Development of Daily Rainfall Simulation Model Based on Homogeneous Hidden Markov Chain

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Received April 16, 2013/ revised June 11, 2013/ accepted July 17, 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵ǤͷǤͳͺ͸ͳ

ǤǤǤ

ᦗ⾆⛯#Hidden Markov Chain ⁦㯓ⴂ#ⴲⱧ㬚#ⴺᇓ⟖ᶇ#⁦ⴖᏮ≓#ᇚ⇚

֫෮෉ȵ׌೾୨ȵจজฅȵ׌೾૽

Kwon, Hyun-Han, Kim, Tae Jeong, Hwang, Seok-Hwan, Kim, Tae-Woong****

Development of Daily Rainfall Simulation Model Based on Homogeneous Hidden Markov Chain

ABSTRACT

A climate change-driven increased hydrological variability has been widely acknowledged over the past decades. In this regards, rainfall simulation techniques are being applied in many countries to consider the increased variability. This study proposed a Homogeneous Hidden Markov Chain(HMM) designed to recognize rather complex patterns of rainfall with discrete hidden states and underlying distribution characteristics via mixture probability density function. The proposed approach was applied to Seoul and Jeonju station to verify model’s performance. Statistical moments(e.g. mean, variance, skewness and kurtosis) derived by daily and seasonal rainfall were compared with observation. It was found that the proposed HMM showed better performance in terms of reproducing underlying distribution characteristics. Especially, the HMM was much better than the existing Markov Chain model in reproducing extremes. In this regard, the proposed HMM could be used to evaluate a long-term runoff and design flood as inputs.

Key words : Markov chain model, Homogeneous, Hidden markov chain model, Precipitation

Ⅹಾ

↽ɝʑ⬥ᄡ⪵ᩢ⨆ᮝಽᯙ⧕ᙹྙᄡ࠺ᖒᯕⓍí᷾aࡹŁᯩᮝ໑ᯕ్⦽ᄡ࠺ᖒᮥŁಅ⦹ʑ᭥⦽ႊᦩᮝಽᕽvᙹప༉᮹ၽᔾʑჶᨱݡ⦽ᵲ

᫵ᖒᯕݡࢱࡹŁᯩ݅. ᅙᩑǍᨱᕽ۵ᅖᰂ⦽vᙹၽᔾ➉▕ᮥᯙḡ⦹Łvᙹప᮹݅᧲⦽ᇥ⡍✚ᖒᮥŁಅ⧁ᙹᯩ۵⪝⧊ᇥ⡍ෝᯕᬊ⦽࠺ḩᖒ

Hidden Markov Chain(HMM) ༉⩶ᮥᱽᦩ⦹ᩡ݅. HMM ༉⩶᮹}ᖁ⬉ŝෝá᷾⦹ʑ᭥⧕ᕽʑ᳕Markov Chain ༉⩶ŝእƱ⦹ᩡᮝ໑

ᕽᬙš⊂ᗭၰᱥᵝš⊂ᗭෝݡᔢᮝಽᩑǍෝḥ⧪⦹ᩡ݅. ĥᱩvᙹపၰᯝvᙹప॒݅᧲⦽᜽eȽ༉ᨱᕽ༉⩶᮹ᱢ⧊ᖒᮥ⠪a⦹ʑ᭥⧕ᕽ

⃽ᯕ⪶ශ, ⠪Ɂ, ᇥᔑ, ᪽łࠥၰ℉ᩩ॒ࠥᮥእƱ⦹ᩡᮝ໑HMM ༉⩶ᯕʑ᳕Markov Chain ༉⩶ᨱእ⧕ᕽ}ᖁࡽ༉᮹܆ಆᮥ⪶ᯙ⧁ᙹᯩ

ᨩ݅. ✚⯩, HMM ༉⩶ᮡɚ⊹vᙹపᮥᰍ⩥⦹۵ߑᯩᨕᕽʑ᳕Markov Chain ༉⩶ᨱእ⧕ᕽᬵ॒⦽༉᮹܆ಆᮥᅕᩍᵝᨩ݅. ᯕ్⦽ᱱᨱᕽ

ᰆʑᮁ⇽పၰ⪶ශ⪮ᙹప॒ᮥᔑᱶ⦹ʑ᭥⦽᯦ಆᯱഭಽ⪽ᬊᯕ∊ᇥ⯩a܆⧁äᮝಽ❱݉ࡽ݅.

áᔪᨕ Markov chain ༉⩶, ࠺ḩᖒ, Hidden markov chain ༉⩶, vᙹ

1. ᕽು

↽ɝʑᔢᄡ࠺ᖒ᷾aၰʑ⬥ᄡ⪵ᩢ⨆ᮝಽᯙ⧕ᙹྙᄡ࠺ᖒᯕⓍí᷾aࡹŁᯩᮝ໑ᯕ్⦽ᄡ࠺ᖒᮥŁಅ⦹ʑ᭥⦽ႊᦩᮝಽᕽ

vᙹప༉᮹ၽᔾʑჶᨱݡ⦽ᵲ᫵ᖒᯕݡࢱࡹŁᯩ݅. ᙹྙᄡ࠺ᖒᮝಽᯙ⧕ၽᔾ⦹۵ᇩ⪶ᝅᖒᨱ⬉ŝᱢᮝಽݡ᮲⦹Łᝁ഑ᖒᯩ۵

Ύ

սėॡ

(2)

ᙹŖǍ᳑ྜྷᖅĥၰᙹᯱᬱĥ⫮ᮥᙹพ⦹۵ߑᯩᨕᕽʑᅙᱢᮝಽ

᫵Ǎࡹ۵ᔍ⧎ᮡᰆʑe᮹ᙹྙᯱഭ⪶ᅕ௝⧁ᙹᯩ݅. ↽ɝᙹᯱᬱ ᇥ᧝ᨱᕽvᙹ༉᮹ʑჶᮡ݅᧲⦽༊ᱢᮝಽ⪽ᬊࡹŁᯩᮝ໑ᯝၹ ᱢᮝಽᯝvᙹపᮥ༉᮹⦹۵ᯕᮁ۵ᔢݡᱢᮝಽṈᮡᯱഭᩑ⦽ᮥ

w۵ᙹྙᯱഭĥᩕ᮹☖ĥᱢᯙ✚ᖒᮥŁಅ⦹ᩍᰆʑe༉᮹⧉ᮝ ಽ៉, ᰆʑᱢᯙ༊ᱢᮥaḡŁᙹ⧪ࡹ۵ᙹᯱᬱĥ⫮ᙹพၰᇩ⪶ᝅ ᖒᮥ ၹᩢ⦽ ⠪aෝ ᭥⧉ᯕ݅. ə్ӹ ᬑญӹ௝ෝ ⡍⧉⦽ ᩍ్

ӹ௝ᨱᕽ۵∊ᇥ⦽ᙹྙᯱഭ⪶ᅕaᨕಖʑভྙᨱ☖ĥᱢᯙႊჶ

ᮥ᯦ࠥ⦹ᩍᯱഭෝ⪶∊⦹Łᯕෝ☖⦹ᩍᙹྙᄡ࠺ᖒᮥ⠪a⧁

ᙹᯩ۵ႊᦩᯕᯝၹᱢᮝಽ₥┾ࡹŁᯩ݅. ✚⯩, ↽ɝࠥ᜽⪵᪡

ᔑᨦ⪵ಽᯙ⦽⪵ᕾᩑഭ᮹ᔍᬊᯕɪ᷾⦹໕ᕽḡǍ᪉ӽ⪵ಽʑᯙ

⦹۵ʑ⬥ᄡ⪵aӹ┡ӹŁᯩᮝ໑ᯕ᪡޵ᇩᨕᨹܩى᪡௝ܩԱ

॒᮹ݡȽ༉ʑᔢᄡ࠺ᖒᯕӹ┡ӹŁᯩ݅. ᯕ్⦽ᱱᮥqᦩ⦹ᩍ

ᙹᯱᬱĥ⫮ᙹพ᜽ၽᱥࡽ⧕ᕾʑჶᮥ☖⦹ᩍᙹྙᯱഭෝ⪶∊⦹

Łᯕෝᯕᬊ⦹ᩍᙹྙʑᔢ⦺ᱢᄡ࠺ᖒᮥ⠪a⦹Łᯱ⦹۵ᩑǍa

⪽ၽ⦹í ḥ⧪ࡹŁ ᯩ݅.

vᙹ༉᮹ʑჶᮡๅ}ᄡᙹ᮹᜽eᱢᄡ࠺ᖒၰๅ}ᄡᙹ᮹⇵ᱶ

ႊჶᨱ঑௝Ǎᇥ⧁ᙹᯩ݅. ℌṙ, ๅ}ᄡᙹᨱ᜽eᱢᄡ࠺ᖒ᮹

Łಅ ᩍᇡᨱ ঑௝ ࠺ḩᖒ ༉⩶ŝ እ࠺ḩᖒ ༉⩶ᮝಽ Ǎᇥࡽ݅.

༉⩶ᄥಽᱶญ⦹໕࠺ḩᖒ༉⩶ᮡŝÑ᮹☖ĥᱢ✚ᖒᯕၙ௹ᨱࠥ

ᮁḡࡽ݅۵aᱶᮥᵲᝍᮝಽvᙹ༉᮹ෝ᭥⦽ๅ}ᄡᙹॅᯕŁᱶ

ࡹᨕᔍᬊࡽ݅. ၹ໕እ࠺ḩᖒ༉⩶ᮡ࠺ᩎ⦺ᱢ(dynamic) ⩶┽ෝ

aḡ໑᜽eᨱ঑௝vᙹ༉᮹ෝ᭥⦽ๅ}ᄡᙹॅᯕᄡ⪵⦹íࡹ໑

ʑ⬥ᄡ⪵ᩑǍෝ᭥⧕ᕽᔍᬊࡹ۵Downscaling ʑჶᯕݡ⢽ᱢᯙ

እ࠺ḩᖒ vᙹ༉᮹ʑჶᯕ௝ ⧁ ᙹ ᯩ݅. ↽ɝ ʑ⬥ᄡ⪵ᨱ ঑ෙ

ᙹᯱᬱ᮹ᩢ⨆⠪aෝ᭥⦽Downscaling ʑჶ᮹ၽᱥၰᱢᬊᯕ

ǎԕ᫙ᱢᮝಽๅᬑ⪽ၽ⦹íᯕ൉ᨕḡŁᯩ݅(ǭ⩥⦽॒, 2009).

