Mobile QR Code QR CODE : Journal of the Korean Society of Civil Engineers

  1. ์ „๋ถ๋Œ€ํ•™๊ต ํ† ๋ชฉ๊ณตํ•™๊ณผ ๋ฐ•์‚ฌ์ˆ˜๋ฃŒ ๋ฐฉ์žฌ์—ฐ๊ตฌ์„ผํ„ฐ (Chonbuk National University)
  2. ์ „๋ถ๋Œ€ํ•™๊ต ํ† ๋ชฉ๊ณตํ•™๊ณผ ๋ถ€๊ต์ˆ˜, ๊ณตํ•™๋ฐ•์‚ฌ, ๋ฐฉ์žฌ์—ฐ๊ตฌ์„ผํ„ฐ (Chonbuk National University)
  3. ์ „๋ถ๋Œ€ํ•™๊ต ํ† ๋ชฉ๊ณตํ•™๊ณผ ๊ต์ˆ˜, ๊ณตํ•™๋ฐ•์‚ฌ (Chonbuk National University)


IDF ๊ณก์„ , Bayesian GLM, Scaling ํŠน์„ฑ, ๋ถˆํ™•์‹ค์„ฑ
IDF curve, Bayesian GLM, Scaling property, Uncertainty

  • 1. ์„œ ๋ก 

  • 2. ๋ณธ ๋ก 

  •   2.1 Scaling ํŠน์„ฑ

  •   2.2 Bayesian GLM ๋ชจํ˜•

  • 3. ์ ์šฉ ๋ฐ ๊ณ ์ฐฐ

  •   3.1 ๋Œ€์ƒ์œ ์—ญ ๋ฐ Scaling ํŠน์„ฑ ๋ถ„์„ ๊ฒฐ๊ณผ

  •   3.2 ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฒฐ๊ณผ

  • 4. ๊ฒฐ ๋ก  ๋ฐ ํ† ์˜

1. ์„œ ๋ก 

์ˆ˜๊ณต๊ตฌ์กฐ๋ฌผ ์„ค๊ณ„์— ์žˆ์–ด ์‹ ๋ขฐ์„ฑ ์žˆ๋Š” ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์‚ฐ์ •์€ ๋งค์šฐ ์ค‘์š”ํ•œ ๊ณผ์ • ์ค‘ ํ•˜๋‚˜๋ผ ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ผ๋ฐ˜์ ์œผ๋กœ ๊ตญ๋‚ด์—์„œ๋Š” ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์‚ฐ์ •์‹œ ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€์ž๋ฃŒ๋ฅผ ์ถ”์ถœํ•˜์—ฌ ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ด ์‚ฐ์ •ํ•˜๊ฒŒ ๋œ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๊ตญ๋‚ด์—์„œ๋Š” 30๋…„ ์ด์ƒ ์ž๋ฃŒ๋ฅผ ํ™•๋ณดํ•˜๊ณ  ์žˆ๋Š” ์ง€์ ์ด ๋งŽ์ง€ ์•Š์•„ ๊ฐ•์šฐ์ž๋ฃŒ์˜ ์ œ์•ฝ๊ณผ ๋ถ„์„์ƒ์˜ ํŽธ์˜๋ฅผ ์œ„ํ•ด ๋ช‡๋ช‡ ์ง€์†์‹œ๊ฐ„์— ๋Œ€ํ•œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ • ํ•œ ํ›„ IDF ๊ณก์„ ์„ ์ถ”์ •ํ•˜์—ฌ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์‚ฐ์ •์— ํ™œ์šฉํ•˜๊ณ  ์žˆ๋‹ค. ๊ตญ๋‚ด์™ธ์—์„œ ์ผ๋ฐ˜์ ์œผ๋กœ ์‚ฌ์šฉ๋˜๋Š” IDF ๊ณก์„ ์€ Sherman (1931)๊ณผ Bernard (1932) ์ด๋ž˜๋กœ ๋งŽ์€ ์ด๋ก  ๋ฐ ์‘์šฉ ์ˆ˜๋ฌธํ•™์—์„œ ์ฃผ์š” ์—ฐ๊ตฌ ๋ถ„์•ผ๋กœ ์ž๋ฆฌ ์žก๊ณ  ์žˆ๋‹ค.

