ǎ᳑ᱢ ✚ᖒᨱ ݡ⦽ ᮁᩎ᮹ ၹ᮲ᮥ ᩑǍ⦽ ℌ ჩṙ ᔍಡಽᕽ

GIUH(Geomorphologic Instantaneous Unit Hydrograph)(Rodriquez-Iturbe and Valdes, 1979; Gupta et al., 1980) ෝॅᙹᯩ݅.

GIUH۵ ᙽe݉᭥vᬑa ᮁᩎᨱ ᵝ᯦ࡹᨩᮥ ভ ᮁᩎ ⇽Ǎᨱᕽ ࠥݍ᜽e᮹ ᇥ⡍a ⦹⃽ ᩑđǍ᳑᪡ zᮡ ᮁᩎ᮹ ḡ⩶⦺ᱢ ✚ᖒŝ

᳑ࠥĥᙹ᪡ zᮡ ⮱෥᮹ ᙹญ⦺ᱢ ✚ᖒᮥ ၹᩢ⧉ᮥ ᅕᩍᵡ݅(Franchini᪡ O’Connell, 1996).

 սėॡ

GIUH ႊჶᮡ ⦹⃽᮹ ₉ᙹ᪡ ḡ⩶⦺ᱢ ᇥᔑᮥ Łಅ⦹۵ߑ, ᯕ۵ᔢඹ⦹⃽᮹}ᙹಽb⦹⃽ॅ᮹₉ᙹෝๅĉᯕॅᮥᇥඹ⦹۵

äᯕ݅(Strahler, 1957). ᯕ᪡ݡ᳑ᱢᮝಽ⦹⃽฾ᮝಽᇡ░Ḣᱲ

᨜ᮥᙹᯩ۵⡎⧉ᙹ(width function)ෝᯕᬊ, ⦹⃽฾᮹᭥ᔢ⦺ᱢ

✚ᖒᮥÑญ᮹eఖ⦽⧉ᙹ⩶┽ಽӹ┡ԕᨕ(Moussa, 2008a, b) ᯕෝᮁ⇽ĥᔑᨱᯕᬊ⦹۵ႊჶࠥᯩ݅. ᮁᩎ᮹ᙹྙၹ᮲ᮡ⡎⧉ᙹ

᪡ ၡᱲ⦹íšಉᯕ ᯩᮝӹ(Gupta᪡ Waymire, 1983), ᯕ్⦽

ၹ᮲ᨱݡ⦽ᱶᅕ۵bḡඹॅᮥə൚ᮝಽྗᮥĞᬑ, ᷪGIUH᪡

zᮡႊჶᮥᯕᬊ⧁Ğᬑᔢᝅ⧁ᙹᯩ݅(TroutmanŝKarlinger, 1985). ঑௝ᕽ ⡎⧉ᙹෝ ݉᭥ᮁపࠥ }ֱᨱ ᱢᬊ⦽WFIUH(the Width Function Instantaneous Unit Hydrograph) ᮹Ğᬑ, ⦹⃽฾

ᩑđǍ᳑᮹✚ᖒᮥ₉ᙹಽӹ┡ԕʑᅕ݅⡎⧉ᙹ᮹⩶┽ಽəݡಽ

ᯕᬊ⧉ᮝಽ៉GIUHᅕ݅ᔢݚ⯩eఖ⧕ḥ݅(Di Lazzaro, 2009).

Mesa᪡Mifflin(1986)ŝNaden(1992)۵⡎⧉ᙹ᪡⪮ᙹ❭᮹ᯕ ᘂ⪶ᔑႊᱶ᜾ᮥđ⧊⦹ᩍᮁᩎၹ᮲ᨱݡ⦽ᙹญᱢᯙᇥᔑᮥ⪮ᙹ

❭ᱥ❭ᗮࠥ᪡᳦ႊ⨆⪶ᔑĥᙹಽӹ┡ԕᨩ݅. ᯕভ⧕᮹ๅ}ᄡᙹ

ॅᮡᄥࠥ᮹⇵ᱶᱩ₉ᨧᯕ⦹⃽Ğᔍ, ݉໕⩶ᔢ॒ᮝಽᇡ░ྜྷญᱢ ᮝಽđᱶࡽ݅(Franchini᪡O’Connell, 1996). Ḳᵲ⩶ᙹྙ༉⩶

(Lumped hydrologic model) ŝ እƱ⦹ᩍ WFIUH۵ ᵡᇥ⡍⩶

༉⩶(Semi-distributed model)ᯕ௝Ł⧁ᙹᯩ݅. ᵡᇥ⡍⩶༉⩶

᮹✚ᖒᔢ౩ᯕ޵vᬑ᪡zᮡvᬑ᮹᜽Ŗeᱢᇥ⡍ෝŁಅ⧁

ᙹᯩᮝ໑⋉⚍ప॒᮹ĥᔑੱ⦽Ċᯱ݉᭥ಽᙹ⧪ᯕa܆⦹݅.