ࢹṙ, ๅ}ᄡᙹ᮹⇵ᱶႊჶᨱ঑௝ๅ}ᄡᙹᱢႊჶŝእๅ}ᄡᙹ ᱢႊჶᮝಽӹ٭ᙹᯩ݅. ᯝၹᱢᯙMarkov Chain ༉⩶ᮡ⃽ᯕ⪶ශ

⧪಍ᮥ☖⦹ᩍvᙹ᪡ྕvᙹ॒᮹vᙹၽᔾ(rainfall occurrence)

➉▕ᮥ ༉᮹⦽ ⬥ vᙹప(rainfall amount)ᮥ ✚ᱶ ⪶ශᇥ⡍ಽ

aᱶ⦹ᩍvᙹపᮥ༉᮹ၽᔾ᜽┅۵ႊჶᮥᔍᬊ⦹ᩡ݅. ၹ໕እๅ }ᄡᙹᱢႊჶᮡ⃽ᯕ⪶ශᐱอᦥܩ௝vᙹపᮥ༉᮹⦹۵ߑᯩᨕ ᕽ✚ᱶ⪶ශᇥ⡍⩶᮹aᱶᨧᯕᯱഭᯱℕ᮹ᇥ⡍✚ᖒᮥ⧖ၡࠥ⧉

ᙹ(kernel density function)ෝ☖⧕ࠥ⇽⦹۵ႊᦩᮝಽᕽvᙹ᮹

☖ĥᱢ ✚ᖒᮥ ᅕ݅ ⩥ᝅᱢᮝಽ ༉᮹⧁ ᙹ ᯩ۵ ᰆᱱᯕ ᯩ݅.

ᯝvᙹపᮥ༉᮹⦹۵ߑᯩᨕᕽvᙹĥᩕ᮹݉ʑeʑᨖ(memory)

ᮥ⪽ᬊ⦽ 2-State 1₉ Markov Chain༉⩶ᯕ aᰆ ᯝၹᱢᮝಽ

ᔍᬊࡽ݅. ᩍʑᕽ, ⃽ᯕ⪶ශᮡ vᙹ᮹ ၽᔾᮥ ཹᔍ⦹ʑ ᭥⧕ᕽ

ᯕᬊࡹ໑vᙹపᮡᵝಽqษᇥ⡍(gamma distribution), ḡᙹᇥ⡍

(exponential distribution) ॒ᨱ᮹⧕ᕽ༉᮹ࡽ݅. Katz(1996)۵

ʑ᳕Richardson ༉⩶᮹☖ĥᱢ✚ᖒᮥeఖ⪵⦹Łๅ}ᄡᙹ᮹

ᄡ࠺ᖒᮥŁಅ⦹ᩍvᙹపᮥ༉᮹⦹۵༉⩶ᮥᱽᦩ⦹ᩡ݅. Wilks (1992)۵࠺ᯝ⦽}ֱᮝಽᕽvᙹపᮥ༉᮹⦹ʑ᭥⦽ᇥ⡍⩶ᮝಽ

ḡᙹᇥ⡍ݡᝁᨱqษᇥ⡍ෝ⪽ᬊ⦹ᩍʑ⬥ᄡ⪵ᩢ⨆ᨱ঑ෙvᙹ ప᮹ᄡ࠺ᖒᮥ⠪a⦹ᩡ݅. ᩍʑᕽ, ʑ⬥ᄡ⪵ᨱ঑ෙๅ}ᄡᙹ᮹

ᄡ࠺ᖒᮥŁಅ⦹ʑ᭥⧕ᕽₙ᳑ʑe(baseline climate)ᮥᵲᝍᮝಽ

⇵ᱶࡽእᮉᮥᬵ݉᭥(monthly)ಽๅ}ᄡᙹᨱၹᩢ⧉ᮝಽ៉ʑ⬥

ᄡ⪵ᩢ⨆ᮥŁಅ⦹ᩡ݅. ᷪ, ๅᬵ⩥ᰍʑ⬥᳑Õᮥʑᵡᮝಽၙ௹

ၽᔾ⧁ʑ⬥᳑Õᮥ⠪Ɂŝᇥᔑᮥ᳑ᱶ⦹ᩍ ၙ௹᮹ᯝvᙹపᮥ

⇵ᱶ⦹ᩡ݅.

ᯕ᪡zᮡᯝvᙹప༉᮹đŝෝ☖⦹ᩍྜྷᙹḡᇥᕾ॒ᰆʑe᮹

ᙹྙ⦺ᱢᄡ࠺ᖒᮥ⠪a⦹ʑ᭥⧕ᕽ۵ᯝၹᱢᮝಽᦺᔢት⩶┽᮹

ᯝvᙹపᯱഭa᯦ಆᯱഭಽ⪽ᬊࡹíࡹ໑, 2-State 1₉Markov Chain ༉⩶ᯕ ǎԕ᫙ᨱᕽ ᵝಽ ᯕᬊࡹŁ ᯩ݅. ʑ᳕ ᙹྙᯱഭ

⪶∊ႊჶᮝಽᕽᯝvᙹᯱഭၰᙹྙᯱഭ᮹༉᮹ၽᔾੱ۵ᅕ᪥ᮥ

᭥⧕ᖁ⩶(linear) ੱ۵݅ᵲ⫭ȡႊᱶ᜾(regression equation)ᯕ

ᯕᬊࡹᨩ݅(⨩ᵡ⧪, 1997). Markov Chain ᯕುᨱ᮹⦽vᙹప༉

᮹ၽᔾᮥᯕᬊ⦹ᩍvᙹపᮥ⪶∊⬥ᯕෝvᬑ-ᮁ⇽༉⩶ᨱᯕᬊ⦹

ʑࠥ⦹ᩡ݅. ᯕ₞⬩॒(1995)ᮡ⫭ȡᇥᕾŝᵝᖒᇥᇥᕾᮥᯕᬊ⦹

ᩍ đ⊂ࡽ ᬵvᙹప ᯱഭෝ ᅕ᪥⦹۵ߑ Markov Chain ༉⩶ᮥ

ᯕᬊ⦹ᩡ݅. ʡᄲ᜾॒(1999)ᮡᯝvᬑప༉᮹ၽᔾᮥ☖⦽iᙹᮁ

పĥᩕ᮹ᔑᱶၰኩࠥᇥᕾᩑǍෝᙹ⧪⦹ᩡᮝ໑, ᱶᩢ⬩॒(2005)

ᮡʑ᳕2-State 1₉Markov Chain ༉⩶ᮥᯕᬊ⦹ᩍ⇵ᱶࡽᯝvᙹ పᯱഭෝNWC-PC ༉⩶᮹᯦ಆᯱഭಽ ⪽ᬊ⦹ᩍr⃽ᮁᩎᨱ

iᙹᮁపᨱ঑ෙ⦥᫵ᮁపᮥᔑᱶ⦹ᩡ݅. ੱ⦽ǭ⩥⦽॒(2011)ᮡ

ᇩᩑᗮKernel-Pareto ᇥ⡍ෝᯕᬊ⦽ᯝvᙹప༉᮹ʑჶᮥ}ၽ⦹

ᩍ ⦽vᮁᩎᨱ ᱢᬊ⦽ၵ ᯩ݅. ੱ⦽ ǭ⩥⦽ ॒(2013)ᮡ ᇩᩑᗮ

Kernel-Pareto ᇥ⡍ෝᯕᬊ⦽݅ḡᱱvᙹ༉᮹ʑჶŝBayesian HEC-1 ༉⩶ᮥ ᩑĥ⦹ᩍ ݡℎݱ ᮁᩎᨱ ᱢᬊ⦽ ၵ ᯩ݅.

ʑ᳕Markov Chainᮥᔍᬊ⦽ᯝvᙹ༉᮹ʑჶᮡš⊂ࡽvᙹ᜽

ĥᩕ᮹➉▕ᮥ༉⩶⪵⦹۵ߑᯩᨕᕽᝅᱽvᙹ✚ᖒᮥ᪽ł⦹۵

⩥ᔢᯕᯩ݅. ᯝvᙹෝ༉᮹⦹۵ߑᯩᨕᕽ↽ɝ᮹ᵝࡽšᝍᔍ۵

vᙹၰྕvᙹᯝᮥ✚ᱶᯝʑᔢ┽(weather state)ෝ☖⧕ཹᔍ⦹ʑ

᭥⧕ᕽ᳦šʑ⬥⦺ᱢݡʑ➉▕ᮥŁಅ⧁ᙹᯩ۵༉⩶ᮥǍᖒ⦹۵

äᯕ݅. ᯕ్⦽ᱱᮥŁಅ⦹ᩍᯝʑᔢ┽ෝŁಅ⦽vᙹ༉᮹ʑჶ᮹

}ၽᯕ ᯕ൉ᨕḡŁ ᯩ݅(Hughes and Guttorp, 1994; Bellone et al., 2000; Kwon et al., 2009). ᅙ ᩑǍᨱᕽ۵ ᯝʑᔢ┽ෝ

Łಅ⦹Łbᯝʑᔢ┽ᄥಽ⪝⧊ᇥ⡍(mixture distribution) ⩶┽᮹

⪶ශᇥ⡍ෝ ᱢᬊ⧁ ᙹ ᯩ۵ ᯝvᙹ ༉᮹ʑჶᮥ }ၽ⦹ᩡ݅.