์šฐ๋ฆฌ๋‚˜๋ผ์—์„œ๋Š” ์ผ๋ฐ˜์ ์œผ๋กœ IDF ๊ณก์„  ์‚ฐ์ •์‹œ Talbot, Sherman, ๋ฐ Heo et al. (1999)์ด ์ œ์•ˆํ•œ ํ†ตํ•ฉํ˜• ํ™•๋ฅ ๊ฐ•์šฐ๊ฐ•๋„์‹์„ ํ™œ์šฉํ•˜๊ณ  ์žˆ๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ IDF ๊ณก์„ ์€ ์ง€์†์‹œ๊ฐ„๊ณผ ์žฌํ˜„๊ธฐ๊ฐ„๋ณ„๋กœ ์‚ฐ์ •๋œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ํ†ตํ•œ ์ผ์ข…์˜ ํšŒ๊ท€๋ถ„์„์„ ์ˆ˜ํ–‰ํ•จ์œผ๋กœ์จ ๋ถ„์„๋˜์ง€ ์•Š์€ ์ง€์†์‹œ๊ฐ„์˜ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ๋‚ดยท์™ธ์‚ฝํ•˜์—ฌ ํ™œ์šฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ์•ˆ์ด๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ IDF ๊ณก์„ ์˜ ์ถ”์ •๊ณผ์ •์—์„œ ํšŒ๊ท€์‹์„ ์‚ฐ์ •ํ•˜์—ฌ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์ถ”์ •ํ•˜๋ฏ€๋กœ ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ด ์ถ”์ •ํ•œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰๊ณผ ๋‹ค์†Œ ์˜ค์ฐจ๊ฐ€ ๋ฐœ์ƒํ•  ๊ฐœ์—ฐ์„ฑ์ด ์žˆ๋‹ค(Kim et al., 2008). ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๊ทน์น˜์ž๋ฃŒ์˜ Scaling ํŠน์„ฑ๊ณผ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜๊ณ ์ž ํ•œ๋‹ค.

