* ᯙ⦹ݡ⦺Ʊ ᙹᯱᬱᜅ▽ᩑǍᗭ ᩑǍƱᙹ, Ŗ⦺ၶᔍ ([email protected]) ** ⪮ᯖݡ⦺Ʊ ☁༊Ŗ⦺ŝ ᳑Ʊᙹ, Ŗ⦺ၶᔍ ([email protected])
Received July 17, 2013/ revised August 16, 2013/ accepted August 21, 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵ǤǤʹʹͻ͵ Ǥ ǤǤ
FOAἺ#ⴲⱧ㬚#㰋⟖≒ᵊᦂ#ጪ㍓⮎⛚#⍆㰓⢢⛯#ⱒ❊ⴖ#↺ᇎᦂ#⍂⛛
୨ઽผ ȵࢮ୪߆ ȵָܛ ȵଲૈ
Jung, Younghun*, Park, Jeryang**, Yeo, Kyu Dong***, Lee, Seung Oh****
Sensitivity Analysis of Uncertainty Sources in Flood Inundation Mapping by using the First Order Approximation Method
ABSTRACT
Flood inundation map has been used as a fundamental information in flood risk management. However, there are various sources of uncertainty in flood inundation mapping, which can be another risk in preventing damage from flood. Therefore, it is necessary to remove or reduce uncertainty sources to improve the accuracy of flood inundation maps. However, the entire removal of uncertainty source may be impossible and inefficient due to limitations of knowledge and finance. Sensitivity analysis of uncertainty sources allows an efficient flood risk management by considering various conditions in flood inundation mapping because an uncertainty source under different conditions may propagate in different ways. The objectives of this study are (1) to perform sensitivity analysis of uncertainty sources by different conditions on flood inundation map using the FOA method and (2) to find a major contributor to a propagated uncertainty in the flood inundation map in Flatrock at Columbus, U.S.A. Result of this study illustrates that an uncertainty in a variable is differently propagated to flood inundation map by combination with other uncertainty sources. Moreover, elevation error was found to be the most sensitive to uncertainty in the flood inundation map of the study reach.
Key words : Sensitivity analysis, FOA method, Flood inundation map, Uncertainty propagation, Flood risk management
Ⅹಾ
⪮ᙹ᭥⨹šญᨱᕽ⪮ᙹჵ௭ࠥ۵aᰆʑᅙᱢᯙᯱഭಽᔍᬊࡹŁᯩ݅. ə్ӹ⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱᕽ݅᧲⦽⩶┽ಽᇩ⪶ᝅᖒᯕၽᔾ⦹ʑভ
ྙᨱᯕ۵ᱶ⪶⦽⪮ᙹႊᰍĥ⫮ᙹพᨱÙฝ࠭ಽ᯲ᬊ⧁ᙹᯩ݅. ə్အಽᇩ⪶ᝅᖒᗭෝᱽÑ⦹Ñӹ}ᖁ⦹ᩍ⪮ᙹჵ௭ࠥ᮹ᱶ⪶ᖒᮥ⨆ᔢ
┅۵äᯕ⦥⦹ӹ, ༉ुᇩ⪶ᝅᖒᮥ᪥ᄞ⦹íᱽÑ⦹۵äᮡĞᱽᱢ┡ݚᖒŝ⪮ᙹᨱݡ⦽ḡ᮹⦽ĥভྙᨱᇩa܆⦹໑ๅᬑእ⬉ᮉᱢᯝ
ᙹᯩ݅. ੱ⦽, ⪮ᙹჵ௭ࠥᨱᱥݍࡹ۵ᇩ⪶ᝅᖒᗭ᮹ᩢ⨆ᮡ݅ෙ⪹Ğᄡᙹᨱ݅ෝᙹᯩʑভྙᨱ݅᧲⦽ᵝᄡ⪹Ğ᮹᳑ÕᮥŁಅ⦽ᇩ
⪶ᝅᖒᗭᨱݡ⦽ၝqࠥᇥᕾᯕ⦥⦹݅. ᯕෝ☖⦹ᩍᱽÑ⧕⦹Ñӹ}ᖁ⍽⧁ᇩ⪶ᝅᖒᗭ᮹ᬑᖁᙽ᭥ෝᱶ⧉ᮝಽ៉ᱥఖᱢᯕ໕ᕽ
ࠥ⬉ᮉᱢᯙ⪮ᙹ᭥⨹šญෝᮁࠥ⧁ᙹᯩᮥäᮝಽ❱݉ࡽ݅. ᅙᩑǍ۵ᵝᄡ⪹Ğ᮹᳑Õᨱ⪮ᙹჵ௭ࠥᨱၙ⊹۵ᇩ⪶ᝅᖒᗭ᮹ၝqࠥ
ෝFOAႊჶᮥᯕᬊ⦹ᩍᇥᕾ⦹Ł, ᯕෝၙǎIndianaᵝColumbusɝ᮹Flatrock vᨱᱢᬊ⦹ᩍ⪮ᙹჵ௭ࠥᨱaᰆⓑᇩ⪶ᝅᖒᮥᱥݍ
⦹۵ᗭෝᖁᄥ⦹ᩡ݅. ᅙᩑǍđŝ۵⦹ӹ᮹ᇩ⪶ᝅᖒᗭa݅ෙ᯦ಆᄡᙹӹๅ}ᄡᙹ᪡zᮡᵝᄡ⪹Ğᨱ᮹⧕⪮ᙹჵ௭ࠥᨱ݅íᩢ⨆
ᮥᵡ݅۵äᮥ⪶ᯙ⦹ᩡᮝ໑ੱ⦽, ݡᔢᮁᩎ᮹⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱᕽaᰆⓑᇩ⪶ᝅᖒᗭ۵ḡ⩶ᯱഭಽ❱ࡹᨩ݅.
áᔪᨕၝqࠥᇥᕾ, FOA ႊჶ, ⪮ᙹჵ௭ࠥ, ᇩ⪶ᝅᖒᱥ❭, ⪮ᙹ᭥⨹šญ
սėॡ
1. ᕽು
↽ɝʑ⬥ᄡ⪵᪡ࠥ⪵॒ᮝಽᯙ⦹ᩍᖙĥฯᮡŔᨱᕽ⪮ᙹ᮹
vࠥ᪡⬀ᙹᨱݡ⦽⇵ᖙaᄡ⦹Łᯩ۵ḡᩎᯕ۹Łᯩ݅(Milly et al., 2002; Villarini et al., 2009). ᯕᨱ⪮ᙹ᭥⨹ᨱݡ⦽
ᯙŝšᝍᯕ׳ᦥḡŁ, ⪮ᙹ᭥⨹šญ᮹ᵲᖒᯕv᳑ࡹŁᯩ݅.
⪮ᙹ᭥⨹šญ۵ᯝၹᱢᮝಽᖅĥ⪮ᙹపᨱݡ⦽⪮ᙹჵ௭ḡᩎၰ
ჵ᭥᮹ᩩ⊂ᮥ☖⧕ᯕᨕḥ݅. ᩩෝॅᨕ, ၙǎᨱᕽ۵FEMA (Federal Emergency Management Agency)aᵝࠥᱢᮝಽၙǎ ᱥᩎ᮹⪮ᙹᅕ⨹ᮥ⡍⧉⦽ ᳦⧊ᱢ⪮ᙹ᭥⨹šญෝ⦹Łᯩ۵ߑ
ᯕ۵ 100֥ ኩࠥ᮹ ⪮ᙹᔍᔢᨱ ݡ⦽ ⪮ᙹჵ௭ᩩ⊂ᨱ ɝÑ⦹Ł
ᯩ݅. ə్ӹ, ᯕ్⦽ᩩ⊂đŝ᮹ᱶ⪶ࠥ۵༊⢽ḡᩎ᮹ᙹᨱ
Ⓧíݍḡ໑, ᖙᇡ᳑ᔍđŝᩎᱽ⦽ࡽᯱᬱၰᰍᱶᨱ
ᇩ⪶ᝅᖒᯕ ⧎ᔢ ᳕ᰍ⦹í ࡽ݅(Merwarde et al., 2008).
ᕽ, ᵝ⪮ᙹᔍᔢᨱݡ⦽ᯙᱢၰĞᱽᱢᗱᝅᮥႊḡ⦹ʑ
᭥⦽ ⪮ᙹ ჵ௭ࠥ᪡ zᮡ ⪮ᙹᩩ⊂᮹ ᱶ⪶ᖒᮥ }ᖁ⦹۵ äᮡ
ᦥḢʭḡࠥ ⪮ᙹ ᭥⨹šญᨱᕽ ᵝ⦽ ŝᱽಽ ԉᦥᯩ݅.