ᅙᩑǍᨱᕽᯝʑᔢ┽۵ᮡܪᔢ┽(hidden state)᮹⩶┽ෝaḡ ۵äᮝಽŁಅ⦹ᩡᮝ໑ᮡܪᔢ┽ᦩᨱᕽ᮹ ⃽ᯕ⪶ශᮡ᜽eᨱ

঑௝ᄡ⪵⦹ḡᦫ۵äᮝಽaᱶ⦹ᩡ݅. ᷪ, ᜽eᨱ঑ෙ⃽ᯕ⪶ශ

ၰMixtureᇥ⡍᮹ᄡ࠺ᖒᮡŁಅ⦹ḡᦫ۵࠺ḩᖒHidden Markov

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Chain(HMM) ༉⩶ᮥ}ၽ⦹ᩡ݅. HMM ༉⩶ᮡᮡܪᔢ┽ษ݅

᳑Õᇡ⪶ශᇥ⡍ෝᇡᩍ⦹Łᯕॅ᳑Õᇡ⪶ශᇥ⡍ಽᇡ░ᯝvᙹ

ෝ ༉᮹⦹۵ ႊჶᮝಽ ᬑญӹ௝᪡ zᯕ ĥᱩᨱ ঑௝ vᙹၽᔾ

✚ᖒᯕᅖᰂ⦽Ğᬑᨱᱢ⧊⦽ႊჶᮝಽ⪽ᬊᯕa܆⦹݅. HMM

༉⩶ᮡ 1960֥ݡ ᮭᖒ⃹ญෝ ᭥⧕ ᯕᬊࡹʑ ᜽᯲⧩݅. Ⅹʑ᮹

HMMᮡݡᇡᇥᮭᖒᇥ᧝ᨱǎ⦽ࡹᨕᔍᬊࡹᨩᮝӹᙹྙ⦺ᇥ᧝ᨱ ᕽ۵HMM ༉⩶ᮡၙǎᬭᝒ▕ḡᩎ᮹vᙹၽᔾᮥ༉ߙย⦹ʑ

᭥⧕ᕽ⃹ᮭᯕᬊࡹᨩ݅(Hughes and Guttorp, 1994). Bengioet al.(1995)۵ᮡܪᔢ┽⃽ᯕ⪶ශ᮹࠺ᱢᄡ⪵ᐱอᦥܩ௝⇽ಆᯱഭ a ᮡܪᔢ┽ၰ ᯦ಆ ᯱഭᨱ᳑Õᇡಽ ᄡ⪵⦹۵ äᮥ⨩ᬊ⦹۵

᯦⇽ಆHMM ༉⩶ᮥᱽᦩ⦹ᩡ݅. Bellone et al.(2000)ᮡvᙹప

ᮥ༉ߙย⦹ʑ᭥⧕ᕽHMM༉⩶ᮥᯕᬊ⦹ᩡᮝ໑vᙹపᮥ༉᮹⦹

ʑ᭥⦽⪶ශᇥ⡍⩶ᮝಽᕽGamma ᇥ⡍ෝᔍᬊ⦹ᩡ݅. ᅙᩑǍᨱ ᕽ۵ᦿᕽᨙɪ⦹ᩡॐᯕGamma ᇥ⡍, Exponential ᇥ⡍ෝ࠺᜽ᨱ

Łಅ⧁ ᙹ ᯩࠥಾ ⪝⧊ᇥ⡍ෝ ⪽ᬊ⦹ᩍ ༉⩶ᮥ Ǎᖒ⦹ᩡ݅.

đುᱢᮝಽᯝၹᱢᯙMarkov Chain ༉⩶ᨱእ⧕ᕽš⊂ḡᱱ᮹

☖ĥᱢ✚ᖒᮥ⬉ŝᱢᮝಽᅖᬱ⦹໑᳦šʑᔢ⦺ᱢ➉▕ᮥ❭ᦦ⦹

۵ߑ ᮁญ⦽ vᙹ༉᮹ʑჶᮥ }ၽ⦹۵ äᯕ ᅙ ᩑǍ᮹ ༊ᱢᯕ

݅. ᷪ, ʑ᳕Markov Chain ༉⩶ʑၹ᮹vᙹ༉᮹ʑჶᮥݡℕ⧁

ᙹᯩ۵݉ḡᱱHMM ᯝvᙹప༉᮹ʑჶᮥ}ၽ⦹Łᯱ⦹໑ʑᔢ ℎᔑ⦹᮹ᕽᬙš⊂ᗭ᪡ᱥᵝš⊂ᗭ᮹vᙹపᮥݡᔢᮝಽ༉⩶᮹

ᱢ⧊ᖒᮥ⠪a⦹ᩡ݅. ᅙםྙ᮹Ǎᖒᮡ݅ᮭŝz݅. 1ᰆᨱᕽ۵

םྙ᮹႑Ğၰ༊ᱢᨱݡ⧕ᕽᨙɪ⦹ᩡᮝ໑, 2ᰆᨱᕽ۵ʑ᳕᮹

ᱶᔢᖒ2-State Markov Chain ༉⩶ŝHMM ༉⩶ᨱݡ⦹ᩍʑᚁ

⦹ᩡ݅. 3ᰆᨱᕽ۵HMM ༉⩶ᱢᬊđŝෝ᫵᧞⦹ᩍӹ┡ԕᨩᮝ໑

ษḡสᮝಽ đು ၰ ☁᮹ෝ 4ᰆᨱ ᙹಾ⦹ᩡ݅.

2. Markov Chain ʑၹᯝvᙹప༉᮹ʑჶ

2.1 ୨ঃনMarkov Chain Model

ᯝၹᱢᮝಽྕ᯲᭥᜽ĥᩕᯱഭe᮹ĥᩕᔢšᖒŝၙ௹᮹ᔢ┽

ෝ⩥ᰍ᪡ŝÑ᮹ᔢ┽ॅŝ᮹ᔢššĥᇥᕾอᮝಽ⇵ĥ⦺ᱢᮝಽ

⇵⇽⦹۵ŝᱶᮥMarkov ŝᱶᯕ௝Ł⦹Ł⦽ᱶᱢᯙᔢ┽Ŗeᨱᕽ ᮹ Markov ŝᱶᮥ Markov Chain௝ ⦽݅.

ǎԕ᮹Ğᬑᯝvᙹᯱഭ۵ฯí۵100ᩍ֥ᱶࠥᨱᕽᇡ░ᱢí ۵10ᩍ֥ᱶࠥʭḡ݅᧲⦽ʙᯕಽ᳕ᰍ⦹Łᯩ݅. ə్ӹ⩥ᰍ

ᬑญӹ௝᮹ݡᇡᇥ᮹ᮁᩎᨱᕽš⊂ࡽᙹྙᯱഭ۵ๅᬑᱽ⦽ᱢᯕ Łđ⊂ᯱഭa᳕ᰍ⦹ᩍ ᙹྙ⩥ᔢᮥᇥᕾ⦹۵ߑᨕಅᬡᯕᯩ۵

ᝅᱶᯕ݅. ᅙםྙᨱᕽ≉ɪ⧁ᯝvᙹపᯱഭĥᩕᮡᮁ⇽పᯱഭĥ

ᩕᨱ እ⦹ᩍ ᄡ࠺ᖒᯕ ⓍŁ ᙹྙ⦺ᱢᯙ ḡᗮᖒ ᷪ ᯱʑᔢšᖒ (autocorrelation)ᯕⓍḡᦫᮡ᜽ĥᩕᯱഭಽᕽᯕ᪡zᮡĞᬑ

Markov Chainᮥᱢᬊ⦹໕ə✚ᖒᮥ᯹ཹᔍ⦹۵äᮝಽ᦭ಅᲙ

ᯩ݅(Nord, 1975). Markov Chain᮹ʑᅙ}ֱᮡṈᮡŝÑ᮹

ʑᨖᮥ☖⧕ၙ௹ᔢ┽ෝᩩ⊂⦹۵ä(Hann ॒, 1976)ᮝಽᕽ݅ᮭ

ŝ zᮡ ᳑Õᇡ ⪶ශಽ ӹ┡ԝ ᙹ ᯩ݅.

ƎÞ«

ƌ âÎ

«

ƌ

ì«

_{ƌ àÎ}

ìzì«

_Î

ß

(1)

ᩍʑᕽᔢ┽

«

_ƌ۵⩥ᰍ᮹vᙹᔢ┽,

«

_{ƌ àÎ}

ì «

_ƌ

ì «

_ÎᮡŝÑ᮹

vᙹᔢ┽ෝӹ┡ԕ໑ၙ௹᮹vᙹᔢ┽۵ŝÑ᮹ᔢ┽᪡۵ࠦพ (independence)ᯕ໑݉ḡaᰆɝᱲ⦽⩥ᰍ᮹vᙹᔢ┽ᨱ᮹⧕ᕽ อᩢ⨆ᮥၼ۵݅໕ᯕভMarkov Chain᮹ᖒḩᮡ݅ᮭŝzᮡ

᳑Õᇡ⪶ශಽӹ┡ԝᙹᯩ݅. ᯕ్⦽ŝᱶᮥ1₉Markov Chainᯕ

௝ ⦽݅.

ƎÞ±

ƌ âÎ

±

ƌ

ß

(2)

ᩍ෥ŝzᯕᬑʑʑeԕ᮹vᙹపeᨱ۵᯲ᮡĥᩕᔢš(serial correlation)ᯕ᳕ᰍ⧁ᙹᯩᮝӹ᳦ᗮᖒᯕᯩ݅Łᅕʑᨱ۵ྕญa

ฯ݅. ঑௝ᕽvᙹపᮥ༉᮹⦹ʑ᭥⦹ᩍᩑᗮ⦹۵ᔍᔢe᮹ࠦพᖒ

ᮥ aᱶ⦹Ł ᯕುᱢᯙ ⪶ශᇥ⡍ෝ ᱢ⧊ ᜽┅۵ ႊᦩॅᯕ ᵝಽ

⪽ᬊࡹŁᯩ݅. 2-State ᮹1₉Markov Chain༉⩶ᨱᕽbᔢ┽Ŗe ᨱ᳕ᰍ⦹۵vᙹᔍᔢ᮹ĥᩕᯙᄂ░(S)᪡ᔍᔢ᮹ၽᔾ(vᙹᯝ)ŝ

vᙹ ၽᔾ(ྕvᙹ)᮹ ⪶ශᮥ ӹ┡ԕ۵ ⃽ᯕ⪶ශ(

©

ƒƐ)ᮡ ݅ᮭŝ

zᮡ ᜾ᮝಽ ⢽⩥ ࢁ ᙹ ᯩ݅.

©

_ƒƐ_{Ƈì ƈ}

á ć

ā

ƈ á Î Ï

¬

_Ƈìƈ

¬

Ƈìƈ

(3)

ᩍʑᕽ, ⧪಍᮹ ᬱᗭ

©

_ƒƐ_{Ƈì ƈ}۵ ᔢ┽

Ƈ

ᨱᕽ ᔢ┽

ƈ

ಽ ⃽ᯕࡹ۵

᜾(3)ᮝಽ⢽⩥ࡹ۵⃽ᯕ⪶ශ(transition probability)᮹bᬱᗭ (element)۵༉ࢱ0ᅕ݅ⓍÑӹzᮝ໑, b⧪᮹ᬱᗭ᮹⧊ᯕ1ᯝ

ভ᮹⧪಍ᮥ⪶ශ⧪಍(probability matrix)ᯕ௝ᱶ᮹⦽݅. bb᮹

⪶ශ⧪಍ᮡ ⦹ӹ᮹Markov ŝᱶᮥ ᱶ᮹⦹໑, vᙹ ၽᔾᩍᇡෝ

❱݉⦹íࡽ݅. ঑௝ᕽ⃽ᯕ⪶ශ

©

_ƒƐᯕđᱶࡹ໕Markov Chain᮹

Ⅹʑ ᔢ┽อᮥ ☖⧕ vᙹၽᔾᮥ ༉᮹⧁ ᙹ ᯩ݅. 2-State 1₉

Markov Chain ༉⩶ᨱ ᮹⦽ vᙹၽᔾ ŝᱶᮥ Table 1ŝ zᮡ

⃽ᯕ⪶ශ⧪಍(transition probability matrix)ಽӹ┡ԝᙹᯩ݅.