Ḳᵲ⩶ᙹྙ༉⩶᮹ĥᙹॅᯕ༉⩶ᮥǍᖒ⧁ভษ݅ĥᙹ⇵ᱶ᮹

ŝᱶᯕ⦥᫵⦽äŝእƱ⦹ᩍWFIUH᮹ĥᙹॅᮡྜྷญᱢᮝಽ

đᱶࡽ݅۵ᰆᱱᯕᯩ݅. ੱ⦽ə⦥᫵ᯱഭ᮹⊂໕ᨱᕽ᪥ᱥᇥ⡍⩶

༉⩶(Fully-distributed model)ᨱእ⦹ᩍᱢᬊᖒᯕ୑ᨕӽvᱱᯕ

ᯩ݅.

ǎԕᨱᕽ۵GIUHaLee᪡Park(1987)ᨱ᮹⧕ᗭ}ࡽᯕ⬥,

݅᧲⦹íᱢᬊࡹᨕ᪅Łᯩ݅(Ahn ॒, 2002; Heo᪡Lee, 2002;

Kim ॒, 2003; Choi ॒, 2006; Ham ॒, 2008; Choi ॒, 2010;

Joo ॒, 2011). ᯕᨱၹ⧕əᰆᱱၰᯕುᱢᯙ݉ᙽᖒᨱࠥᇩǍ⦹Ł

WFIUHᨱݡ⧕ᕽ۵ǎԕᨱᕽᩑǍaḥ⧪ࡽᔍಡaᱢ݅. Choi

॒(2010)ŝKim ॒(2011)ᮡၙĥ⊂ᮁᩎᨱ᮹ᱢᬊᮥ᭥⦹ᩍ⡎⧉ᙹ

ෝᯕᬊ⦽⧊ᖒ݉᭥ࠥʑჶᮥᱽ᜽⦹ᩡᮝӹ༉ࢱDi Lazzaro(2009) ᮹ᱲɝႊ᜾ᮥ঑௝ᮁᩎ᮲ݖ᮹࠺ᙹᩎ⦺ᱢᇥᔑ(hydrodynamic dispersion)ᮥŁಅ⦹ḡᦫᦹᮝ໑✚⯩Ɂ॒vᬑෝaᱶ⦽݉᭥ࠥ

᮹ᔾᖒᨱᵲᱱᮥࢱᨩ݅. ঑௝ᕽᅙᩑǍᨱᕽ۵࠺ᙹᩎ⦺ᱢᇥᔑᮥ

Łಅ⦽WFIUHෝᝅᱽᮁᩎᯙℎၙ⃽ᮁᩎᨱᱢᬊ⦹Ł, əđŝෝ

š⊂⊹᪡እƱ⦹ᩍ༉⩶᮹ᱢᬊᖒᮥá☁⦹ᩡᮝ໑, vᬑ᮹ᯕ࠺

ၰ᜽Ŗeᇥ⡍ෝŁಅ⧁ᙹᯩ۵ᵡ⣝⡍༉⩶ᮝಽᕽ᮹⪽ᬊa܆ᖒ ᨱ ᵲᱱᮥ ࢱŁᯱ ⦹ᩡ݅.