⪮ᙹᩩ⊂ᨱᯩᨕᕽᇩ⪶ᝅᖒᮥ᷾a┅۵ᯙॅᯕฯᮡᩑǍ ᨱᕽ ᗭ}ࡹᨕ ᪵ḡอ ᱽ⦽ࡽ ᰍᱶŝ ⪮ᙹ✚ᖒᨱ ݡ⦽ ḡ᮹
ᇡ᳒ᮝಽᯕ్⦽ᇩ⪶ᝅᖒᮥ᪥ᄞ⦹íᱽÑ⦹۵äᮡ⩥ᝅᱢᮝಽ
ᇩa܆⦹݅. ə్ӹᯕ్⦽ᇩ⪶ᝅᖒᮥ↽ᗭ⪵⦹ᩍ⪮ᙹᩩ⊂᮹ᱶ
⪶ᖒᮥ׳ᯕŁᯱ⦹۵יಆᮡḡᗮᱢᮝಽḥ⧪ࡹᨕ᪵݅(Merwade et al., 2008; Bale, 2009). ᩍ్ᇩ⪶ᝅᖒᯙᯱॅᵲ✚⯩᳑ࠥĥᙹ,
ᮁప, ḡ⩶ᯱഭ॒ᮡ⪮ᙹ༉ߙยᨱᕽၽᔾ⧁ᙹᯩ۵ᇩ⪶ᝅᖒᨱ
ݡ⦽ᵝᯙᯱॅಽᯙࡹᨕ᪵݅(Aronica et al., 2002; Herschey, 2002; Bates et al., 2004; Hine and Hall, 2006; Weichel, 2007;
Purvis et al., 2008). ᮁపᯱഭ۵ᯝၹᱢᮝಽ⊂ᱶࡽᙹ᭥ᯱഭෝ
ᙹ᭥-ᮁపšĥᨱᕽݡ᯦⦹໕ᕽᔑᱶࡹ۵ߑ, əᙹ᭥-ᮁపšĥ
ᮡᅕ☖100֥ኩࠥၙอ᮹ᮁపၰᙹ᭥ᯱഭෝʑၹᮝಽࠥ⇽ࡽ݅.
ə్အಽԏᮡኩࠥ᮹ᮁపᯝᙹಾəᇩ⪶ᝅᖒᮡ⍅ḡ໑, ᯕ۵
⪮ᙹᩩ⊂᮹ᔑ⇽ྜྷᯙ⪮ᙹჵ௭ࠥᨱᱥݍࡹíࡽ݅. ᳑ࠥĥᙹ۵
ྜྷ᮹⮱ᯕᯩ۵Ğĥ໕᮹⩶┽ၰᖒḩᨱᱶపᱢᮝಽᱶ᮹ԕ ญʑᨕಅᬭᙹญ༉⩶ᨱᕽᅕᱶ⧁ᙹᯩ۵ๅ}ᄡᙹಽᯙࡹᨕ
᪵݅(Pilotti et al., 2011). ə్အಽ᳑ࠥĥᙹ᮹ ᇩ⪶⦽ sᮡ
ᇩ⪶ᝅᖒ᮹ ⦽ ᗭa ࡽ݅. ੱ⦽, ᙹญ༉⩶ᨱᕽ ᙹ᭥ ၰ ྜྷ᮹
⮱ႊ⨆ᨱᩢ⨆ᮥၙ⊹۵ᙹ⊹ḡࠥ۵᳑ᔍႊჶၰǍ⇶ŝᱶᨱᕽ
ᙹ⠪ၰᙹḢ᪅₉aၽᔾ⦽݅. ᯕ్⦽᪅₉ॅᮡᙹญ༉⩶ᮥᯕᬊ⦽
ᙹ⊹༉᮹ෝ᭥⧕Ǎ⇶ࡹ۵⬂݉໕ࠥ᪡ᙹᝍ⊂పᐱอᦥܩᙹ໕ Łಽᇡ░ḡ⩶Łෝq⧉ᮝಽ៉ᔾᖒࡹ۵⪮ᙹჵ௭ࠥᨱᕽࠥᇩ⪶ᝅ ᖒ᮹ᗭಽ᯲ᬊ⦽݅(Vazquez et al., 2002; Bates et al., 2003;
Omer et al., 2003; Wang and Zheng, 2005).
⪮ᙹჵ௭ࠥ᮹ᱶ⪶ᖒᮥ}ᖁ⦹ʑ᭥⧕⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱ
ᕽၽᔾ⦹۵ᇩ⪶ᝅᖒᮥᇥᕾ⦹۵ฯᮡᩑǍॅᯕḥ⧪ࡹŁᯩ݅
(Jung and Merwade, 2012; Romanowicz et al., 2012). ੱ⦽
ᯕ్⦽ŝᱶᨱᕽ⦹ӹ᮹ᇩ⪶ᝅᖒᗭa݅ෙ᯦ಆᄡᙹӹๅ}ᄡ ᙹ᪡zᮡᵝᄡ⪹Ğᨱ᮹⧕ᕽࠥᩢ⨆ᮥၼᮥᙹᯩ݅. ᩩෝॅᨕ,
᳑ࠥĥᙹ᮹᪅₉aᮁప᳑ÕᯕŁᮁపᯝĞᬑ᪡ ᱡᮁపᯝĞᬑ
⪮ᙹჵ௭ࠥᨱᱥݍࡹ۵ᇩ⪶ᝅᖒ᮹Ⓧʑ۵݅ෝäᯕ݅(Merwade et al., 2008). ᕽᯕ్⦽ᵝᄡ⪹Ğ᮹᳑ÕᮥŁಅ⦽bb᮹
᯦ಆᄡᙹၰๅ}ᄡᙹᨱݡ⦽ၝqࠥᇥᕾᮡᱽ⦽ࡽᯱᬱŝᰍᱶ⦹
ᨱᕽᨕਅᇩ⪶ᝅᖒᗭෝᬑᖁᱢᮝಽqᗭ⍽⦹۵ḡᨱݡ⦽
ᱶᅕෝᱽŖ⧉ᮝಽ៉ᱥఖᱢ, Ğᱽᱢᮝಽ⪮ᙹ᭥⨹šญෝa܆⦹
í ⧁ äᮝಽ ❱݉ࡽ݅.
ᅙᩑǍ᮹༊ᱢᮡ1) ⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱᕽᕽಽ݅ෙᇩ⪶ᝅ ᖒᮥaḡ۵ᵝᄡᄡᙹॅ᮹᳑Õ᮹᳑⧊ᨱ۵bb᮹ݡᔢᄡᙹ
ॅ᮹ᇩ⪶ᝅᖒᱥݍእ(uncertainty propagation rate; UPR)ෝᔑᱶ
⦹ᩍ First-order approximation (FOA) ႊჶᮥ ᯕᬊ⦽ ၝqࠥ
ᇥᕾᮥᙹ⧪⦹Ł; 2) ၝqࠥᇥᕾᮥʑၹᮝಽݡᔢᮁᩎ᮹⪮ᙹჵ௭
ࠥ᮹ᵝᇩ⪶ᝅᖒᗭෝᖁᄥ⦹۵äᯕ݅. ᯕෝ᭥⧕ၙǎIndiana ᵝColumbusFlatrock v(Flatrock ⦹ࠥ)ᮥᔍಡݡᔢḡಽᖅᱶ
⦹ᩍᮁప, ᳑ࠥĥᙹ, ḡ⩶ᯱഭᨱᕽ᮹ᇩ⪶ᝅᖒᗭa⪮ᙹჵ௭ࠥ
ᨱ ၙ⊹۵ ᩢ⨆ᮥ ᇥᕾ⦹Łᯱ ⦹ᩡ݅.
2. ၝqࠥᇥᕾ
2.1 ࠤࡦ෴(HEC-RAS)
FOAෝᯕᬊ⦽ၝqࠥᇥᕾ᮹Monte Carlo ༉᮹ŝᱶᨱᕽྕ᯲᭥
ᄡᙹ(random variable)ᨱݡ⦽⪮ᙹ᭥ෝᔑᱶ⦹ʑ᭥⧕Hydrologic Engineering Center River Analysis System (HEC-RAS) ᙹญ
༉⩶ᮥᔍᬊ⦹ᩡ݅. HEC-RAS۵ၙŖᄲ݉(United States Army Corps of Engineers; USACE)᮹Hydrologic Engineering Center (HEC)ᨱ᮹⧕ᕽ}ၽࡹᨩᮝ໑, əᱢᬊᯕእƱᱢe݉⦹ʑভྙᨱ
⦹ᖅĥ॒ ݅᧲⦽ ᇥᨱᕽaᰆ ฯᯕ ᔍᬊࡹ۵ᙹญ༉⩶ ᵲ
⦹ӹᯕ݅. HEC-RAS۵ ᵝ⦹ࠥ᪡ ჵ௭ᬱᮥ ⡍⧉⦽ ⦹⦹ࠥᨱ
ݡ⦽ ᱶᔢඹ᪡ እᱶᔢඹ ⮱᳑Õᨱ ݡ⦹ᩍ ᙹ᭥ෝ ༉᮹⧁ ᙹ
ᯩ۵1₉ᬱ༉⩶ᯕ݅. อ᧞ᵝᨕḥ⮱᳑Õᨱݡ⦹ᩍჵ௭ᬱᯕ
ᱡඹḡಽᕽəʑ܆ᮥ⦽݅໕݅₉ᬱ᮹ᙹญ༉⩶ᮥᯕᬊ⦹۵äᯕ
ᱢᱩ⧁ᙹᯩᮝӹ, ᅙᩑǍᨱᕽ۵⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱᕽ᮹
⪮ᙹ᭥༉᮹ෝᙹ⧪⦹ʑভྙᨱᵝ⦹ࠥ᪡ჵ௭ᬱᮥ⦹ӹ᮹⦹ࠥಽ
aᱶ⦹ᩍHEC-RASෝᔍᬊ⦹ᩡ݅. ᯕ్⦽aᱶᮡᵝ⦹ࠥ᪡ჵ௭ ᬱᨱᕽ᮹ྜྷ᮹⮱ႊ⨆ᯕ⦹᮹ᵲᦺᖁŝ⠪⧪⦹݅۵äᮥ᮹ၙ
⦽݅. ᕽᙹ⊹⢽Ł༉ߙ(digital elevation model; DEM)ಽᇡ░
ᨕḥ⦹⬂݉໕ᮡᵝ⦹ࠥ᪡ჵ௭ᬱᮥ⡍⧉⦹໑, ᳑ࠥĥᙹ۵
b ☁ḡᯕᬊࠥᨱ ⦽ ݉໕ᨱ 20}ʭḡ ᖅᱶࢁ ᙹ ᯩ݅.