Table 1ᨱᕽ0ⴌaⴌ1, 0ⴌbⴌ1ಽᕽ, a۵ྕvᙹᯝ݅ᮭᨱvᙹ ᯝᯕၽᔾ⧁⪶ශᯕŁb۵vᙹᯝ݅ᮭᨱྕvᙹᯝᯕၽᔾ⧁⪶ශᯕ ໑ ᯕෝ ⃽ᯕ⪶ශ ᜾ᮝಽ ӹ┡ԕ໕ ᦥ௹ ᜾ŝ z݅.

(4)

Table 1. Transition Probability Matrix for State 2-1 Markov Chain t(day)

t-1 (day) Dry Wet

Dry 1-a a

Wet b 1-b Fig. 1. Bayesian Network Representation of a Homogeneous

HMM Satisfying Conditional Independence Assumptions

© á ç ^{Î à ſ ſ} ^{ƀ Î à ƀ} ç

⁽⁴⁾

Markov Chain ༉⩶ᨱ ᮹⦽ vᙹၽᔾŝᱶᨱ۵ Ⅹʑ ⪶ශŝ

⃽ᯕ⪶ශ⧪಍ᯕ⦥᫵⦹íࡽ݅. Markov Chain ༉⩶ᨱᕽⅩʑ

⪶ශᮡྕ᯲᭥ӽᙹಽᇡ░Ⅹʑ⪶ශᮥ⇵⇽⦹ᩍvᙹၽᔾᩍᇡෝ

đᱶ⦽݅. ษḡสᮝಽŝÑvᙹపᯱഭಽᇡ░⇵ᱶࡽ⪶ශၡࠥ⧉

ᙹ᮹ๅ}ᄡᙹෝᯕᬊ⦹ᩍMonte Carlo ༉᮹ෝᝅ᜽⦹ᩍvᙹᯝᨱ

⧕ݚ⦹۵ vᙹపᮥ đᱶ⦽݅.

2.2 Hidden Markov Chain Model

2.2.1 ׆࣭ࡦ෴֜ন

HMMᮡ᳑Õᇡࠦพaᱶᮥʑᅙᮝಽš⊂ᯱഭಽᇡ░ᮡܪᔢ

┽᮹⪶ශುᱢŝᱶ(stochastic process)ᮥš⊂ᯕa܆⦹ࠥಾၽᔾ

᜽⍽݅ෙ⪶ශುᱢŝᱶᮥ☖⦹ᩍ༉ߙย⦹۵ᯕᵲ᮹⪶ශುᱢ

ŝᱶᯕ݅. ᬑᖁ᜽e᮹₉ᬱᮥw۵vᙹపᯱഭෝ᜽eT᮹ᩑᗮ

ᄂ░ಽ ӹ┡ԕ໕ ݅ᮭŝ z݅.

«

Î é

á Þ«

_Îìíííì

«

ß

(5)

ੱ⦽ ᜽e tᨱ ⧕ݚ⦹۵ ᮡܪᔢ┽(hidden state)ෝ ӹ┡ԕ۵

ᩑᗮ ĥᩕᙽᕽ(sequence)۵ ݅ᮭŝ z݅.

¬

_{Î é}

á Þ¬

_Îìíííì

¬

ß

(6)

HMM༉⩶ᮡࢱaḡ᳑Õᇡࠦพaᱶॅᮥᯕᬊ⦹ᩍ

«

Î é

᪡

¬

_{Î é}᮹đ⧊⪶ශ(joint probability) ᇥ⡍ಽᱶ᮹⦹Łࢱaḡ

᳑Õᇡ ࠦพ aᱶᮡ ݅ᮭŝ z݅.

ℌṙ, ᵝᨕḥᮡܪᔢ┽᪡kᯝᯕᱥ᮹vᙹపᮝಽᯕ൉ᨕḥ༉⩶

ᨱᕽš⊂vᙹᄂ░۵݅ෙ༉ुᄡᙹ᪡᳑Õᇡᱢᮝಽࠦพᯕ௝Ł

(7)

ࢹṙ, ᜽ĥᩕ᮹ ၵಽ ᯕᱥ᮹ ᮡܪᔢ┽ᨱอ ᔢšᖒᯕ ᯩ݅Ł

ᅕ۵Ğᬑෝ1₉HMMᯕ௝Ł⦹໑ᯝၹᱢᮝಽMarkov Chainᯕ

௝Ł⦹໕1₉Markov Chainᮥั⦹۵äᮝಽᷪᮡܪᔢ┽᮹

⪶ශᇥ⡍۵ ᜽eᱢᮝಽ ᪅Ḣ ᯕᱥ ᮡܪᔢ┽ᨱ ᮹᳕⦽݅.

©ÞƑ

_ƒ

çƑ

_{Î é ƒ àÎ}

ß á å ^©ÞƑ

^ƒ

^çƑ

ƒ àƉ é ƒ àÎ

ß ƒ ð Ɖì

©ÞƑ

ƒ

çƑ

_{Î é ƒ àÎ}

ß ƒ = Ɖí

(8)

᭥᮹Eq. (8)ᨱᕽ⇵aᱢᮝಽ໦᜽ࡽᨙɪᯕᨧᮝ໕ᯝၹᱢᮝಽ

k=1᮹ ᮡܪᔢ┽ ⪶ශᇥ⡍۵ ݅ᮭŝ z݅.

©ÞƑ

ƒ

çƑ

_{Î é ƒ àÎ}

ß á å ^©ÞƑ ^ƎÞƑ

^Î^ƒ

^çƑ ^ß

^{ƒ àÎ}

^ß ^{ƒ > Ïì} ^{ƒ á Îí}

⁽⁹⁾

࠺ḩᖒHMMᮡ᳑Õᇡ⪶ශ

©ÞƑ

ƒ

çƑ

_{ƒ àÎ}

ß

ᮥ⇵ᱶ⦹۵ߑᯩᨕᕽ

Fig. 1ŝzᮡᱶᔢᖒaᱶᮥʑᅙᮝಽᯕ൉ᨕḥ݅. ᦿᕽᨙɪࡽ

ᮡܪᔢ┽ᨱ᳑Õᇡ⪶ශ

©ÞƑ

ƒ

çƑ

_{ƒ àÎ}

ß

a᜽eᨱ঑௝ᕽᯝᱶ⦹݅۵

ᱶᔢᖒaᱶᨱʑᅙᮥࢱŁᯩ݅. ࠺ḩᖒHMMᨱݡ⧕ᕽ

Į

= (

_ņ

_Îìíííì

_ņ

_¤)۵Ⅹʑ⪶ශᄂ░௝⦹Ł

ġ á ÞĹ

ÎÎ

ìíííìĹ

_¤¤

ß

ෝ⃽ᯕ⪶ශᮥ

w۵ ⧪಍(transition probability matrix)ಽ ᱶ᮹⦹ᯱ.

ᩍʑᕽ

ś

ෝ ᮡܪᔢ┽

¬

ƒᨱ ᳑Õᇡಽ ᵝᨕḡ۵ vᙹప

Ɛ

ƒ᮹

ၽᔾ⪶ශ

_Ƈ

ÞƐß á ©ÞƐ

_ƒ

ç¬

_ƒ

á Ƈß

ᮡbb᮹ᮡܪᔢ┽ᄥಽđᱶࡹ۵

⇽ಆ(emission) ⪶ශၡࠥ⧉ᙹ᮹ ๅ}ᄡᙹॅಽ Ǎᖒࡽ݅.

©ÞƐ

Î é ì

¬

Î é

á Ƒ

_{Î é}

çĮìġìśß

á ƙ

Ɯ ƚ ņ

_Ƒ_Î

Ă

_{ƒ á Ï}

^Ĺ

^Ƒ^{ƒ à Î}^Ƒ^ƒ

^ƛ _Ɲ ^ƞ ^ƙ _Ɯ ^ƚ Ă

_{ƒ á Î}

^Ƒ^ƒ

^ÞƐ

^ƒ

^çƐ

^{ƒ àÎ}

^ß ^ƛ _Ɲ ^ƞ

⁽¹⁰⁾

2.2.2 ଠێঃ೾ंඑ(hidden state distribution)

ᯝၹᱢᮝಽš⊂ࡽvᙹపᯱഭෝᯕᬊ⦹ᩍᮡܪᔢ┽᮹⪶ශၡ

_{Î é}

ß

(11)

(5)

ᯱഭ᮹ᬑࠥ

©ÞƐ

Î é

çƖ

_{Î é}

ß

ෝĥᔑ⦹ʑ᭥⧕ᕽForward-back- ward ŝᱶᮥ☖⦽ၹᅖჶᮥᯕᬊ⦹ᩡ݅. bᮡܪᔢ┽

¬

_ƒᨱݡ⧕ᕽ, ၹᅖᱢᮝಽᖁ⧪ᮡܪᔢ┽(

ķ

ƒ)᪡ᯕॅᔢ┽ෝअ঑෕۵ᮡܪᔢ┽

(

_ĸ

ç¬

_Î

á Ƈß

ķ

ƒ âÎ

ÞƇß á

©ÞƐ

_{ƒ âÎ}

ç¬

_{ƒ âÎ}

á ƈìƐ

_ƒ

ß ā

_{Ƈ á Î}^¤

^©Þ¬

^{ƒ âÎ}

^{á ƈç¬}

^ƒ

^{á Ƈì Ɩ}

^{ƒ âÎ}

^ßķ

^ƒ

^ÞƇß

ĸ

ÞƇß á Î ĸ

_ƒ

ÞƇß á

ā

^©Þ¬

^{á ƇìƐ}

^{Î é}

^çƖ

^{Î é}

^{ß á} ā

_{Ƈ á Î}^¤

^ķ

^ÞƇß

^(12c)