์ตœ๊ทผ ๊ตญ๋‚ด์™ธ์—์„œ ์ž๋ฃŒ์˜ Scaling ํŠน์„ฑ์„ IDF ๊ณก์„  ๋ถ„์„์— ์ด์šฉํ•œ ์—ฐ๊ตฌ๊ฐ€ ๋งŽ์ด ์ง„ํ–‰๋˜๊ณ  ์žˆ๋‹ค(Gupta and Waymire, 1993; Harris and Austin 1998; Deidda, 2000; Menabde and Sivapalan, 2000; Veneziano and Langousis, 2005). ์ด๋Š” Scaling ํŠน์„ฑ์ด ์ง€์†์‹œ๊ฐ„ D๋ฅผ ๊ฐ€์ง€๋Š” ๋‹ค์–‘ํ•œ ๊ฐ•์šฐ์‚ฌ์ƒ์˜ ๋ถ„ํฌํ˜•์„ ํŠน์„ฑํ™” ํ•˜๋Š”๋ฐ ์ด์šฉํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์ด ์žˆ๊ธฐ ๋•Œ๋ฌธ์ด๋‹ค. ๋˜ํ•œ ์ด๋Ÿฌํ•œ ๋ชจํ˜•๋“ค์€ ์ผ๋ฐ˜์ ์œผ๋กœ ์ง€์†์‹œ๊ฐ„ D์™€ ์žฌํ˜„๊ธฐ๊ฐ„ T๋ฅผ ๊ฐ€์ง€๋Š” ๊ฒฝํ—˜์ ์ธ IDF ๊ณก์„ ๋“ค๊ณผ ๋ฉฑํ•จ์ˆ˜(power function)ํ˜•ํƒœ๋ฅผ ๊ฐ€์ง€๊ณ  ์ถ”์ •ํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์ด ์žˆ๋‹ค(Willems, 2000). Menabde and Pegram (1999)๋Š” ๊ฐ„๋‹จํ•œ scaling ํŠน์„ฑ ๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ ์ง€์†์‹œ๊ฐ„๋ณ„ ๊ฐ•์šฐ์ž๋ฃŒ์˜ ๋ˆ„๊ฐ€ํ™•๋ฅ ๋ถ„ํฌ๋ฅผ ๊ธฐ๋ฐ˜์œผ๋กœ Scaling ํŠน์„ฑ ๋ถ„์„์„ ์ˆ˜ํ–‰ํ•˜๊ณ  IDF ๊ณก์„ ์„ ์ œ์‹œํ•˜์˜€์œผ๋ฉฐ, ์ด๋Š” ๊ธฐ์กด ์—ฐ๊ตฌ๋ณด๋‹ค ๊ฐ„ํŽธํ•˜๊ฒŒ IDF ๊ณก์„ ์„ ์–ป์„ ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒฐ๊ณผ๋ฅผ ๋„์ถœํ•˜์˜€๋‹ค. Yu et al. (2004)๋Š” Piecewise simple scaling๊ณผ Gumbel ๋ถ„ํฌ๋ฅผ ์—ฐ๊ฒฐํ•˜์—ฌ IDF ๊ณก์„  ์‚ฐ์ •์„ ์œ„ํ•œ Scaling ๊ณต์‹์„ ๊ฐœ๋ฐœํ•˜์˜€์œผ๋ฉฐ, ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€๊ฐ•์šฐ์ž๋ฃŒ์™€ ์ด์— ํ•ด๋‹นํ•˜๋Š” Moment ๊ฐ’์„ ํ™œ์šฉํ•˜์—ฌ Scaling ํŠน์„ฑ ๋ถ„์„์„ ์ˆ˜ํ–‰ํ•˜๊ณ , ๊ธฐ์กด IDF ๊ณก์„  ๊ฒฐ๊ณผ์™€ ๋น„๊ต ๊ฒฐ๊ณผ ์ œ์•ˆ๋œ ๋ชจํ˜•์ด ์šฐ์ˆ˜ํ•œ ์„ฑ๋Šฅ์„ ์ž…์ฆํ•˜๋Š” ๊ฒƒ์œผ๋กœ ๊ฒฐ๊ณผ๋ฅผ ๋„์ถœํ•˜์˜€๋‹ค. Garcรญa-Marรญn et al. (2013)์€ IDF ๊ณก์„ ์— ์ƒ์‘ํ•˜๋Š” ์Šค์ผ€์ผ ํŠน์„ฑ์„ ํ™œ์šฉํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜์  ํ™•๋ฅ ๋ถ„ํฌํ˜• ๋ชจ๋ธ์„ ํ™œ์šฉํ•˜์—ฌ IDF ๊ณก์„ ์„ ์‚ฐ์ •ํ•˜์˜€์œผ๋ฉฐ, ์ถ”์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰ํ™” ํ•˜์˜€๋‹ค.