HEC-RASᨱᕽᙹ᭥۵ᩑᗮႊᱶ, ᨱթḡႊᱶEq. (1), Manning
ႊᱶ Eq. (2) ॒ᨱ ᮹⧕ ĥᔑࡽ݅.
²Îâ³Îâ ćÏƅ ķίÎÏ
á ²Ïâ³Ïâ ćÏƅ ķϯÏÏ
âƆƃ (1)
ᩍʑᕽ, Y1ŝY2۵݉໕1ŝ2ᨱᕽ᮹ᙹᝍᮥӹ┡ԕ໑, V1ŝ
V2۵⠪Ɂᮁᗮ, Z1ŝZ2۵᭥⊹ᙹࢱ, ķÎŝķÏ۵ᗮࠥaᵲĥᙹ, g۵ ᵲಆĥᙹ, əญŁ he۵ ᨱթḡ ᗱᝅᮥ ӹ┡ԙ݅.
HEC-RASᨱᕽⅾ☖ᙹ܆(total conveyance, Q)ᮡbb᮹ᖙ
ᇡᇥᨱ ݡ⦹ᩍ Manningႊᱶŝ ᩑᗮႊᱶᨱ ᮹⦹ᩍ ĥᔑࡽ
b☖ᙹ܆᮹⧊ᮝಽᔑᱶࡽ݅. Eq. (2)۵SI݉᭥᮹Manningႊᱶ
ᮥ ӹ┡ԙ݅.
ª á ćƌΫćÐ
Ï
¬ƄćÏÎ
(2)
ᩍʑᕽ, nᮡ ᳑ࠥĥᙹ, A۵ ⮱໕ᱢ, Rᮡ ࠺ᙹၹĞ, əญŁ
Sf۵ ษₑĞᔍෝ ӹ┡ԙ݅.
HEC-RASᨱ᮹⦽ᙹ᭥༉᮹۵ʑ⦹⦺ᱢ(geometric) ᯱഭ(ᩩෝॅ
໕. ⦹ࠥᵲᝍᖁ, ⬂݉໕, ⬂݉໕ᔍᯕ᮹eĊ), ⦹ḡ⩶(bathymetry)
ᯱഭ, ⮱᳑Õ, ᳑ࠥĥᙹ, Ğĥ᳑Õ(boundary condition) ॒ᯕ⦥
⦹݅. ⦹ࠥ᮹ʑ⦹⦺ᯱഭ᪡ḡ⩶ᯱഭ۵ḡญᱶᅕᜅ▽(geographic information system; GIS)ᨱᕽ⪽ᬊ⧁ᙹᯩ۵HEC-GeoRASෝ
ᯕᬊ⦹ᩍᙹ⊹⢽Ł༉ߙಽᇡ░ᔾᖒࡹᨩ݅. ᅙᩑǍᨱᕽHEC-RAS ᮹ ⦹ඹ᮹Ğĥ᳑Õᮡ॒ඹᙹᝍ(normal depth)ᮝಽᖅᱶ⦹ᩡ݅.
2.2 લՋࠤԧண౿࣪ԩ࣑
(inverse distance weighting; IDW)
HEC-RASᨱ᮹⧕༉᮹ࡽ⪮ᙹ᭥۵b݉໕ᨱݡ⦹ᩍᔑᱶࡹ໑,
⪮ᙹჵ௭໕ᱢᮥᔑᱶ⦹ʑ᭥⧕b݉໕ᨱᕽ༉᮹ࡽ⪮ᙹ᭥ෝ⦹ࠥ
ᱥℕᨱݡ⧕Ŗeᱢᮝಽᅕe⦹۵äᯕ⦥⦹݅. ᖁ⩶, Kriging, Natural Neighbor, Spline, Trend ॒ŝzᮡᩍ్aḡᅕeჶᯕ
ᯩᮝӹ ᅙ ᩑǍᨱᕽ۵ ᵝ᭥ ḡᱱ᮹ ⪮ᙹ᭥ෝ ⠪Ɂ⦹ᩍ ᖡsᮥ
⇵ᱶ⦹۵ IDWෝ ᔍᬊ⦹ᩡ݅(Eq. (3)).
ÞƖìƗß á
ā
ƕƇ_ ƄƇ (3)ᩍʑᕽ, F(x,y)۵ x, yḡᱱᨱᕽ ᅕeࢁ ⪮ᙹ᭥, fi۵ i ḡᱱ᮹
⪮ᙹ᭥, wi ۵ aᵲ⊹ෝ ӹ┡ԙ݅.
ƕƇá ć
ā
ƈ á Î ƌ ƆƈàƎƆƇàƎ
ᩍʑᕽ, p۵ḡᙹᄡᙹಽ៉ᯝၹᱢᮝಽ2᮹sᯕᔍᬊࡹ໑, hi۵
x, yḡᱱŝ i ḡᱱᔍᯕ᮹ Ñญ(ƆƇáöćÞƖ àƖƇßÏâÞƗ àƗƇßÏ)ෝ
ӹ┡ԙ݅. ᅕeࡽ⪮ᙹ᭥۵ᙹ⊹⢽Ł༉ߙŝbb᮹ᖡᨱݡ⦹ᩍ
እƱ⦽⬥, ḡ⩶⢽Łᅕ݅׳ᮡ⪮ᙹ᭥ෝᖁᄥ⦹ᩍŖeᱢ⪮ᙹჵ௭
ࠥෝ ᔾᖒ⦽݅.
2.3 First-order approximation (FOA) ࢢԮܑंজ Morris, PEST, RSA (regionalized sensitivity analysis), ⫭ȡᇥ ᕾ॒݅᧲⦽ႊჶᯕᔍᬊࡹᨕ᪵݅. ᯕ్⦽݅᧲⦽ၝqࠥᇥᕾ
ႊჶaᬕߑ, FOA۵ḡᩎᱢၝqࠥᇥᕾႊჶᵲ⦹ӹಽᕽUPRᮥ
ᱶప⪵⦹۵ߑᔍᬊࡹᨩ݅(Bates and Townley, 1988; Melching, 1992). Benjamin and Cornell (1970)ᨱ᮹⧕ᱽᦩࡽFOA۵đᱶ
⩶ ༉ߙ(deterministic model)ᮥᯕᬊ⦽ᩩ⊂ᨱᕽ݅ᄡᙹᨱ᮹⧕
ᱥݍࡹ۵ᇩ⪶ᝅᖒᮥᱶప⪵⦹۵e݉⦽ႊჶᮝಽࠦพ߅ᄡᙹಽ
Ǎᖒࡽ⧉ᙹᨱݡ⦽༉ູ✙ᇥᕾᨱʑⅩ⦹໑, ᇩ⪶ᝅᖒᮥaḡ۵
bᄡᙹॅᨱ᮹⧕ၽᔾ⦹۵༉ߙđŝ᮹ᇥᔑእᮉᮥđᱶ⧁ᙹ
ᯩ݅. ᯕ۵ᙹྙ༉⩶, ⧕ඹ༉⩶, ḡ⦹ᙹ༉⩶, ᙹḩ༉⩶, ⪮ᙹ᭥⨹
ᇥᕾ(Lei and Schilling 1994; Sitar et al. 1987; Johnson and Rinaldi 1998; Liu et al. 2001; Zhang et al. 2004; Blumberg and Georgas 2008) ॒ ฯᮡ ᇥᨱᕽ ᱢᬊࡹᨕ ᪵݅.
FOAႊჶᮥᯕᬊ⦹ᩍUPRᮥᔑᱶ⦹ʑ᭥⧕ᕽ۵ᬑᖁ߅ᄡᙹ
±ᨱݡ⦹ᩍ᳦ᗮᱢᯙ༉ߙđŝෝY⦽݅໕⪶ᰆᱱ(expansion point;Ɩƃ)ᮥ ⇵a⧉ᮝಽ ⧉ᙹᱢ šĥ۵ Eq. (4)ŝ zᯕ ⢽⩥⧁
ᙹ ᯩ݅.
Ɨá ƄÞƖß á ƄãƖƃâÞƖ à Ɩƃßä (4)
᭥᮹⧉ᙹ۵⪶ᰆᱱᨱݡ⦹ᩍTaylor᮹ᯕುᨱEq. (5)᪡
zᯕ ⪶ᰆࢁ ᙹ ᯩ݅.