ᯝvᙹప༉᮹ෝ᭥⧕ᕽᬑญӹ௝᮹vᙹᇥ⡍ᇥᕾᨱᱢ⧊⦽

⪶ශᇥ⡍ಽᯝၹᱢᮝಽᔍᬊࡹŁᯩ۵Gamma ੱ۵Exponential ᇥ⡍aᯕᬊࡹ໑ྕvᙹෝᱽ᫙⦹Łvᙹᨱݡ⧕ᕽอ⪶ශᇥ⡍ෝ

_ƒ

á Ƈß á

_{Ƌ á Î}

Ă

^¦

©ÞƐƋƒç¬

^ƒ

á Ƈß á

_{Ƌ á Î}

Ă

^¦

^ſ

^ƇƋ ⁽¹³⁾

ᩍʑᕽ

ſ

_ƇƋ

á Ē ē Ĕ

ĕ ĕ

Ǝ

_ƇƋ×

ƐƋƒá×ì

ā

Ɓ á Î

Ǝ

_ƇƋƁ

Ł

_ƇƋƁ

Þà Ł

_ƇƋƁ

ƐƋƒß Ɛ Ƌ ƒ ð ×

©ÞƐ

_ƒ

ç¬

_ƒ

á Ƈß á

_{Ƌ á Î}

Ă

^¦

^©ÞƐ

^ƒ^Ƌ

^ç¬

^ƒ

^{á Ƈß á}

_{Ƌ á Î}

Ă

^¦

^ſ

^ƇƋ ⁽¹⁴⁾

ᩍʑᕽ

ſ

_ƇƋ

á Ē ē Ĕ

ĕ ĕ

Ǝ

ƇƋ×

ƐƋƒá×ì

ā

Ɓ á Î

Ǝ

_ƇƋƁ

ć ġÞķ

ƇƋƁ

ß

ĸ

_ƇƋƁ^ķ^ƇƋƁ

ÞƐ

_ƒ^Ƌ

ß

^ķ^ƇƋƁ^àÎ

Þà ĸ

ƇƋƁ

Ɛ

ƒƋ

ß ƐƋƒð ×

3. ᱢᬊ

1974֥ᇡ░2012֥ʭḡᕽᬙš⊂ᗭ᪡ᱥᵝš⊂ᗭ॒2}᮹

š⊂ᗭ᮹ᯝvᙹపᯱഭෝݡᔢᮝಽ༉⩶ᮥᱢᬊ᜽⎑݅. ༉⩶ᱢᬊ

ŝᱶᮡᵝಽᕽᬙš⊂ᗭෝݡᔢᮝಽᖅ໦⦹Łᱢ⧊ᖒᮥ⠪a⦹۵

ŝᱶᮡᱥᵝš⊂ᗭෝ⡍⧉⦹ᩍᱽ᜽⦹ᩡ݅. HMM ༉⩶᮹ᱢ⧊ᖒ

ᮥ⠪a⦹ʑ᭥⧕ᕽGamma ⪶ශၡࠥ⧉ᙹʑၹ᮹2-State 1₉

Markov Chain ༉⩶ŝ እƱ⦹ᩍ ᇥᕾ⦹ᩡ݅.

༉⩶᮹ ᱢᬊᨱ ᦿᕽ ᮡܪᔢ┽ ᙹෝ đᱶ⦹ʑ ᭥⦹ᩍ HMM

༉⩶᮹ ᱢ⧊ᖒ ᱶࠥෝ ⠪a⦹۵ߑ ᔍᬊࡹ۵ ݡᙹᬑࠥ⧉ᙹ(log- likelihood function)ෝᔍᬊ⦹ᩍᕽಽ݅ෙᮡܪᔢ┽ᙹKෝaḡ Ł⠪a⦹ᩡ݅. ᮡܪᔢ┽ᙹKෝᇥʑᄥಽ2~7ʭḡᄡ⪵⦹໕ᕽ

ᬑࠥෝᔑ⇽⦹ᩡŁəŝᱶᨱᕽKa᷾a⧉ᨱ঑௝ᬑࠥ⧉ᙹੱ⦽

᷾a⦹Łᯝᱶ⦽ᮡܪᔢ┽ᙹᯕᔢᨱᕽ۵ᙹಕ⦹۵đŝෝ⪶ᯙ⧁

ᙹᯩᨩ݅. ⦹ḡอᮡܪᔢ┽ᙹෝྕ⦽⯩᷾a⧁Ğᬑ༉⩶ᯕŝᱢ⧊

(overfitting)ࡹ۵ྙᱽᱱᯕᯩᮝအಽᬑࠥaᙹಕ⦹۵ᇡᇥᨱᕽ

↽ᱢ᮹ ᮡܪᔢ┽ ᙹෝ đᱶ⦹ᩡ݅. ᅙ ᩑǍᨱᕽ۵ ᩍ෥ ĥᱩᨱ

ݡ⧕ᕽHMM ༉⩶ᮥᱢᬊ⦹ᩡ݅. ᷪ, ᕽᬙၰᱥᵝš⊂ᗭᯝvᙹప ᨱݡ⧕ᕽ6ᬵᇡ░9ᬵ(JJAS, June-July-August-September)᮹

ᩍ෥vᙹపᮥݡᔢᮝಽᩑǍෝḥ⧪⦹ᩡ݅. םྙ᮹ḡ໕šĥᔢ

ᱥᵝḡᱱ᮹ Ğᬑ ᕽᬙḡᱱŝ ᮁᔍ⦽ đŝෝ ᅕᩍᵝ۵ əฝ ၰ

⢽۵ᔾఖ⦹Łᖅ໦ᮝಽݡℕ⦹ᩡ݅. vᙹĥᩕᮥĥᱩಽǍᇥ⦽

äᮡvᙹᔍᔢ᮹ĥᱩᱢ✚ᖒᮥᅕ݅⬉ŝᱢᮝಽၹᩢ⦽༉⩶ᮥ

Ǎ⇶⦹ʑ ᭥⧉ᯕ݅.

↽ᱢᮡܪᔢ┽ᙹđᱶᮡFig. 2᪡zᯕݡᙹᬑࠥ⧉ᙹෝᯕᬊ⦹

ᩍᯕ൉ᨕḥ݅. Fig. 2۵bš⊂ᗭ᮹JJAS ĥᱩᨱ⧕ݚ⦹۵ᮡܪᔢ

┽ᙹᨱ঑ෙݡᙹᬑࠥ⧉ᙹෝӹ┡ԩᮝ໑↽ᱢᬑࠥෝaḡ۵ᮡܪ ᔢ┽ ᙹෝ ᖁ┾⦹ᩍ vᙹ༉᮹ ᇥᕾᮥ ᝅ᜽⦹ᩡ݅.

Fig. 3ŝFig. 4۵ᬑญӹ௝᮹ᬑʑʑeᨱ⧕ݚ⦹۵6ᬵᨱᕽᇡ░

9ᬵʭḡ᮹ᕽᬙš⊂ᗭᨱᕽš⊂ࡽvᙹప᮹vᙹ✚ᖒᮥᇥᕾ⦽

đŝᯕ໑5}᮹ᮡܪᔢ┽ᙹෝᔍᬊ⦹ᩍbb᮹ᮡܪᔢ┽᮹vᙹၽ ᔾ ኩࠥ᪡ vᙹప᮹ ✚Ḷᮥ ❭ᦦ⦹ʑ ᭥⦽ əฝᯕ݅. Fig. 3ᮡ

ๅ֥6ᬵᇡ░9ᬵʭḡⅾ122ᯝᨱݡ⧕ᕽᮡܪᔢ┽ෝᇥඹ⦽əฝ ᮝಽᕽ ݅ᖐ ჩṙ ᮡܪᔢ┽(S5)a aᰆ ׳ᮡ ኩࠥෝ ₉ḡ⦹۵

(6)

Seoul Station

Jeonju Station

Fig. 2. Log-likelihood Estimations for Amounts Models Using Mixture of two Exponential Distributions for Each Station Rainfall on Wet Days

Fig. 3. The Estimated State Sequence Via Vieterbi Algorithm for JJAS Season at Seoul Station

Fig. 4. The Estimated Percentage of Amount and Frequency of Seasonal Rainfall According to Each State at Seoul Station ʑᔢᔢ┽ಽ❱݉ࡹ໑ᮡܪᔢ┽S1, S3 ၰS4۵ᔢݡᱢᮝಽԏᮡ

ኩࠥෝӹ┡ԕŁᯩ݅. Fig. 4᮹᫝἞əฝᮡ༉᮹ʑeᨱݡ⦹ᩍ

ၽᔾࡽvᙹ᮹ⅾపᮥӹ┡ԕ໑᪅ෙ἞ᨱ᭥⊹⦽əฝᮡbb᮹

ᮡܪᔢ┽ᨱ ঑ෙ vᙹ ၽᔾኩࠥෝ ӹ┡ԕŁ ᯩ݅.

ℌჩṙᮡܪᔢ┽(S1)᮹Ğᬑᨱ۵ᱥℕvᙹప᮹78%ᱶࠥෝ

₉ḡ⦹Łᯩ۵ߑእ⦹ᩍvᙹᔍᔢ᮹ၽᔾኩࠥ۵10%ᱶࠥෝӹ┡

ԕŁᯩ۵äᮝಽᅕᦥᕽḲᵲ⪙ᬑ᮹⩶┽ෝaḡ۵ʑᔢᔢ┽ಽ

❱݉⧁ᙹᯩ݅. օჩṙᮡܪᔢ┽(S4)᪡zᮡĞᬑ۵vᙹపᯕ

Ñ᮹ 0%ᨱ aʾḡอ vᙹᔍᔢ᮹ ၽᔾኩࠥ۵ 58%ෝ ӹ┡ԕŁ

ᯩᮭᮥ⪶ᯙ⧁ᙹᯩ݅. ᯕ۵Ñ᮹vᙹaၽᔾ⦹ḡᦫÑӹྕvᙹᨱ

aʭᬕʑᔢᔢ┽ಽ❱݉⧕ᅝᙹᯩ݅. ᷪ, vᙹపᮡݡᇡᇥᮡܪᔢ

┽S1, S2, S3ᯕ₉ḡ⦹Łᯩᮝ໑, əᵲS1ᮡԏᮡኩࠥಽၽᔾ⦹ḡ อɚ⊹vᙹపᮥၽᔾ᜽┅۵vᙹᔍᔢ᮹✚ḶᮥᅕᩍᵝŁᯩ݅.