์šฐ๋ฆฌ๋‚˜๋ผ์—์„œ๋Š” Shin et al. (2007)์€ ๊ธฐ์กด ์„ ํ˜•ํšŒ๊ท€๋ถ„์„์„ ํ†ตํ•ด ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ถ”์ •ํ•˜๋Š” ๋‹จ์ ์„ ๊ทน๋ณตํ•˜๊ธฐ ์œ„ํ•ด ์œ ์ „์ž์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ์ ์šฉํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ์œ ์ „์ž์•Œ๊ณ ๋ฆฌ์ฆ˜ ๊ธฐ๋ฒ•์ด ๋” ๋†’์€ ์ •ํ™•๋„๋ฅผ ๋ณด์—ฌ์ค€๋‹ค๋Š” ์—ฐ๊ตฌ ๊ฒฐ๊ณผ๋ฅผ ๋„์ถœํ•˜์˜€๋‹ค. Yoo et al. (2001)์€ ๊ตฌํ˜•ํŽ„์Šค๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ IDF ๊ณก์„ ์„ ์œ ๋„ํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์—ฌ ์ƒ๋Œ€์ ์œผ๋กœ ๊ฐ„๋‹จํ•œ IDF ๊ณก์„ ์„ ์œ ๋„ํ•  ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ, ๊ฐ•์ˆ˜๋ฅผ ๋ณด๋‹ค ์ ์ •ํžˆ ์ •๋Ÿ‰ํ™” ํ•˜์˜€๋‹ค. ๋˜ํ•œ ๊ธฐํ›„๋ณ€ํ™”์˜ ์˜ํ–ฅ์„ ๊ฐ„์ ‘์ ์œผ๋กœ ํŒŒ์•…ํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ์žฅ์ ์„ ์ œ์‹œํ•˜๋Š” ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰๋˜์–ด ์™”๋‹ค. ์ด์™ธ ๋‹ค์ˆ˜์˜ ๊ตญ๋‚ด์™ธ ์—ฐ๊ตฌ์—์„œ๋Š” IDF ๊ณก์„  ์‚ฐ์ •์‹œ ํ†ต๊ณ„ํ•™์  ๊ฐœ๋…์„ ๋„์ž…ํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜๋Š” ๊ฒฝํ–ฅ์ด ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ์กฐ์‚ฌ๋˜์—ˆ๋‹ค(Singh and Zhang, 2007; Ariff et al., 2012; Kuo et al., 2013). ์ง€์—ญ๋นˆ๋„ ํ•ด์„์˜ ๊ฒฝ์šฐ Kwon et al. (2013)๊ณผ Kim et al. (2014)์— ์ œ์‹œ๋œ ๋…ผ๋ฌธ์„ ์‚ดํŽด๋ณด๋ฉด ํ™•๋ฅ ๋ถ„ํฌํ˜•์˜ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ์ผ๋ฐ˜์ ์œผ๋กœ ์ตœ์šฐ๋„๋ฒ•์ด๋‚˜ L-๋ชจ๋ฉ˜ํŠธ ๋ฒ•์„ ํ™œ์šฉํ•˜์ง€๋งŒ, ๋‘๊ฐ€์ง€ ๋ฐฉ๋ฒ• ๋ชจ๋‘ ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ํ•ด์„ํ•˜๋Š”๋ฐ ์–ด๋ ค์›€์ด ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ์•Œ๋ ค์ ธ ์žˆ๋‹ค. ๋˜ํ•œ Katz et al. (2002) ์—ญ์‹œ L-๋ชจ๋ฉ˜ํŠธ๋ฒ•์˜ ๊ฒฝ์šฐ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์™ธ๋ถ€์ธ์ž(covariate)๋ฅผ ๊ณ ๋ คํ•  ์ˆ˜ ์—†๋Š” ๋‹จ์ ์ด ์กด์žฌํ•˜๋Š” ๊ฒฐ๊ณผ๋ฅผ ์ œ์‹œํ•œ๋ฐ” ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ๋ถˆํ™•์‹ค์„ฑ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•ด Bayesian ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•œ ์—ฐ๊ตฌ๊ฐ€ ๋‹ค์ˆ˜ ์ง„ํ–‰๋˜์—ˆ์œผ๋ฉฐ(James and Thomas, 2004; Daniel et al., 2007; Kwon et al., 2012), ๋ถˆํ™•์‹ค์„ฑ์˜ ์ •๋Ÿ‰ํ™”๋ฅผ ํ†ตํ•ด ์ถ”์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ฐ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ์‹ ๋ขฐ์„ฑ์„ ๋†’์ด๋Š” ์—ฐ๊ตฌ๊ฐ€ ์ง„ํ–‰๋˜์–ด ์ง€๊ณ  ์žˆ๋‹ค(Kwon et al., 2009; Lee et al., 2010).

์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ƒ๊ธฐ์™€ ๊ฐ™์ด ์ œ๊ธฐ๋œ ๋ฌธ์ œ๋ฅผ ๊ฐœ์„ ํ•˜๊ธฐ ์œ„ํ•ด ์ง€์†์‹œ๊ฐ„๋ณ„ ๊ฐ•์šฐ์ž๋ฃŒ์˜ Scaling ํŠน์„ฑ๊ณผ ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์„ ํ†ตํ•ฉํ•˜์—ฌ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ „๋ผ๋ถ๋„ ์œ ์—ญ๋‚ด 6๊ฐœ์˜ ๊ธฐ์ƒ์ฒญ ๊ด€์ธก์†Œ ์ง€์ ์„ ํ™œ์šฉํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€์œผ๋ฉฐ, IDF ๊ณก์„ ์„ ํ†ตํ•ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ •ํ•˜์˜€๋‹ค. ์ด๋•Œ ๊ณ„์ธต์  Bayesian ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•จ์œผ๋กœ์จ ์‚ฐ์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ฐ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰ํ™” ํ•  ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ, ์‹ ๋ขฐ์„ฑ ์žˆ๋Š” ์ง€์—ญ์  ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ทจ๋“ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ๋‹ค์Œ๊ณผ ๊ฐ™์ด ๊ตฌ์„ฑ๋˜์–ด ์žˆ๋‹ค. 1์žฅ์—์„œ๋Š” ๋…ผ๋ฌธ์˜ ์ด๋ก ์  ๋ฐฐ๊ฒฝ์— ๋Œ€ํ•ด ์„œ์ˆ ํ•˜์˜€์œผ๋ฉฐ, 2์žฅ์—์„œ๋Š” Scaling ํŠน์„ฑ ๋ฐ ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์— ๋Œ€ํ•ด ์„œ์ˆ ํ•˜์˜€๋‹ค. 3์žฅ์—์„œ๋Š” ๊ฐœ๋ฐœ๋œ ๋ชจํ˜•์„ ์ ์šฉํ•œ ๊ฒฐ๊ณผ๋ฅผ ์ˆ˜๋กํ•˜์˜€์œผ๋ฉฐ, 4์žฅ์—์„œ๋Š” ๊ฒฐ๋ก  ๋ฐ ํ† ์˜์— ๋Œ€ํ•ด ์ˆ˜๋กํ•˜์˜€๋‹ค.