ƄÞƖß á ƄÞƖƃßâ ćƂƖƂƗ
ç
Ɩ á ƖƃÞƖ à Ɩƃßâ ćÏØÎ ćƂƖÏ
ƂÏƗ
ç
Ɩ á ƖƃÞƖ à ƖƃßÏâ ćÐØÎ ćƂƖÐ
ƂÐƗ
ç
Ɩ á ƖƃÞƖ à ƖƃßÐâz (5) ᙹᯱᬱၰ⪹ĞŖ⦺šಉᱢᬊᨱᕽ߅ᄡᙹ᮹⠪Ɂᮡᯝၹᱢᮝ ಽ⪶ᰆᱱᮝಽᔍᬊࡽ݅. ᯕ᪡ᇩᨕ2₉ᯕᔢ᮹⧎༊ᮡℌ⧎༊ᨱ
Fig. 1. Application of FOA Method to Flood Inundation Modeling እ⧕ᕽ ๅᬑ ᯲݅۵ aᱶᦥ௹ ᯝၹᱢᮝಽ ᔾఖ⦽݅.
Ɨ á ƄÞƖß j ƄÞćƖßâ ćƂƖƂƗ
ç
Ɩ á ćƖÞƖ à ćƖß (6)FOAႊჶᮡ1₉⧉ᙹᨱݡ⦹ᩍ⠪Ɂŝᇥᔑᮥᔑᱶ⦹۵ᯝ₉᪡
2₉༉ູ✙ෝᔍᬊ⦽݅. ʑݡs᮹ᖒḩᮥᔍᬊ⧩ᮥভʑݡsᮡ
Eq. (7)᪡ zᯕ ⢽⩥ࢁ ᙹ ᯩ݅.
ã²ä á ćƗá ƙƜƚƄÞćƖßâ ćƂƖƂƗ
ç
Ɩ á ćƖÞƖ à ćƖßƛƝƞ
á ãƄÞćƖßäâ ćƂƖƂƗ
ç
Ɩ á ćƖÞãƖ äà ãćƖäßƛƝƞá ƄÞćƖß (7)
Eqs. (6)᪡(7)ෝVar [y] = E [(y - ȳ )2]᮹šĥᨱݡ᯦⧩ᮥ
ভ Eq. (5)᪡ zᯕ ⢽⩥ࡽ݅.
ƔſƐã²ä á ãÞƗ à ćƗßÏä
á ƙƜƚ
Þ
ƄÞƖß â ćƂƖƂƗç
Ɩ á ćƖÞƖ à ćƖßà ƄÞćƖßß
ÏƛƝƞá ƙƜƚ
Þ
ćƂƖƂƗç
Ɩ á ćƖÞƖ à ćƖßß
ÏƛƝƞáÞ
ćƂƖƂƗç
Ɩ á ćƖß
ÏÞƖ à ćƖßÏá
Þ
ćƂƖƂƗç
Ɩ á ćƖß
ÏƔſƐã±ä (8)r ňƗÏá
Þ
ćƂƖƂƗç
Ɩ á ćƖß
ÏňƖÏ (9)Eq. (7)ᮡ༉ߙđŝ(²)᮹ᇩ⪶ᝅᖒ(ňƗ), ࠦพᄡᙹ(±)᮹ᇩ⪶
ᝅᖒ(ňƖ), ᇩ⪶ᝅᖒ ᱥݍእ(ƂƗîƂƖ)ಽ Ǎᖒࡹᨕ ᯩ݅.
FOA᮹ᱢᬊᮡᯝၹᱢᮝಽࠦพᄡᙹॅಽǍᖒࡽᙹ⦺ᱢ⧉ᙹᨱ
ᱢᬊa܆⦹ḡอ, ⪮ᙹ༉ߙᮥᙹ⦺ᱢ⧉ᙹಽ⢽⩥⦹ʑ۵ᛞḡᦫ݅.
əᯕᮁ۵⪮ᙹ༉⩶ᮡᙹྙ༉⩶, ᙹญ༉⩶, ḡ⩶ᇥᕾ॒᮹ᩍ్
ŝᱶᯕᅖ⧊ᱢᮝಽᯕᨕᲙᯩŁ, ⪮ᙹჵ௭ᨱݡ⦽ḡ⩶ᯙᯱ᪡
zᮡᗭॅ᮹ၹ᮲ᮥᙹ⦺ᱢᮝಽ⢽⩥⦹ʑᨕಖʑভྙᯕ݅. ə్
အಽᅙᩑǍᨱᕽ۵bᄡᙹॅᨱݡ⦽⪮ᙹჵ௭໕ᱢ᮹⫭ȡᇥᕾᮥ
☖⦹ᩍ⧉ᙹෝอु⬥FOAෝᱢᬊ⦹ᩍၝqࠥᇥᕾᮥᙹ⧪⦹ᩡ݅.
Fig. 1ᮡ⪮ᙹჵ௭໕ᱢᨱݡ⦽ᇩ⪶ᝅᖒᗭॅ᮹ၝqࠥᇥᕾᨱ
FOAෝᱢᬊ⦹۵ŝᱶᮥӹ┡ԕ໑əŝᱶᮡ݅ᮭŝz݅. ᬑᖁ, 1) ᄡᙹᨱݡ⦽⪮ᙹჵ௭໕ᱢ᮹ᇥ⡍ෝӹ┡ԕŁ, 2) ⫭ȡᇥᕾᮥ
ᯕᬊ⦽⧉ᙹ᮹⇵ᖙᖁᮥ⇵a⦹Ł, 3) ə⇵ᖙᖁ᮹⧉ᙹᨱݡ⦹ᩍ
FOAෝ ᱢᬊ⦽݅.
3. ݡᔢ⦹ࠥ᪡ᯱഭ
ᅙᩑǍ᮹ݡᔢ⦹ࠥᯙFlatrock vᮡၙǎIndiana ᵝHenry
⋕ᬕ❑ᨱᕽ᯲⦹ᩍColumbusɝᨱᕽDriftwood vŝ⧉̹
East Fork White Riverᨱ⧊ඹ⦹ʑᱥ᧞14 kmᨱÙℱ⮱ෙ݅.
ᅙᩑǍෝ᭥⧕ᖁ┾ࡽFlatrock v᮹⦹ࠥ۵Columbusᇡɝ᮹
᧞4 km᮹Ǎeᯕ໑, ⪮ᙹ᭥༉᮹ෝ᭥⧕ᕽǍ⇶ࡽ⬂݉໕ᮡ11 }ᯕŁ, ⬂݉໕ᔍᯕ᮹⠪ɁeĊᮡ᧞350 mᯕ݅. ੱ⦽, ⬂݉໕᮹
⠪Ɂʙᯕ۵᧞3 kmಽእƱᱢմᮡჵ௭ᬱᮥ⡍⧉⦹Łᯩ݅(Fig.
2).
ᅙᩑǍᨱᕽ⪮ᙹ᭥ෝᔑᱶ⦹ʑ᭥⦹ᩍHEC-RAS᮹⬂݉໕
ᯱഭ۵ၙǎḡḩ᳑ᔍǎ(United States Geological Survey; USGS) ᨱᕽ ᱽŖ⦹۵3 m ⧕ᔢࠥ᮹NED (National Elevation Dataset) DEM (Fig. 2b))ᮝಽᇡ░Ǎ⇶ࡹᨩ݅. DEM᮹ᙹ⠪ၰᙹḢ᪅₉۵
⪮ᙹჵ௭ࠥǍ⇶ᨱᕽၽᔾ⦹۵ᇩ⪶ᝅᖒ᮹đᱶᱢᯙᯕࡽ݅.
ᯕ్⦽ DEM᮹ ᙹ⠪ ၰ ᙹḢ ᪅₉۵ ᕽಽ ᔢššĥa ᯩᮝ໑, ᯝၹᱢᮝಽ ⧕ᔢࠥa ԏᮥᙹಾ ᙹ⠪ ၰ ᙹḢ ᪅₉۵ ⍅ḥ݅.
Sanders (2007)۵⪮ᙹჵ௭ࠥǍ⇶ᨱᯕᬊࡹ۵᪉ᯙᔢ᮹DEM ᮹ ᳦ඹᄥ ᙹḢ᪅₉ᨱ ݡ⦽ ᩑǍෝ ᙹ⧪⦹ᩡᮝ໑, ᅙ ᩑǍᨱᕽ
ᔍᬊ⦽USGSᨱᕽᱽŖ⦽3 m ⧕ᔢࠥ᮹NED DEM᮹Ğᬑ⠪Ɂ
ᱽŒɝ⠙₉(Root Mean Squared Error; RMSE)ෝʑᅙᮝಽ⦽
ᙹḢ᪅₉᮹ჵ᭥۵0.3~0.5 mಽᱽ⦹Łᯩ݅. ᯕᨱ, ᅙ
ᩑǍᨱᕽ⪮ᙹჵ௭໕ᱢᨱݡ⦽ḡ⩶ᯱഭ᪅₉᮹ၝqࠥෝᇥᕾ⦹
ʑ᭥⦽Monte Carlo (MC) ༉᮹ෝᙹ⧪⦹۵ŝᱶᨱᕽḡ⩶ᯱഭ᮹
᪅₉ᨱݡ⦽ྕ᯲᭥ᄡᙹෝ±0.5 m ჵ᭥᮹ᱶȽᇥ⡍ᨱᕽᔾᖒ⦹ᩡ݅.