ᅙᩑǍ᮹aᰆᵲ᫵⦽༊ᱢᯕᯝvᙹపᯱഭĥᩕ᮹✚ᖒ⊹ෝ

↽ݡ⦽š⊂⊹᪡ᮁᔍ⦹í༉᮹⦹۵ߑᯩᮝအಽ, ᅙᩑǍෝ☖⧕

(7)

Fig. 5. A Comparison of Seasonally Averaged Rainfall Statistics for Seoul Weather Stations for JJAS Season

Table 2. A Comparison of Seasonally Averaged Rainfall Statistics for Seoul Weather Station for JJAS Season

Statistics Observation HMM Gamma Rainfall Amount(mm) 1031.58 1014.92 979.87

Wet to Wet 0.57 0.57 0.54

Dry to Dry 0.72 0.70 0.69

Fig. 6. A Comparison of Mean and Standard Deviation of Seasonal Rainfall(JJAS) Between Observation and Simulation. Each Panel Shows Mean, Standard Deviation and Skewness. The Box Plot is Derived by 200 Ensemble Series and the Symbol

G Indicates Observation While G Represents Results Derived From the Existing Markov Chain Model

Fig. 7. Basic Statistics of Daily Rainfall Between Observation and Simulation. Each Panel Shows Mean, Standard Deviation, Skewness and Kurtosis for Seoul Station. The Box Plot is Derived by 200 Ensemble Series and the Symbol  Indicates Observation While GRepresents Results Derived

⇵ᱶࡽᩑǍđŝੱ۵ᯕ్⦽✚ᖒᮥ⠪a⧁ᙹᯩ۵ḡ⢽ॅᮥ

ݡᔢᮝಽš⊂⊹᪡እƱ⦹ᩡ݅. ᷪ, ĥᱩvᙹప᮹ⅾపᮥ᨝ษӹ

ᮁᔍ⦹íᰍ⩥⦹۵ḡෝ⠪a⦹ʑ᭥⧕ᕽĥᱩⅾvᙹపᮥš⊂⊹

᪡⧉̹ӹ┡ԕᨩ݅. ੱ⦽ᯝvᙹప᮹✚ᖒ⊹ᯙ, ⃽ᯕ⪶ශၰ᜖ᮅᯝ

ᮥእƱᇥᕾᮥᝅ᜽⦹ᩡᮝ໑, Boxplotᮡⅾ200}᮹Ensembleಽ

⇵ᱶࡹᨩᮝ໑ š⊂⊹(“⳴”)᪡ ᵲℊ⦹ᩍ ӹ┡ԕᨩ݅.

HMM༉⩶ᮥ☖⧕༉᮹ࡽvᙹప᮹ᱢ⧊ᖒᮥ⠪a⦹ʑ᭥⧕ᕽ

Fig. 5ᨱᕽ۵ 2-State 1₉ Markov Chain ༉⩶ đŝ᪡ ĥᱩᱢ

vᙹ✚ᖒᮥእƱá☁⦹ᩡ݅. bᇥʑᄥಽᝅᱽš⊂ࡽvᙹ✚ᖒŝ

እƱ⦹ᩍ ĥᱩ vᙹⅾప, vᙹᨱᕽ vᙹಽ ᄡ⪵⦹۵ ⃽ᯕ⪶ශ,

ྕvᙹᨱᕽྕvᙹಽᄡ⪵⦹۵⃽ᯕ⪶ශ, vᙹᯝᙹᨱݡ⦹ᩍᇥᕾ

⦽đŝෝӹ┡ԕ۵əฝᮝಽHMM vᙹ༉᮹༉⩶ᮥ☖⦹ᩍ᨜ᮡ

༉᮹vᙹsᮡBoxplotᮥᔍᬊ⦹ᩍӹ┡ԕᨩᮝ໑š⊂sᮡ‘ⶼ’

ᮝಽ ⢽᜽⦹Ł Gamma ༉⩶ᇥ⡍ ʑၹ᮹ 2-State 1₉ Markov Chain ༉⩶ ☖⦽ đŝsᮡ ‘ⶸ’ᮝಽ ⢽᜽⦹ᩡ݅.

Fig. 5ᨱᕽ ᅝ ᙹᯩॐᯕ HMM༉⩶ŝ ʑ᳕ Markov Chain

༉⩶༉ࢱĥᱩ݉᭥ᨱᕽvᙹ᮹☖ĥ✚ᖒᮥ⬉ŝᱢᮝಽ༉᮹⦹۵

äᮥ⪶ᯙ⧁ᙹᯩ݅. ᱥᵝḡᱱ᮹Ğᬑᨱࠥ࠺ᯝ⦽đŝෝ⪶ᯙ⧁

ᙹᯩᨩ݅. ʑ᳕Markov Chain ༉⩶᮹Ğᬑš⊂ࡽ⃽ᯕ⪶ශᮥ

əݡಽᰍ⩥⦹ᩍvᙹෝ༉᮹⦹ʑভྙᨱ⃽ᯕ⪶ශŝvᙹᯝᙹa

š⊂⊹᪡ᮁᔍ⦹í༉᮹ࡹ۵äᮡݚᩑ⦹݅⦹ā݅. ⇵aᱢᮝಽ

ᕽᬙš⊂ᗭ᮹vᙹⅾపŝ⃽ᯕ⪶ශၰvᙹၽᔾᯝᮥTable 2ᨱ

ᱶญ⦹ᩡ݅.

Fig. 6ᨱᕽ۵ᕽᬙš⊂ᗭ᮹JJAS ĥᱩ᮹vᙹపᨱݡ⦽1974֥

ᇡ░2012֥ʭḡ༉᮹đŝෝ⠪Ɂŝ⢽ᵡ⠙₉ෝݡᔢᮝಽእƱ

⠪a⦹ᩡ݅. əฝᨱᕽ ⪶ᯙ ⧁ ᙹ ᯩॐᯕ HMM༉⩶ᨱ ᮹⦹ᩍ

༉᮹ࡽĥᱩvᙹప᮹⠪Ɂsŝ⢽ᵡ⠙₉༉ࢱš⊂⊹(‘ⶼ’)᪡ᮁᔍ

⦽đŝෝӹ┡ԕ۵ၹ໕ʑ᳕Markov Chain ༉⩶ᮥ☖⦽༉᮹vᙹ

s(‘ⶸ’)ᮡ⠪Ɂsᮡᮁᔍ⦹íᰍ⩥⦹ḡอ⢽ᵡ⠙₉۵༉᮹sŝ

š⊂sᯕ ᇩᯝ⊹⦹۵ äᮥ ⪶ᯙ⧁ ᙹ ᯩ݅. ᱥᵝḡᱱᨱ ݡ⧕ᕽ

࠺ᯝ⦹íHMM ༉⩶ᯕʑ᳕Markov Chain ༉⩶ᨱእ⧕}ᖁࡽ

༉᮹đŝෝ ӹ┡ԕᨩ݅. ᯕ۵ HMM ༉⩶ᯕ vᙹ ༉᮹᜽ ɚ⊹

vᙹప᮹ᰍ⩥ᖒᯕʑ᳕Markov Chain ༉⩶ᨱእ⦹ᩍᬑᙹ⦹݅۵

ᱱᮥ ᮹ၙ⦽݅.

ᯕ్⦽ ᱱᮥ ᳡ ޵ ᯱᖙ⯩ ⠪a⦹ʑ ᭥⧕ᕽ ᯝvᙹపĥᩕᮥ

ݡᔢᮝಽ⠪Ɂ, ⢽ᵡ⠙₉, ᪽łࠥ, ℉ᩩ॒ࠥ4₉☖ĥ༉ູ✙ʭḡ

(8)

Table 3. Seasonally-averaged Statistical Moments of Daily Rainfall Between Observation and Simulation

Statistics Observation HMM Gamma

Mean 7.84 8.32 7.00

Standard Deviation 20.22 22.45 18.56

Skewness 4.28 4.17 3.53

Kurtosis 24.04 24.16 16.57

Table 4. Statistical Moments of Daily Rainfall Between Observation and Simulation for Each Month

Statistics June July August September

Obs. HMM Gam. Obs. HMM Gam. Obs. HMM Gam. Obs. HMM Gam.

Mean 3.9 4.76 5.2 11.35 12.51 7.99 9.15 11.19 8.42 3.31 5.14 5.68

Standard Deviation 11.05 12.41 12.77 23.28 26.26 15.17 19.91 24.33 20.47 10.69 15.08 15.45

Skewness 3.27 3.29 2.78 2.73 2.77 2.17 2.55 2.79 2.72 3.39 3.55 2.94

Kurtosis 12.98 14.02 9.11 10.3 10.92 7.93 8.57 10.94 10.14 14.34 15.63 10.58

Table 5. Daily Rainfall Statistics of Seoul Station for Each Month

Statistics June July August September

Obs. HMM Gam. Obs. HMM Gam. Obs. HMM Gam. Obs. HMM Gam.

Rainfall Amount(mm) 142.3 142.7 159.9 393.6 387.6 237.8 342.9 346.8 273.5 152.6 154.1 177.6

Wet to Wet 0.45 0.44 0.36 0.64 0.66 0.5 0.63 0.6 0.61 0.42 0.41 0.47

Dry to Dry 0.72 0.73 0.65 0.63 0.62 0.59 0.67 0.65 0.63 0.76 0.77 0.79

Wet Days 10 10.08 11.04 16 16.16 14.12 14 14.47 15.1 9.0 8.72 8.76

ᰍ⩥✚ᖒᮥእƱá☁⦹ᩍFig. 7ᨱӹ┡ԕᨩ݅. Boxplotᮡⅾ

200}᮹Ensembleಽᇡ░⇵ᱶࡹᨩᮝ໑š⊂⊹(“⳴”)᪡ᵲℊ⦹ᩍ

ӹ┡ԕᨩ݅. əฝᨱᕽᅕ໕ᕽᬙš⊂ᗭᨱᕽHMM ༉⩶ŝʑ᳕

Markov Chain ༉⩶ᮡᯝvᙹప᮹☖ĥ✚ᖒᮥ⬉ŝᱢᮝಽᰍ⩥⦹

Łᯩᮭᮥ⪶ᯙ⧁ᙹᯩ݅. ə్ӹᕽᬙḡᱱ᮹Ğᬑʑ᳕Markov Chain ༉⩶ᮡ3₉༉ູ✙ᯕᔢᨱᕽ᯲ᮡ₉ᯕḡอš⊂sᨱእ⧕

ŝᗭ⇵ᱶࡹ۵äᮥ⪶ᯙ⧁ᙹᯩ݅. ၹ໕HMM ༉⩶ᮡš⊂⊹᪡

Ñ᮹ᯝ⊹⦹۵đŝෝӹ┡ԕŁᯩ۵॒ᱥℕᱢᮝಽʑ᳕Markov Chain ༉⩶ᨱእ⧕ᕽ}ᖁࡽ༉᮹đŝෝӹ┡ԕᨩ݅. 3₉༉ູ✙

ᯕᔢᨱᕽ᯲ᮡ₉ᯕḡอɚ⊹vᙹపᮥᰍ⩥⦹۵ߑᯩᨕᕽⓑ₉ᯕ

ෝӹ┡ԝᙹᯩ݅۵ᱱᨱᕽ༉᮹ࡽvᙹపᮥݡᔢᮝಽᩑ↽ݡ⊹

ᯱഭอᮥ ⇵⇽⦹ᩍ ኩࠥ⧕ᕾᮥ ᙹ⧪⦹ᩍ š⊂⊹᪡ እƱ⦹ᩡ݅.