2. ๋ณธ ๋ก 

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๋Œ€์ƒ์œ ์—ญ๋‚ด ์ง€์ ๋ณ„ ์ง€์†์‹œ๊ฐ„์— ๋Œ€ํ•œ Scaling ํŠน์„ฑ์„ ํŒŒ์•…ํ•˜๊ณ  ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค. ์ด๋•Œ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” Bayesian GLM ๊ฐœ๋…์„ ๋„์ž…ํ•˜์—ฌ ์‚ฐ์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ฐ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ์— ๋Œ€ํ•ด ์ •๋Ÿ‰ํ™” ํ•˜์˜€์œผ๋ฉฐ, ๋ณธ ์žฅ์—์„œ๋Š” ์ด์— ๋Œ€ํ•œ ์ด๋ก ์ ์ธ ์„ค๋ช…์„ ์ˆ˜๋กํ•˜์˜€๋‹ค.

2.1 Scaling ํŠน์„ฑ

์ผ๋ฐ˜์ ์œผ๋กœ ํ™•๋ณด๋œ ๊ฐ•์šฐ์ž๋ฃŒ์— ๋Œ€ํ•ด์„œ ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€์ž๋ฃŒ๋ฅผ ๊ตฌ์ถ•ํ•˜๊ณ  ์ด๋ฅผ ๋นˆ๋„ํ•ด์„ ๋ชจํ˜•์„ ํ†ตํ•ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์ถ”์ •ํ•˜๊ฒŒ ๋œ๋‹ค. ์ด๋•Œ ๋‹ค์–‘ํ•œ ์ง€์†์‹œ๊ฐ„ ๋ณ„ ๊ฐ•์šฐ์ž๋ฃŒ ์ทจ๋“์— ๋Œ€ํ•œ ์ œ์•ฝ๊ณผ ๋ถ„์„์ƒ์˜ ํŽธ์˜๋ฅผ ์œ„ํ•ด ํŠน์ • ์ง€์†์‹œ๊ฐ„์— ๋Œ€ํ•œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ๋จผ์ € ์‚ฐ์ •ํ•œ ํ›„ ์ด๋ฅผ IDF ๊ณก์„ ์œผ๋กœ ๋ณ€ํ™”ํ•˜์—ฌ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์‚ฐ์ •์— ํ™œ์šฉํ•˜๊ณ  ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๋งค๊ฐœ๋ณ€์ˆ˜ ์‚ฐ์ •์‹œ Sampling ์˜ค์ฐจ ์ฆ‰, ์ž๋ฃŒ ์—ฐํ•œ ๋ฐ ์‚ฌ์šฉ๋œ ํ™•๋ฅ ๋ถ„ํฌํ˜•์—์„œ ๊ธฐ์ธํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ์ด ์ƒ๋‹นํžˆ ํฌ๋ฉฐ, ์ด๋Ÿฌํ•œ ์ ์„ ๊ฐœ์„ ํ•˜๊ณ ์ž ๋‹ค์–‘ํ•œ ์—ฐ๊ตฌ๊ฐ€ ์ƒ๋‹น๋ถ€๋ถ„ ์ง„ํ–‰๋œ๋ฐ” ์žˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” Scaling ์„ฑ์งˆ์„ ์ด์šฉํ•œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์‚ฐ์ •์˜ ๊ธฐ๋ณธ ์ด๋ก ์€ Jung et al. (2008)๊ณผ Bougadis and Adamowski (2006)์ด ์ œ์‹œํ•œ Scaling ์„ฑ์งˆ์„ ํ™œ์šฉํ•˜์˜€๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๊ธฐ์กด Scaling ํŠน์„ฑ ๋ถ„์„ ๋ฐ ํ™œ์šฉ ์‹œ ๋‹ค์Œ ๋ฌธ์ œ์ ์„ ๊ฐœ์„ ํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜๊ณ ์ž ํ•˜์˜€๋‹ค.