ੱ⦽, HEC-RAS᮹ๅ}ᄡᙹಽᔍᬊࡹ۵᳑ࠥĥᙹᖅᱶᮥ᭥⧕
30 m ⧕ᔢࠥ᮹2001 NLCD (National Land Cover Data) ☁ḡᯕ ᬊࠥෝᯕᬊ⦹ᩡᮝ໑, Moore (2011)a ᱶญ⦽ 2001 NLCD᮹
ᇥඹᨱෙ᳑ࠥĥᙹsᮥᯕᬊ⦹ᩡ݅(Table 1). Ⅹʑ᳑ࠥĥᙹ
a) Orthography b) DEM Fig. 2. Case Study Area; Flatrock River at Columbus, IN, US
Table 1. Roughness Coefficients for 2001 NLCD (Moore 2011)
2001 NLCD Classification Roughness Coefficients
Sources
Min Mean Max
Open Water 0.025 0.03 0.033 Chow 1959
Developed, Open Space 0.01 0.013 0.16 Calenda et al. 2005
Developed, Low Intensity 0.038 0.05 0.063 Calenda et al. 2005
Developed, Medium Intensity 0.056 0.075 0.094 Calenda et al. 2005
Developed, High Intensity 0.075 0.1 0.125 Calenda et al. 2005
Barren Land 0.025 0.03 0.035 Chow 1959
Deciduous Forest 0.1 0.12 0.16 Chow 1959
Evergreen Forest 0.1 0.12 0.16 Chow 1959
Mixed Forest 0.1 0.12 0.16 Chow 1959
Scrub/Shrub 0.035 0.05 0.07 Chow 1959
Grassland/Herbaceous 0.025 0.03 0.035 Chow 1959
Pasture/Hay 0.03 0.04 0.05 Chow 1959
Cultivated Crops 0.025 0.035 0.045 Chow 1959
Woody Wetlands 0.08 0.1 0.12 Chow 1959
Emergent Herbaceous Wetland 0.075 0.1 0.15 Chow 1959
sᮝಽb☁ḡᯕᬊᄥݡ⢽sᮥᔍᬊ⦹ᩡᮝ໑, ᳑ࠥĥᙹ᮹᪅₉
ჵ᭥۵⢽ŁaእƱᱢԏᮡ☁ḡᯕᬊᨱݡ⦹ᩍChow (1959)᮹
᳑ࠥĥᙹsᨱᕽ↽ݡ·↽ᗭsᨱݡ⦽ݡ⢽s᮹⠪Ɂ₉ᯕᯙ±37.5
%ᮥᔍᬊ⦹ᩡ݅. ᅙᩑǍᨱᕽ༉ु᳑ࠥĥᙹ᮹᪅₉۵±37.5 %᮹
ჵ᭥ᨱᕽɁ॒(uniform) ⪶ශၡࠥᇥ⡍ಽᇡ░ྕ᯲᭥ಽ႒ᇥᮉ᮹
⩶┽aᔾᖒࡹᨕⅩʑ᳑ࠥĥᙹsᨱᱢᬊ⦹ᩍHEC-RASෝᯕᬊ
⦽ ⪮ᙹ᭥༉᮹᮹ ๅ}ᄡᙹಽ ᔍᬊࡹᨩ݅(Table 2). ᩩෝ ॅᨕ,
⦽݉໕ᨱᖙ}᮹Ⅹʑ᳑ࠥĥᙹsᯕ0.3, 0.5, 0.4ಽ⧁ݚࡹŁ
ྕ᯲᭥ᄡᙹa+ 0.2ಽᔾᖒࡹᨩ݅໕, ᳑ࠥĥᙹ۵0.36, 0.6, 0.48ಽ
ᝁࡹᨕ ⪮ᙹ᭥ ༉᮹ෝ ᙹ⧪⦹í ࡽ݅.
ᙹญ༉⩶ᨱᔍᬊࡹ۵ᮁప᳑Õᮡᯝၹᱢᮝಽᙹྙ༉⩶ᯕӹᙹ
᭥-ᮁపšĥᮝಽᇡ░۵݅. ᙹྙ༉⩶ᮝಽᇡ░ᨕḡ۵ᮁప
ᮡ༉⩶᮹ๅ}ᄡᙹ᪡ᯱᩑ⩥ᔢᮥ݉ᙽ⪵⦹۵ŝᱶᨱᕽᮁపᔑᱶ ᨱᯩᨕᕽᇩ⪶ᝅᖒᯕၽᔾ⦽݅. ၹ໕, ᙹ᭥-ᮁపšĥᮡᯱഭ⊂
ᱶŝᱶᨱᕽ᮹᪅₉ӹᯕಆ⩥ᔢ(hysteresis)ᮝಽᇡ░ᇩ⪶ᝅᖒᯕ
ၽᔾ⦽݅. ᅙᩑǍᨱᕽᮁప᳑Õᮥᖁᱶ⦹ʑ᭥⧕ᔍᬊࡽᙹ᭥-ᮁప šĥᮡUSGS Columbusḡᱱ᮹ᮁపš⊂ᗭᨱᕽᱽŖ⦹۵41}
᮹ Ḿᮥ ᯕ۵ ℉ࢱ ᮁపŝ ℉ࢱ ᙹ᭥ᯱഭෝ ᯕᬊ⦹ᩡ݅(Fig.
3). ᅙᩑǍᨱᕽᔍᬊࡽš⊂⪮ᙹ۵2008֥6ᬵ7ᯝᨱၽᔾ⦽
ၙǎᯙॵᦥӹᵝԉᇡḡႊᨱⓑ⦝⧕ෝ᯦⩵100֥ኩࠥᅕ݅
Fig. 3. Stage-Discharge Rating Curve at USGS Flatrock Gauge Station
Table 2. Conditions for Random Generation of Target Variables
Initial (variables) Target Variables estimated by random variable (RV) Min Max Probability Type
Niroughness N = Ni(1 + RV) -0.375 0.375 Uniform
Fi Discharge
F = Exp(a + 1.82 × b) [m3/s]
a = 2.351 + 0.0594 × RV b = 0.830 + 0.0149 × RV
-2.02 2.02 T-distribution
Ei Topography E = Ei + RV [m] -0.5 0.5 Uniform
Table 3. Conditions of Model Variables in Application of the FOA Method
Target variable: N Target variable: F Target variable: E
Cases Conditional Variables (CV)
Cases Conditional Variables (CV)
Cases Conditional Variables (CV)
F E N E F N
N1 Min Min F1 Min Min E1 Min Min
N2 Min Mean F2 Min Mean E2 Min Mean
N3 Min Max F3 Min Max E3 Min Max
N4 Mean Min F4 Mean Min E4 Mean Min
N5 Mean Mean F5 Mean Mean E5 Mean Mean
N6 Mean Max F6 Mean Max E6 Mean Max
N7 Max Min F7 Max Min E7 Max Min
N8 Max Mean F8 Max Mean E8 Max Mean
N9 Max Max F9 Max Max E9 Max Max
ⓑȽ༉᮹⪮ᙹᔍᔢᯕ݅. ⪮ᙹపᮡ1,769 m3/sᯕ໑ᯕভ᮹⪮ᙹ᭥
۵189.61 mᯕ݅. ⮱᳑Õ᮹ၝqࠥᇥᕾᮥ᭥⦽ᇩ⪶ᝅᖒჵ᭥۵
ᙹ᭥ᮁపšĥᨱݡ⦽t-testಽáᱶࡽ±95 %ᨱ᮹⧕đᱶࡹᨩʑ
ভྙᨱ⮱᳑Õ᮹᪅₉۵±95 %ᨱ⧕ݚࡹ۵ჵ᭥ᨱᕽt-ᇥ⡍ಽᇡ
░ ྕ᯲᭥ಽ ᖁ┾ࡹᨕ HEC-RAS᮹ ⮱᳑Õᮝಽ ᔍᬊࡹᨩ݅.
4. Monte Carlo ༉᮹
ၝqࠥ ᇥᕾᮥ ᭥⦽ Monte Carlo ༉᮹۵ HEC-RAS༉⩶ᨱ
ॅᨕi᯦ಆᄡᙹᨱݡ⦽ྕ᯲᭥ᄡᙹෝᔾᖒ⧕⦹໑, ᯕෝ᭥⦹ᩍ
b᯦ಆჵ᭥᪡⪶ශᇥ⡍ෝᖅᱶ⦹ᩍ⦽݅. ᦿᨱᕽᨙɪ⧩ॐᯕ, ᅙᩑǍᨱᕽၝqࠥᇥᕾᮡᖙ}᮹ᄡᙹ(᳑ࠥĥᙹ, ᮁప, ḡ⩶ᯱഭ)
ॅᨱݡ⦹ᩍᙹ⧪ࡹᨩᮝ໑, ྕ᯲᭥ᄡᙹෝ᭥⦽᳑ÕᮡTable 2ᨱ
ᱶญ⦹ᩡ݅. ੱ⦽, ᅙᩑǍ۵⦽ᄡᙹ(ݡᔢᄡᙹ)᮹᪅₉aᯝᱶ⦹
ࠥ݅ෙᄡᙹ(᳑Õᄡᙹ)ॅ᮹᪅₉᪡đ⧊ࡹᨕ⪮ᙹჵ௭ࠥᨱə
᪅₉aᱥݍࡹᨩᮥভ݅ෙᄡᙹॅ᮹᳑Õᨱݡᔢᄡᙹಽᇡ░
⪮ᙹჵ௭ࠥᨱᱥݍࡹ۵ᇩ⪶ᝅᖒ᮹᧲᮹ᄡ⪵ෝ ᔑᱶ⦹ʑ᭥⧕
Table 3ŝzᮡӹญ᪅ෝอॅᨕMonte Carlo ༉᮹ෝᙹ⧪⦹ᩡ
݅. ੱ⦽, ᄡᙹॅ᮹ ݉᭥a ༉ࢱ ݅ʑ ভྙᨱ ᄡᙹॅᨱ ᮹⧕
⪮ᙹჵ௭ࠥᨱᱥݍࡹ۵ᇩ⪶ᝅᖒᮥḢᱲᱢᮝಽእƱᇥᕾ⦹۵ߑ
ྕ₉ᬱ݉᭥ಽᄡ⪹⦹ᩍUPRᮥᔑᱶ⦹ᩍᄡᙹॅ᮹᪅₉ᨱ᮹⧕
ᱥݍࡽ ᇩ⪶ᝅᖒᮥ ᱶపᱢᮝಽ እƱᇥᕾ⦹ᩡ݅.