Table 3 and 4۵ᯝvᙹప᮹ݡ⦽⠪Ɂ, ⢽ᵡ⠙₉, ᪽łࠥ, ℉ᩩࠥෝ

ĥᱩʑᵡŝᬵʑᵡᮝಽ⠪Ɂ⦹ᩍእƱ⦹ᩡ݅. ᅙᩑǍᨱᕽᱽ᜽⦹

Łᯩ۵HMM ༉⩶ᯕʑ᳕Markov Chain ༉⩶ᨱእ⧕ᬑᙹ⦽

༉᮹܆ಆᮥӹ┡ԕᨩ݅. Table 5۵ᬵᄥᯝvᙹపⅾప, ᬵ݉᭥ಽ

⠪Ɂࡽ⃽ᯕ⪶ශၰvᬑᯝᙹෝš⊂sŝእƱ⦹ᩍӹ┡ԕᨩᮝ໑

HMM ༉⩶ᯕʑ᳕༉⩶ᨱእ⧕݅᧲⦽⊂໕ᨱᕽ}ᖁࡽ⬉ŝෝ

⪶ᯙ⧁ᙹᯩᨩ݅. ✚⯩, 7~8ᬵ᮹ᰆษ℁vᙹĥᩕ᮹Ğᬑʑ᳕

༉⩶᮹ Ğᬑ vᬑపᯕ Ⓧí ŝᗭ ⇵ᱶࡹ۵ ྙᱽᱱᯕ ၽᔾ⦹Ł

ᯩᮝӹ HMM ༉⩶ᮡ vᙹప ၰ vᬑᯝᙹᨱ ᅕ݅ ⩥ᝅᖒ ᯩ۵

༉᮹a a܆⦹ᩡ݅.

Fig. 8ŝ9۵bbᕽᬙḡᱱŝᱥᵝḡᱱ᮹š⊂sၰ༉᮹sᮝಽ ᇡ░⇵⇽ࡽɚ⊹ᯱഭĥᩕᨱݡ⧕ᕽ⧖ၡࠥ⧉ᙹ᪡Gumbel ⪶ශၡ

ࠥ⧉ᙹෝᯕᬊ⦽100֥ኩࠥvᙹపᮥእƱ⦽əฝᯕ݅. əฝᨱᕽ

ᅕ໕ʑ᳕Markov Chain᮹Ğᬑš⊂s᮹⪶ශၡࠥ⧉ᙹ᪡ๅᬑ

݅ෙ⩶┽ෝӹ┡ԕŁᯩᮝ໑ᯕಽᯙ⧕⇵ᱶࡽ100֥ኩࠥ⪶ශv ᙹపࠥš⊂sᨱእ⧕Ⓧíŝᗭ⇵ᱶࡹ۵đŝᅕᯕŁᯩ݅. ၹ໕

ᅙᩑǍᨱᕽᱽ᜽⦹Łᯩ۵HMM ༉⩶ᮡ⪶ශၡࠥ⧉ᙹaš⊂s ŝๅᬑᮁᔍ⦽✚ᖒᮥӹ┡ԕŁᯩᮝ໑Gumbelᇥ⡍ෝ☖⧕ᕽ

⇵ᱶࡽ100֥ኩࠥ⪶ශvᙹప᮹Ğᬑࠥš⊂sŝÑ᮹ᯝ⊹⦹۵

đŝෝ᨜ᮥᙹᯩᨩ݅. ᯕ్⦽đŝ۵HMM ༉⩶Ǎ᳑aaḡ۵

ᰆᱱᨱ ʑᯙ⦹۵ đŝಽᕽ ❱݉ࡽ݅. ᷪ, vᙹĥᩕᨱ ԕᰍࡹᨕ

ᯩ۵ᅖᰂ⦽ᩍ෥vᙹప➉▕ᮥᯙḡ⧉ŝ࠺᜽ᨱ݅᧲⦽ᇥ⡍⩶┽

ෝŁಅ⧁ᙹᯩ۵⪝⧊ᇥ⡍ෝvᙹ༉᮹ᨱ᯦ࠥ⧉ᮝಽᕽᯝvᙹప

☖ĥ✚ᖒ, ĥᱩvᙹప☖ĥ✚ᖒ, ɚ⊹vᙹప☖ĥ✚ᖒ॒݅᧲⦽

᜽eȽ༉ᨱᕽʑ᳕༉⩶ᨱእ⧕ᕽ}ᖁࡽ༉᮹܆ಆᮥӹ┡ԙ݅Ł

⧁ ᙹ ᯩ݅.

(9)

Fig. 8. A Comparison of Kernel Density Function of Annual Extreme Rainfall Between Observed and Simulated Rainfall for Seoul Station

Fig. 9. A Comparison of Kernel Density Function of Annual Extreme Rainfall Between Observed and Simulated Rainfall for Jeonju Station

4. đು

ᙹᯱᬱĥ⫮, ᖅĥ, ᬕᩢၰšญෝ᭥⧕ᕽ۵↽ᗭ30֥ᯕᔢ᮹

ᙹྙᯱഭa⦥ᙹᱢᮝಽ᫵Ǎࡽ݅. ✚⯩ݡȽ༉ᙹᯱᬱĥ⫮ᨱᕽ۵

50֥ᯕᔢ᮹ᙹྙᯱഭෝ⪽ᬊ⦹ᩍᰆʑᱢᯙšᱱᨱᕽĥ⫮ᮥᙹพ

⦹۵äᯕᯝၹᱢᯕ໑ᝁ഑ᖒᯩ۵ᇥᕾᮥ᭥⧕ᕽ۵↽ᗭ⦽ĥ⫮ʑ eᮥᔢ⫭⦹۵ᯱഭᩑ⦽ᯕ⦥᫵⦹݅. ə్ӹᬑญӹ௝ෝ⡍⧉⦹ᩍ

ฯᮡӹ௝ᨱᕽđ⊂⊹aᨧ۵30֥ᯕᔢ᮹ᰆʑš⊂ᯱഭ۵₟ᦥᅕ ʑᨕಅᬕᝅᱶᯕ݅. ᯕ్⦽ྙᱽᱱᨱʑᯙ⦹ᩍ݉ʑe᮹ᙹྙᯱഭ

ෝ⪶∊⦹ᩍᙹᯱᬱĥ⫮ᨱᯕᬊ⦹Łᯱ⦹۵ᯝvᙹప༉᮹ʑჶᨱ

š⦽ ᩑǍॅᯕ ݅ᙹ ḥ⧪ࡹᨕ ᪵݅. ə్ӹ ʑ᳕ ᩑǍॅᨱᕽ۵

ᯝvᙹప᮹⠪Ɂၰ⃽ᯕ⪶ශ॒ŝzᯕᯝၹᱢᯙ☖ĥ⊹ෝᰍ⩥⦹

۵ ᇡᇥᨱ Ⅹᱱᮥ ฿⇵ᨕᲙ ᩑǍa ḥ⧪ࡹᨩᮝӹ ᇥᔑ, ᪽łࠥ

॒ɚ⊹vᙹపᰍ⩥ᮥ᭥⦽ᩑǍ۵ᔢݡᱢᮝಽၙḥ⦽ᝅᱶᯕ݅.

ᯕ్⦽ᱱᨱᕽᅙᩑǍᨱᕽ۵vᙹ᮹ၽᔾ➉▕ᮥᯱ࠺ᮝಽᯙḡ⦹

Łvᙹ༉᮹ᨱ⪽ᬊ⦹໑vᙹప᮹ᇥ⡍✚ᖒᮥᱥᩎᱢᮝಽŁಅ⧁

ᙹ ᯩ۵ ⪝⧊ᇥ⡍ෝ ᯦ࠥ⦽ HMM ༉⩶ᮥ }ၽ⦹ᩡ݅.

ᅙᩑǍᨱᕽ۵ʑ᳕ᱶᔢᖒMarkov Chain ༉⩶ᮥ}ᖁ⦽࠺ḩ ᖒHMM ༉⩶ᮥ}ၽ⦹ᩍᕽᬙš⊂ᗭŝᱥᵝš⊂ᗭ᮹vᙹᯱഭᮥ

ᔍᬊ⦹ᩍ༉⩶᮹ᱢ⧊ᖒၰᱢᬊᖒᮥ⠪a⦹ᩡ݅. ᅙᩑǍෝ☖⧕

(10)

᨜ᮡ đುᮡ ݅ᮭŝ z݅.

ℌṙ, ༉᮹ࡽᯝvᙹపᮥĥᱩvᙹపᮝಽᄡ⪹⦹ᩍš⊂sŝ

༉᮹sᮥ እƱ⦽ đŝ š⊂⊹᮹ ☖ĥᱢ ✚ᖒᮥ ᮁḡ⦹۵ äᮥ

⪶ᯙ⧁ᙹᯩᨩᮝ໑✚⯩ĥᱩvᙹప᮹ᇥᔑᮥᰍ⩥⦹۵ߑᯩᨕᕽ

ᅙᩑǍᨱᕽᱽᦩ⦽HMM ༉⩶ᯕʑ᳕Markov Chain ༉⩶ᨱ

እ⧕ ᬑᙹ⦽ ᰍ⩥ ✚ᖒᮥ ӹ┡ԕᨩ݅.

ࢹṙ, ᯝvᙹĥᩕᨱݡ⧕ᕽ4₉༉ູ✙ʭḡ☖ĥᱢ✚ᖒᮥá☁

⦽đŝš⊂sŝÑ᮹ᮁᔍ⦹í༉᮹aࡹ۵äᮥ⪶ᯙ⧁ᙹᯩᨩᮝ ໑ĥᱩvᙹపŝ࠺ᯝ⦹í3₉༉ູ✙ᯕᔢᨱᕽʑ᳕Markov Chain

༉⩶ᨱ እ⧕ᕽ }ᖁࡽ ༉᮹ ܆ಆᮥ ⪶ᯙ⧁ ᙹ ᯩᨩ݅.