2. WFIUH (Instantaneous Unit Hydrograph based on the Width Function)

ᮁᗮᯕᯝᱶ⦹݅Łaᱶ⧩ᮥভ, Ñญෝ᜽eᮝಽᄡ⪹⧉ᮝಽ៉

WF ۵ᯕᔑ⪵ࡽ݉᭥ࠥಽᛞíᄡ⪹⧁ ᙹᯩ݅. ə్ӹᩍʑᕽ

⦹⃽᮹ᱡᙹᬊపŝࠥݍ᜽e᮹ᄡ࠺ᖒᮡྕ᜽ࡽ݅. ᝅᱽ⦹⃽฾ᮡ

ʙᯕ ĢƖ ᮹b}ࠦพᱢᯙ݉᭥⦹⃽ॅ᮹ᩑđಽᅝᙹᯩᮝ໑, bbᮡ⊂໕ᮁ᯦ᯕᯩᮥäᯕŁ, Ñญ Ɩ ᨱ᭥⊹⦽ᮁᩎ⇽Ǎಽ

ᩑđࡽ݅. Van de Nes(1973)ᮡḩప-ᬕ࠺పᅕ᳕ႊᱶ᜾ᮥʑၹᮝ ಽ ⦹ᩍ ᦥ௹᮹ ⪮ᙹ❭᮹ ᯕᘂ⪶ᔑ ႊᱶ᜾ᮥ ᱽᦩ⦹ᩡ݅.

ć Şª á ć Şƒ ŞƖ

Ş

ª à Ɓć Şª ŞƖ (1)

ᩍʑᕽĞĥ᳑Õᮡ ªÞ×ìƒß á ĺÞƒß , ªÞƖì×ß á × , əญŁ ªÞtìƒß á × ᯕ໑, ª ۵ ᮁ⇽ప(⽎/s),  ۵ ⪶ᔑĥᙹ(⽊/s), Ɓ ۵ ᬕ࠺❭

ᱥ❭ᗮࠥ(m/s), ƒ ۵᜽e(s), əญŁ Ɩ ۵⦹ࠥᔢ݉ᮝಽᇡ░᮹Ñญ (m)ᯕ݅. Franchini᪡O’Connell(1996)ᮡWFIUH᮹ᱢᬊᮥ᭥

⧕ᯱᩑ⦹⃽ᨱݡ⦹ᩍŲ⡎Ḣᔍb⩶⦹⃽݉໕ᮥaᱶ, ⪶ᔑĥᙹ

 ᪡ ᬕ࠺❭ ᱥ❭ᗮࠥ Ɓ ෝ ᦥ௹᪡ zᯕ ᱽ᜽⦹ᩡ݅.

Ɓ á ƉƔì Ɖ j ÎíÒ (2)

j ć Ï¬ ª á ć

Ï¬

Ɨ

Ɣ á ć Ï¬

ƔƗ

á ć Ð¬

ƁƗ

(3)

ᩍʑᕽ Ɣ ۵ᮁᗮ(m/s), ª ۵ᮁప(⽎/s), ¬

۵⦹⃽Ğᔍ(mm

), Ɨ

۵ ⦹⃽݉໕᮹ ʫᯕ(m),  ۵ ⦹⃽݉໕᮹ թእ(m)ᯕ݅.

ĥᙹಽᱢᬊࡹ۵  ᪡ Ɓ ෝᔢᙹಽࢱŁ, ᜾(1)ŝᔢඹᯥ⟥ᜅ

ǤǤǤ

ছ૳଀ȵࢮஜ෴ȵଲܛথȵ׌ઽૈ

Seo, Yongwon, Park, Junehyeong, Rhee, Dong Sop, Kim, Young-Oh****

áᔪᨕ ݉᭥ࠥჶ, ᯕ࠺vᬑ, ⡎⧉ᙹ

սėॡ

ć Şª á ć Şƒ ŞƖ

ᩍʑᕽĞĥ᳑Õᮡ ªÞ×ìƒß á ĺÞƒß , _{ªÞƖì×ß á ×} , əญŁ ªÞtìƒß á × ᯕ໑, ª ۵ ᮁ⇽ప(⽎/s), ۵ ⪶ᔑĥᙹ(⽊/s), Ɓ ۵ ᬕ࠺❭

᪡ ᬕ࠺❭ ᱥ❭ᗮࠥ Ɓ ෝ ᦥ௹᪡ zᯕ ᱽ᜽⦹ᩡ݅.

Ɓ á ƉƔì Ɖ j ÎíÒ ⁽²⁾

j ć Ï¬ ª á ć

Ï¬

Ɨ

۵ ⦹⃽݉໕᮹ ʫᯕ(m), ۵ ⦹⃽݉໕᮹ թእ(m)ᯕ݅.

ĥᙹಽᱢᬊࡹ۵ ᪡ Ɓ ෝᔢᙹಽࢱŁ, ᜾(1)ŝᔢඹᯥ⟥ᜅ

ƓÞƖìƒß á ć ö ^ć Ñņƒ

Ɩ ƙ

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