5. đŝၰŁₑ
⪮ᙹ ༉ߙยŝᱶᨱᕽ ᇩ⪶ᝅᖒ᮹ ᵝ ᯙᯙ ᳑ࠥĥᙹ, ᮁప, ḡ⩶ᯱഭ॒ᖙ}᮹ᄡᙹᨱݡ⦹ᩍၝqࠥᇥᕾᮥᙹ⧪⦹ᩡ݅.
✚⯩ ၝqࠥ ᇥᕾ ŝᱶᨱᕽ ᖙ }᮹ ᄡᙹ aᬕߑ ⦹ӹ۵ ݡᔢ
ᄡᙹaࡹŁ ӹນḡ ࢱ}᮹ ᄡᙹॅᮡ ݡᔢᄡᙹ᮹᪅₉a ⪮ᙹ
ჵ௭ࠥᨱᱥݍࡹ۵ŝᱶᨱᕽᵝᨕḥ᳑Õᮥđᱶ⦹۵᳑Õᄡᙹಽ
(a) Error in Discharge
(b) Error in Roughness
(c) Error in Elevation
Fig. 4. Simulated Flood Inundation Area by Errors Involved in
Table 4. Estimated Uncertainty Propagation Rate by using the FOA Method [km2]
a) Target variable: Discharge (F)
Case Nmin Nmean Nmax
Emin 1.570 0.858 0.475
Emean 1.291 0.739 0.538
Emax 1.054 0.714 0.710
b) Target variable: Roughness (N)
Case Fmin Fmean Fmax
Emin 1.645 0.861 0.494
Emean 1.408 0.774 0.570
Emax 1.184 0.788 0.782
c) Target variable: Elevation (E)
Case Nmin Nmean Nmax
Fmin 2.341 1.623 1.246
Fmean 1.766 1.231 0.965
Łಅࡹᨩ݅. Fig. (4)ᮡӹญ᪅ᄥbᄡᙹ᮹᪅₉ᨱݡ⦽⪮ᙹჵ௭ ᮹໕ᱢ᮹ᄡ⪵ෝᅕᩍᵡ݅. ᮁప᮹Ğᬑ᪅₉a᷾a⧁ᙹಾ⪮ᙹჵ ௭໕ᱢᮡ ᱥℕᱢᮝಽ ᖁ⩶ᱢᯙ ᷾a⇵ᖙෝ ᅕᯕ໑, ᳑ࠥĥᙹ᪡
ᮁప᮹Ğᬑ᳑Õᄡᙹॅᯕ᯲ᮡsᮥaḩভ۵⪮ᙹჵ௭໕ᱢᮡ
እᖁ⩶ᱢᮝಽ᷾a⦹ḡอ᳑Õᄡᙹॅᯕⓑsᮥaḩᙹಾᖁ⩶ᱢ ᯙ᷾a⇵ᖙෝᅕᩡ݅. ᯕᨱݡ⧕ᕽbb⫭ȡᇥᕾᮥ☖⦹ᩍ⇵ᖙᖁ ᨱݡ⦽⧉ᙹෝǍ⇶⦹ᩡŁ, ༉ु⇵ᖙᖁᨱݡ⦽ᔢšĥᙹ۵0.99 ᯕᔢᯕᩡ݅. bݡᔢᄡᙹᄥ᳑Õᄡᙹ᮹ᱥℕ᪅₉ჵ᭥ෝŁಅ⧩ᮥ
ভ ᮁప᮹ ᪅₉ಽ ᯙ⦹ᩍ ၽᔾࡹ۵ ⪮ᙹ ჵ௭໕ᱢ᮹ ჵ᭥۵
1.687~5.385 km2 ᯕ໑, ᳑ࠥĥᙹ᮹ Ğᬑ۵ 1.684~5.394 km2 ಽᔑᱶࡹᨩ݅. ੱ⦽, ḡ⩶ᯱഭᨱݡ⧕ᕽᱥݍࡽᇩ⪶ᝅᖒ᮹ჵ᭥۵
1.778~5.368 km2ᮝಽᔑᱶࡹᨩ݅. ᯕ్⦽đŝಽᇡ░᳑Õᄡᙹ ᮹ᱥℕ᪅₉ჵ᭥ᨱݡ⦹ᩍ᳑ࠥĥᙹa᧞3.71 km2᮹aᰆⓑ
ᇩ⪶ᝅᖒᮥ ᱥݍ ⎑ᮝ໑, ḡ⩶ᯱഭa 3.59 km2᮹ aᰆ ᯲ᮡ
ᇩ⪶ᝅᖒᮥᱥݍ⎑݅. ə్ӹə₉ᯕaๅᬑᱢᨕ᳑Õᄡᙹॅ᮹
ᱥℕ᪅₉ჵ᭥ᨱݡ⦽ᖙᄡᙹॅ᮹᪅₉ॅᮡÑ᮹እ⦽ᇩ⪶ᝅᖒ
ᮥ⪮ᙹჵ௭໕ᱢᨱᱥݍ⦹۵äᮝಽӹ┡ԍ݅. ᳑Õᄡᙹ᮹ᱥℕ᪅
₉ᨱݡ⦽đŝ᪡۵݅íӹญ᪅ᨱ᮹⦽ᖙᇡᱢᯙ᳑Õᄡᙹॅ
ᨱ ݡ⦽ b ᄡᙹॅ᮹ ᪅₉ᨱ ᮹⧕ ᱥݍࡽ ⪮ᙹჵ௭໕ᱢᨱᕽ᮹
ᇩ⪶ᝅᖒᮡⓑ₉ᯕᱱᮥᅕᩡ݅. ᩩෝॅᨕ, ᳑ࠥĥᙹ᪡ᮁప᮹
᪅₉a༉ࢱ↽ᗭᯝভḡ⩶ᯱഭ᮹ ᪅₉ಽᇡ░⪮ᙹჵ௭໕ᱢᨱ
ᱥݍࡽᇩ⪶ᝅᖒᮡ1.778~4.113 km2ಽ᧞2.335 km2ಽaᰆ
ⓑᄡ⪵ෝᅕᩡ݅(Case E1). ၹ໕, ᳑ࠥĥᙹ᮹᪅₉aᵲesᮥ
aḡŁ, ḡ⩶ᯱഭ᮹sᯕ↽ݡ᮹᪅₉ෝaḩভᮁప᮹᪅₉۵
⪮ᙹჵ௭໕ᱢᨱ᧞0.538 km2᮹aᰆ᯲ᮡᇩ⪶ᝅᖒಽᱥݍࡹᨩ݅
(Case F6).