ᖬṙ, ษḡสᮝಽɚ⊹vᙹపᰍ⩥⬉ŝෝá☁⦹ʑ᭥⧕ᕽ༉᮹

ᯱഭ᪡š⊂sᨱݡ⧕ᕽኩࠥ⧕ᕾᮥᙹ⧪⦹ᩍእƱá☁⦹ᩡ݅.

á☁đŝᅙᩑǍᨱᕽᱽᦩ⦽HMM ༉⩶ᮡʑ᳕š⊂sᮝಽ⇵ᱶ

ࡽ⪶ශၡࠥ⧉ᙹ᪡ๅᬑᮁᔍ⦽ᇥ⡍✚ᖒᮥӹ┡ԕŁᯩ۵ၹ໕

ʑ᳕Markov Chain ༉⩶ᮡๅᬑ᪽łࡽᇥ⡍✚ᖒᮥᅕᩍᵝᨩ݅.

ᯕ్⦽ᱱᮝಽᯙ⧕⇵ᱶࡽ100֥ኩࠥvᙹప᮹ĞᬑᨱࠥHMM

༉⩶ᮡš⊂sᮥʑᵡᮝಽ⇵ᱶࡽ⪶ශvᙹపŝÑ᮹࠺ᯝ⦽sᮥ

w۵ ၹ໕ᨱ ʑ᳕ Markov Chain ༉⩶ᮡ ŝᗭ ⇵ᱶࡹ۵ äᮥ

⪶ᯙ⧁ ᙹ ᯩᨩ݅.

᭥ᨱᕽᨙɪࡽԕᬊᮥᵲᝍᮝಽ❱݉⧕ᅕ໕ᅙᩑǍᨱᕽᱽ᜽⦽

HMM ༉⩶ᯕ ʑ᳕ Markov Chain ༉⩶ᨱ እ⧕ᕽ ɚ⊹vᙹప

ᰍ⩥ᇡᇥᨱ✚⯩ᱢᬊᖒᯕᬑᙹ⦽äᮝಽ❱݉ࡹ໑ᰆʑᮁ⇽పᇥ ᕾၰݡȽ༉ᮁᩎ᮹⪶ශ⪮ᙹపᮥ⇵ᱶ⦹۵ߑᯩᨕᕽ᯦ಆᯱഭಽ

⪽ᬊᯕa܆⧁äᮝಽ❱݉ࡽ݅. ⇵⬥ᩑǍಽᕽᮁᩎ݉᭥ᨱ໕ᱢv ᙹపᔑᱶᮥ᭥⦽݅ḡᱱ(multi-site) vᙹ༉᮹ʑჶᮝಽ༉⩶ᮥ

⪶ᰆ⦹۵ äᯕ ⦥᫵⧁ äᮝಽ ❱݉ࡽ݅. ᯕ᪡ ޵ᇩᨕ ʑ⬥ᄡ⪵

ᩑǍෝ᭥⧕ᕽʑ⬥ᄡ⪵᜽ӹญ᪅ෝ᯦ಆᯱഭಽ⪽ᬊ⧁ᙹᯩ۵

እᱶᔢᖒ ༉⩶ᮝಽ ⪶ᰆᯕ ⦥᫵⧁ äᮝಽ ❱݉ࡽ݅.

qᔍ᮹ɡ

ᅙᩑǍ۵⦽ǎÕᖅʑᚁᩑǍᬱᵝ᫵(᜽ऽ)ᔍᨦ(ḡᩎ✚ᖒᮥၹ

ᩢ⦽ᔢᖙĊᯱvᬑపᔾᔑʑᚁ}ၽ)᮹ᩑǍእḡᬱᨱ᮹⧕ᙹ⧪ࡹ

ᨩ᜖ܩ݅. ᱡᯱॅᮡᱥᇢݡ⦺ƱႊᰍᩑǍᖝ░ᨱᗭᗮࡹᨕᩑǍෝ

ᙹ⧪⦹ᩡ᜖ܩ݅.

References

Kim, B. S., Kang, K. S. and Seoh, B. H. (1999). “Low flow frequency analysis of streamflows from the stochastically generated daily rainfall series.” Journal of Korean Water Resources Association,

Vol. 32, No. 3, pp. 265-279.

Bellone, E., Hughes, J. P. and Guttorp, P. (2000). “A hidden markov model for downscaling synoptic atmospheric patterns to precipitation amounts.” Climate Research, Vol. 15, pp. 1-12.

Haan, C. T., Allen, D. M. and Street, J. O. (1976). “A markov chain model of daily rainfall.” Water Resour. Res., Vol. 12, No. 3, pp.

443-449.

Hughes, J. P. and Guttorp. P. (1994). “A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena.” Water Resour. Res., Vol. 30, No. 5, pp. 1535-1546.

Kwon, H. H. and Kim, B. S. (2009). “Development of statistical dwonscaling model using nonstationary markov chain.” Journal of Korean Water Resources Association, Vol. 42, No. 3, pp.

213-225.

Kwon, H.-H., Kim, J.-G. and Park, S.-H. (2013) “Derivation of flood frequency curve with uncertainty of rainfall and rainfall- runoff model.” Journal of Korean Water Resources Association, Vol. 46 No. 1, pp. 59-71.

Jung Y. H., Yi, C. S., Kim, H. S. and Shim, M. P. (2005).

“Estimation of needed discharge considering frequency based low flow in gabcheon basin.” Journal of Korean Society of Civil Engineer, Vol. 25, No. 2, pp. 97-105.

Heo, J.-H. (1997). “Introduction to statistical hydrology(v).”

Journal of Korean Water Resources Association, Vol. 30 No. 1, pp. 88-96.

Katz, R. W. (1996). “Use of conditional stochastic models to generate climate change scenarios.” Climate. Change, Vol. 32, pp. 237-255.

Kwon, H.-H. and So, B.-J. (2011). “Development of daily rainfall simulation model using piecewise kernel-pareto continuous distribution.” Journal of Korean Society of Civil Engineer, Vol.

31, No. 3B, pp. 277-284.

Kwon, H.-H., Lall, U. and Obeysekera, J. (2009). “Simulation of daily rainfall scenarios with interannual and multidecadal climate cycles for south florida.” Stochastic Environmental Research and Risk Assessment, Vol. 23, No. 7, pp. 879-896.

Lee, C. H. and Kim, S. (1995). “Estimation of mean annual and monthly precipitations in south korea by the regression analysis.”

Journal of Korean Society of Civil Engineer, Vol. 15, No. 5, pp.

1255-1266.

Nord, J. (1975). “Some applications of markov chains, proceedings fourth conference on probability and statistics in atmospheric science.” Tallahas, pp.125-130.

Development of Daily Rainfall Simulation Model Based on Homogeneous Hidden Markov Chain

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֫෮෉ ȵ׌೾୨ ȵจজฅ ȵ׌೾૽

Kwon, Hyun-Han*, Kim, Tae Jeong**, Hwang, Seok-Hwan***, Kim, Tae-Woong****

Development of Daily Rainfall Simulation Model Based on Homogeneous Hidden Markov Chain

ABSTRACT

Key words : Markov chain model, Homogeneous, Hidden markov chain model, Precipitation

Ⅹಾ

↽ɝʑ⬥ᄡ⪵ᩢ⨆ᮝಽᯙ⧕ᙹྙᄡ࠺ᖒᯕⓍí᷾aࡹŁᯩᮝ໑ᯕ్⦽ᄡ࠺ᖒᮥŁಅ⦹ʑ᭥⦽ႊᦩᮝಽᕽvᙹప༉᮹ၽᔾʑჶᨱݡ⦽ᵲ

᫵ᖒᯕݡࢱࡹŁᯩ݅. ᅙᩑǍᨱᕽ۵ᅖᰂ⦽vᙹၽᔾ➉▕ᮥᯙḡ⦹Łvᙹప᮹݅᧲⦽ᇥ⡍✚ᖒᮥŁಅ⧁ᙹᯩ۵⪝⧊ᇥ⡍ෝᯕᬊ⦽࠺ḩᖒ

Hidden Markov Chain(HMM) ༉⩶ᮥᱽᦩ⦹ᩡ݅. HMM ༉⩶᮹}ᖁ⬉ŝෝá᷾⦹ʑ᭥⧕ᕽʑ᳕Markov Chain ༉⩶ŝእƱ⦹ᩡᮝ໑

ᕽᬙš⊂ᗭၰᱥᵝš⊂ᗭෝݡᔢᮝಽᩑǍෝḥ⧪⦹ᩡ݅. ĥᱩvᙹపၰᯝvᙹప॒݅᧲⦽᜽eȽ༉ᨱᕽ༉⩶᮹ᱢ⧊ᖒᮥ⠪a⦹ʑ᭥⧕ᕽ

⃽ᯕ⪶ශ, ⠪Ɂ, ᇥᔑ, ᪽łࠥၰ℉ᩩ॒ࠥᮥእƱ⦹ᩡᮝ໑HMM ༉⩶ᯕʑ᳕Markov Chain ༉⩶ᨱእ⧕ᕽ}ᖁࡽ༉᮹܆ಆᮥ⪶ᯙ⧁ᙹᯩ

ᨩ݅. ✚⯩, HMM ༉⩶ᮡɚ⊹vᙹపᮥᰍ⩥⦹۵ߑᯩᨕᕽʑ᳕Markov Chain ༉⩶ᨱእ⧕ᕽᬵ॒⦽༉᮹܆ಆᮥᅕᩍᵝᨩ݅. ᯕ్⦽ᱱᨱᕽ

ᰆʑᮁ⇽పၰ⪶ශ⪮ᙹప॒ᮥᔑᱶ⦹ʑ᭥⦽᯦ಆᯱഭಽ⪽ᬊᯕ∊ᇥ⯩a܆⧁äᮝಽ❱݉ࡽ݅.

áᔪᨕ Markov chain ༉⩶, ࠺ḩᖒ, Hidden markov chain ༉⩶, vᙹ

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2. Markov Chain ʑၹᯝvᙹప༉᮹ʑჶ

2.1 ୨ঃনMarkov Chain Model

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֫෮෉ȵ׌೾୨ȵจজฅȵ׌೾૽

Kwon, Hyun-Han, Kim, Tae Jeong, Hwang, Seok-Hwan, Kim, Tae-Woong****

áᔪᨕ Markov chain ༉⩶, ࠺ḩᖒ, Hidden markov chain ༉⩶, vᙹ

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