Table 4۵FOAႊჶᮥᯕᬊ⧕ᔑᱶࡽᇩ⪶ᝅᖒᱥݍᮉᮥᅕᩍ ᵡ݅. bݡᔢᄡᙹᄥྕ₉ᬱ݉᭥1ᨱݡ⦽ᇩ⪶ᝅᖒᱥݍᮉᮡ
ᮁప᮹ Ğᬑ 0.475~1.570 km2, ᳑ࠥĥᙹ᮹ Ğᬑ 0.494~1.645 km2,ḡ⩶ᯱഭᨱݡ⦹ᩍ0.955~2.341 km2ಽᔑᱶࡹᨩ݅. ᅙᩑǍ ᨱᕽᔑᱶࡽݡᔢᄡᙹ᮹᪅₉ᨱݡ⦽ᇩ⪶ᝅᖒᱥݍᮉᮡݡᇡᇥ
a) Case E1 b) Case E9 Fig. 5. Comparison of Flood Inundation Maps for Elevation Error
᳑Õᄡᙹ᮹ ᪅₉a ⓑ sᮥ aḩᙹಾ ᯲ᦥḥ݅. ᯕ۵ ⦹ࠥᨱᕽ
᳑Õᄡᙹॅ᮹᪅₉a᷾a⧁ভ☖ᙹ܆(conveyance)ᯕ᷾a⦹í
ࡹŁ, ۹ᨕӽ☖ᙹ܆ᨱᕽݡᔢᄡᙹ᮹ᯝᱶ᪅₉۵ᔢݡᱢᮝಽᱢí
⪮ᙹჵ௭໕ᱢᨱᱥݍࡹʑভྙᯕ݅. ✚⯩, ᮁపᯱഭ᪡᳑ࠥĥᙹ᮹
᪅₉۵ᙹญ༉⩶ԕḡ႑ႊᱶᨱ᮹⧕⪮ᙹ᭥ಽᱥݍࡹḡอ, ੱ
݅ෙ᳑Õᄡᙹᯙḡ⩶ᯱഭ᮹ ᪅₉۵☖ᙹ܆᮹Ⓧʑ᪡ᔢšᨧᯕ
Ḣᱲᱢᮝಽ⪮ᙹ᭥ᨱᱥݍࡽ݅. ə్ӹ↽ݡ᮹sᮥaḡ۵᳑ࠥĥ ᙹa᳑Õᄡᙹಽ᯲ᬊ⦹Łݡᔢᄡᙹaᮁపᯝভ, ੱ݅ෙ᳑Õᄡᙹ ᯙḡ⩶ᯱഭ᮹sᯕ᷾a⧁ᙹಾᇩ⪶ᝅᖒᱥݍᮉᮡ᪅⯩ಅ᷾a⦹
۵༉ᮥᅕᯙ݅. ᯕ᪡እ⦹í↽ݡ᮹᪅₉ෝaḡ۵ᮁపᯕ
᳑Õᄡᙹಽ᯲ᬊ⦹Łݡᔢᄡᙹa᳑ࠥĥᙹᯝĞᬑࠥḡ⩶ᯱഭ᮹
sᯕ᷾a⧁ᙹಾᇩ⪶ᝅᖒᱥݍᮉᯕ᷾a⦽݅. ᯕ۵ᙹญ༉⩶ŝ
ḡ⩶ᇥᕾ॒ᨱ᮹⦽ᅖᰂ⦽ŝᱶ᮹đŝಽᯕzᮡ⩥ᔢᨱݡ⦽
ᬱᯙᮥᦥԕʑ۵ๅᬑᨕಖ݅. ə్ӹᯕॅŖ☖ᱱᮡࢱ}᮹
᳑Õᄡᙹᵲ⦹ӹ۵ḡ⩶ᯱഭᯕ໑, ӹນḡ⦹ӹ᮹᳑Õᄡᙹ۵↽ݡ sᮥaḥ݅۵ᱱᯕ݅. ᳑Õᄡᙹᯙḡ⩶ᯱഭ᪡↽ݡsᮥaḡ۵
ੱ݅ෙ᳑Õᄡᙹ᮹đ⧊ᮡݡᔢᄡᙹ᮹aᰆ᯲ᮡ᪅₉(-0.5)ᨱᕽࠥ
⪮ᙹ᭥a׳ᮡእƱᱢȽ༉aⓑ☖ᙹ܆᳑ÕᮥอॅŁᯕಽᯙ⦹ᩍ
մᮡ⪮ᙹჵ௭໕ᱢ᮹đŝಽᕽ᳑Õᄡᙹ᮹ᄡ⪵ᨱݡ⦽ݡᔢᄡᙹ ᮹ ᯲ᮡ ᪅₉(-0.5)ᨱᕽ ⪮ᙹჵ௭໕ᱢ᮹ ₉ᯕෝ ᵥᩍ ᳑Õᄡᙹ
᪅₉᷾aᨱෙݡᔢᄡᙹ᮹ᇩ⪶ᝅᖒᱥݍᮉᮥ׳ᯝᙹᯩ݅(ᩩ,
Fig. 4ᨱᕽCase F3, F6, F9, N3, N6, N9). ੱ⦽, ᨕਅ✚ᱶᙹ᭥ᨱᕽ
r᯲ᜅí⪮ᙹჵ௭໕ᱢᮥ᷾a┍ᙹᯩ۵ ḡ⩶⩶ᔢᄡ⪵᮹
a܆ᖒᮝಽ ᯙ⧕ ݡᔢᄡᙹ᮹ ᇩ⪶ᝅᖒ ᱥݍᮉᮥ ׳ᯝ ᙹ ᯩ݅.
ḡ⩶ᯱഭ᮹ᇩ⪶ᝅᖒᱥݍᮉᮥŁಅ⧩ᮥভݡᔢᄡᙹa݅ෙ
ᄡᙹᯝĞᬑᅕ݅ ᱥၹᱢᮝಽ əၝqࠥa Ⓧʑ ভྙᨱᅙ ݡᔢ
ᮁᩎ᮹⪮ᙹჵ௭Ǎ⇶ŝᱶᨱᕽᇩ⪶ᝅᖒᮥၽᔾ┅۵ᵝᯙᮡ
ḡ⩶ᯱഭ᮹᪅₉ಽ❱݉ࡽ݅. ੱ⦽, ݡᔢᄡᙹ᮹zᮡ᪅₉ჵ᭥ࠥ
᳑Õᄡᙹॅ᮹Ǎᖒᨱ⪮ᙹჵ௭ࠥᨱᱥݍࡹ۵ᇩ⪶ᝅᖒᱥݍ ᮉᮡⓍíݍḩᙹᯩ݅(Table 3, Fig. 4). Fig. 5۵᳑Õᄡᙹᯙ
ᮁపŝ᳑ࠥĥᙹa↽ᗭsᮥaḩĞᬑ(case E1)᪡↽ݡsᮥaḩ
Ğᬑ(case E9)ᨱᕽḡ⩶ᯱഭ᮹᪅₉aᱥݍࡽ⪮ᙹჵ௭໕ᱢ᮹₉ ᯕෝ ᅕᩍᵡ݅.
6. đು
ᅙ ᩑǍᨱᕽ۵ ၙǎ Indianaᵝ Columbus ɝ Flatrockv (Flatrock ⦹ࠥ)᪡2008֥6ᬵ7ᯝᨱၽᔾ⦽⪮ᙹᔍᔢᨱݡ⦹ᩍ
⪮ᙹჵ௭ࠥǍ⇶ᨱᯩᨕᮁప, ᳑ࠥĥᙹ, ḡ⩶ᯱഭᨱᗮ⧕ᯩ۵
᪅₉a⪮ᙹჵ௭ࠥᨱᱥݍ⦹۵ᇩ⪶ᝅᖒᮥFOA ႊჶᮥᯕᬊ⦹ᩍ
ᇩ⪶ᝅᖒ ᱥݍᮉᮥ ᔑᱶ⦹ᩡ݅. ᅙ ᩑǍෝ ☖⧕ ᨕḥ đುᮡ
݅ᮭŝ z݅.
(1) FOAෝᱢᬊ⦹ʑ᭥⧕ᖙ}᮹᯦ಆᄡᙹෝ⡍⧉⦹۵⧉ᙹෝ
Ǎ⇶⦹۵ߑᨕಅᬡᯕᯩʑভྙᨱb᯦ಆᄡᙹᨱݡ⦽⪮ᙹჵ ௭໕ᱢ᮹⧉ᙹෝ⫭ȡᇥᕾᮥ☖⦹ᩍǍ⇶⦹ᩡŁ, ᯕভ༉ु
⧉ᙹᨱݡ⦽ᔢšĥᙹ۵0.99 ᯕᔢ᮹sᮥᅕᩡ݅. ⪮ᙹჵ௭໕ ᱢᨱݡ⦽bݡᔢᄡᙹ᮹᪅₉۵᳑Õᄡᙹ᮹༉ु᪅₉ჵ᭥ᨱ
ݡ⦹ᩍๅᬑእ⦹íᇩ⪶ᝅᖒᮥᱥݍ⎑݅. ə్ӹbӹ ญ᪅ෝ Łಅ⧩ᮥ ভ ݡᔢᄡᙹ᮹ ᪅₉۵ ᳑Õᄡᙹ᮹ Ǎᖒᨱ
ๅᬑ݅í⪮ᙹჵ௭໕ᱢ᮹ᇩ⪶ᝅᖒᮥၽᔾ⎑ᮝ໑,
᳑Õᄡᙹॅᯕ↽ᗭᯝভḡ⩶ᯱഭ᮹᪅₉aaᰆⓑᇩ⪶ᝅᖒ
ᮥ ᱥݍ⎑݅.
(2) ᅙᩑǍෝ☖⦹ᩍ᳑Õᄡᙹॅ᮹ᩢ⨆ᨱݡᔢᄡᙹ᮹᪅₉ a݅í⪮ᙹჵ௭໕ᱢᨱᱥݍࡹ۵äᯕ⪶ᯙࡹᨩ݅. ᇩ⪶ᝅ ᖒᱥݍᮉᮡݡᇡᇥ᳑Õᄡᙹॅ᮹᪅₉a᯲ᮥᙹಾ᷾a⦹ᩡᮝ ໑᳑Õᄡᙹॅ᮹ᩢ⨆ᨱ᮹⧕ǍᖒࡽⅩʑ☖ᙹ܆Ⓧʑ᮹ᩢ⨆
᮹Ⓧʑaⓕᙹಾݡᔢᄡᙹ᮹ᇩ⪶ᝅᖒᱥݍᮉᮡ᯲ᦥᲭ݅.
ݡᔢᄡᙹ᮹ᇩ⪶ᝅᖒ᮹ᱥݍᮉᮥእƱ⧩ᮥভ݅ෙᄡᙹॅᨱ
እ⧕ⓑၝqࠥෝaḡ۵ḡ⩶ᯱഭaᅙᩑǍᨱᕽ⪮ᙹჵ௭
ࠥᨱaᰆฯᮡᇩ⪶ᝅᖒᮥᱥݍ⦹۵ᯙᯱಽ❱ࡹᨩ݅. ᯕ۵
ᇩ⪶ᝅᖒᱥݍᮉอŁಅ⧩ᮥভᅙݡᔢḡᩎᨱᕽ⪮ᙹჵ௭ࠥ᮹
ᱶ⪶ᖒᮥ⨆ᔢ┅ʑ᭥⧕ᕽḡ⩶ᯱഭ᮹ᇩ⪶ᝅᖒᗭෝ}ᖁ
⪚ᮡᱽÑ⦹۵ߑaᰆⓑᬑᖁᙽ᭥ෝࢱᨕ⦽݅۵äᮥ᮹ၙ
⦽݅.
ᅙᩑǍ۵⪮ᙹ᭥⨹šญᨱᕽaᰆʑᅙᱢᮝಽᔍᬊࡹ۵⪮ᙹჵ ௭ࠥෝǍ⇶⦹۵ŝᱶᨱᕽၽᔾ⧁ᙹᯩ۵ᇩ⪶ᝅᖒaᬕߑᮁప,
᳑ࠥĥᙹ, ḡ⩶ᯱഭ॒ᨱᗮ⧕ᯩ۵᪅₉ॅᮥŁಅ⦹ᩍᯕॅᯕ⪮ᙹ ჵ௭ࠥᨱᱥݍ⦹۵ᇩ⪶ᝅᖒᨱݡ⦽ၝqࠥෝFOAႊჶᮥᯕᬊ⦹
ᩍᇥᕾ⦹ᩡ݅. ᅙᩑǍᨱᕽࠥ⇽ࡽđŝ۵⪮ᙹჵ௭ࠥǍ⇶ŝᱶᨱ ᕽ ᇩ⪶ᝅᖒ᮹ ᗭෝ ᱽÑ⦹ʑ ᭥⦽ ❱݉ᮥ ԕญ۵ ŝᱶᨱᕽ
ᬑᖁᙽ᭥ෝࢱᨕ⬉ᮉᱢᮝಽ ⪮ᙹჵ௭ࠥ᮹ᱶ⪶ࠥෝ}ᖁ⧁ᙹ
ᯩ۵ɝÑෝᱽŖ⦹ᩡ݅. ə్ӹᅕ݅݅᧲⦽ݡᔢᮁᩎᨱ᮹ᱢᬊŝ
ᇩ⪶ᝅᖒ᮹݅ෙᗭॅᮥŁಅ⦽݅໕⬉ᮉᱢ⪮ᙹ᭥⨹šญᨱᯩ
ᨕᅕ݅ᮁᬊ⦽ᯱഭಽᔍᬊࢁᙹᯩ݅Łᔾbࡽ݅. ⇵⬥bᗭ᮹
ᇩ⪶ᝅᖒᮥᱽÑ⦹Ñӹ}ᖁ⦹۵ߑ ḡᇩࡹ۵እᬊᮥᔑᱶ⧁ᙹ
ᯩ݅໕ ᅕ݅ Ğᱽᱢᯙ ⪮ᙹ᭥⨹šญᨱ ⓑ ʑᩍෝ ⧁ äᯕ݅.
qᔍ᮹ɡ
ᅙᩑǍ۵ǎ☁⧕᧲ᇡa⇽ᩑ⦹Ł⦽ǎÕᖅƱ☖ʑᚁ⠪aᬱᨱᕽ
᭥┢⧪⦽Õᖅʑᚁ⩢ᝁᔍᨦ(08ʑᚁ⩢ᝁF01)ᨱ᮹⦽₉ᖙݡ⪮
ᙹႊᨕʑᚁ}ၽ ᩑǍ݉᮹ ᩑǍእ ḡᬱᨱ ᮹⧕ ᙹ⧪ࡹᨩܩ݅.
References
Aronica, G., Bates, P. D. and Horritt, M. S. (2002). “Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE.” Hydrological Processes, Vol.
16, pp. 2001-2016.
Bales, J. D. and Wagner, C. R. (2009). “Sources of uncertainty in flood inundation maps.” J. Flood Risk Manage, Vol. 2, No. 2, pp.
139-147.
Bates, B. C. and Towntey, L. R. (1988). “Nonlinear, discrete flood event models, 1. Bayesian estimation of parameters,” J. Hydrol, Vol. 99, pp. 61-76.
Bates, P. D., Horritt, M. S., Aronica, G. and Beven, K. J. (2004).
“Bayesian updating of flood inundation likelihoods conditioned on flood extent data.” Hydrol. Process, Vol. 18, pp. 3347-3370.
Bates, P. D., Marks, K. J. and Horritt, M. S. (2003). “Optimal use of high-resolution topographic data in flood inundation models.”
Hydrolog. Process, Vol. 17, No. 3, pp. 537-557.
Benjamin, J. R. and Cornell, C. A. (1970). Probability, statistics and decision making for civil engineers. McGraw-Hill, New York, N.Y.
Blumberg, A. F. and Georgas, N. (2008). “Quantifying uncertainty in estuarine and coastal ocean circulation modeling.” J. Hydr.
Eng, Vol. 134, No. 4, pp. 403-415.
Herschey, R. W. (2002). “The uncertainty in a current meter measurement.” Flow Measur Instru, Vol. 13, pp. 281-284.
Hine, D. J. and Hall, J. W. (2006). “Convex analysis of flood inundation model uncertainties and info-gap flood management decisions.” 05, Proc. 9th Int. Symp. on Stochastic Hydraulics, Nijmegen, Netherlands.
Johnson, P. A. and Rinaldi, M. (1998). Uncertainty in stream channel restoration. Uncertainty modeling and analysis in civil engineering, B. M. Ayyub, ed., CRC Press, Boca Raton, Fla, pp. 425-437.
Jung, Y. and Merwade, V. (2012). “Uncertainty quantification in flood inundation mapping using generalized likelihood uncertainty estimate and sensitivity analysis.” J. Hydrol. Eng, Vol. 17, No. 4, pp. 507-520.
Lei, J. and Schilling, W. (1994). “Parameter uncertainty propagation analysis for urban rainfall runoff modeling.” Water Science and Technology, Vol. 29, No. 1-2, pp. 145-154.
Liu, J., Tian, F. and Huang, Q. (2001). “A risk analyzing method for reservoir flood control.” Hydrology, Vol. 21, No. 3, pp. 1-3.
Melching, C. S. (1992). “An improved first-order reliability approach for assessing uncertainties in hydrologic modeling.” Journal of Hydrology, Vol. 132, pp. 157-177.
Merwade, V., Olivera, F., Arabi, M. and Edleman, S. (2008).
“Uncertainty in flood inundation mapping-Current issues and future directions.” J. Hydrol. Eng, Vol. 13, No. 7, pp. 608-620.
Milly, P. C. D., Wetherald, R. T., Dunne, K. A. and Delworth, T. L.
(2002) “Increasing risk of great floods in a changing climate.”
Nature, Vol. 415, No. 31, pp. 514-517.
Moore, M. R. (2011). Development of a high-resolution 1D/2D
coupled flood simulation of Charles city, Iowa, Master's Thesis, University of Iowa.
Omer, C. R., Nelson, E. J. and Zundel, A. K. (2003). “Impact of varied data resolution on hydraulic modeling and floodplain delineation.” J. Am. Water Resour. Assoc, Vol. 39, No. 2, pp.
467-475.
Pilotti, M., Maranzoni, A., Tomirotti, M. and Valerio, G. (2011).
“1923 Gleno dam break: Case study and numerical modeling.” J.
Hydraul. Eng, Vol. 137, No. 4, pp. 480-492.
Purvis, M., Bates, P. D. and Hayes, C. M. (2008). “A probabilistic methodology to estimate future coastal flood risk due to sea level rise.” Coastal Eng. Vol. 55, pp. 1062-1073.
Romanowicz, R. J., Kiczko, A. and Osuch, M. (2012). “Influence of model reduction on uncertainty of flood inundation predictions.”
EGU General Assembly Conference Abstracts, Vol. 14, p. 4688.
Sanders, B. (2007). “Evaluation of on-line DEMs for flood inundation modeling.” Advances in Water Resources, Vol. 30, No. 8, pp.
1831-1843.
Sitar, N., Cawfield, J. D. and Der Kiureghian, A. (1987). “First-order reliability approach to stochastic analysis of subsurface flow and contaminant transport.” Water Resour. Res, Vol. 23, pp. 794-804.
Vazquez, R. F., Feyen, L., Feyen, J. and Refsgaard, J. C. (2002).
“Effect of grid size on effective parameters and model performance of the MIKE-SHE code.” Hydrolog. Process, Vol. 16, No. 2, pp.
355-372.
Wang, Y. and Zheng, T. (2005). “Comparison of digital elevation models and understanding of their impact on the flood extent mapping on a coastal floodplain of North Carolina.” Nat. Hazards Rev, Vol. 6, No. 1, pp. 34-40.
Weichel, T., Pappenberger, F. and Schulz, K. (2007). “Sensitivity analysis framework.” Adv. Geosci, Vol. 11, pp. 31-36.
Zhao, X., Shen, Z., Xiong, M. and Qi, J. (2011). “Key uncertainty sources analysis of water quality model using the first order error method.” Int. J. Environ. Sci. Tech, Vol. 8, No. 1, pp. 137-148.