1)์ผ๋ฐ˜์ ์œผ๋กœ IDF ๊ณก์„  ๊ฐœ๋ฐœ์‹œ ์ง€์†์‹œ๊ฐ„๋ณ„๋กœ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์ถ”์ • ํ›„ ์ด๋ฅผ ํšŒ๊ท€์‹์œผ๋กœ ์‚ฐ์ •ํ•˜๋Š” 2๋‹จ๊ณ„๋กœ ๊ตฌ์„ฑ๋˜์–ด ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ๊ฒฝ์šฐ ๋ชจํ˜• ๊ตฌ์ถ•์„ ์œ„ํ•ด ์‚ฌ์šฉ๋˜์—ˆ๋˜ ์ง€์†์‹œ๊ฐ„ ์ด์™ธ์˜ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์€ ๋‚ด์‚ฝ ๋ฐ ์™ธ์‚ฝ์˜ ํ˜•ํƒœ๋กœ ์ถ”์ •๋  ์ˆ˜ ๋ฐ–์— ์—†๋‹ค. ์ด๋Ÿฌํ•œ ๊ฒฝ์šฐ ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ํŠน์„ฑ์ด ๋ฐ˜์˜์ด ๋  ์ˆ˜ ์žˆ์œผ๋‚˜, ์ผ๋ถ€ ์˜ค์ฐจ๊ฐ€ ๋ฐœ์ƒํ•  ๊ฐ€๋Šฅ์„ฑ์ด ์—ฌ์ „ํžˆ ๋‚จ์•„์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ ์—์„œ ์ถ”์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜์™€ ์ง€์†์‹œ๊ฐ„์˜ ๊ด€๊ณ„๋ฅผ ๋ช…ํ™•ํ•˜๊ฒŒ ์ •๋Ÿ‰ํ™”ํ•˜๊ณ  ์ด๋ฅผ ํ•จ์ˆ˜์ ์œผ๋กœ ์ œ์‹œํ•จ์œผ๋กœ์„œ IDF ๊ณก์„ ์‹์˜ ์‹ ๋ขฐ์„ฑ์„ ๊ฐœ์„ ํ•˜๋Š” ๋ฐฉ๋ฒ•๋ก ์˜ ๊ฐœ๋ฐœ์ด ํ•„์š”ํ•˜๋ฉฐ, ์ด๋Ÿฌํ•œ ์ผ๋ จ์˜ ๋ถ„์„ ๊ณผ์ •์ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์ถ”์ • ์‹œ ๋™์‹œ์— ์ด๋ฃจ์–ด์ง€๋Š” ๊ฒƒ์ด ๋ฐ”๋žŒ์งํ•  ๊ฒƒ์œผ๋กœ ํŒ๋‹จ๋œ๋‹ค. ์ฆ‰, ์ผ๋ฐ˜์ ์œผ๋กœ Scaling ์‹œ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋จผ์ € ์ถ”์ •ํ•œ ํ›„ ์ด๋ฅผ ์ง€์†์‹œ๊ฐ„์˜ ํ•จ์ˆ˜๋กœ ํšŒ๊ท€๋ถ„์„ํ•˜๋Š” ๊ณผ์ •์„ ๊ฑฐ์น˜๋Š”๋ฐ ์ด๋Ÿฌํ•œ ๊ฒฝ์šฐ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •๊ณผ Scaling์ด ๋…๋ฆฝ์ ์œผ๋กœ ์ˆ˜ํ–‰๋˜์–ด ์ตœ์ ์˜ IDF ๊ณก์„ ์‹ ์ œ๊ณต์ด ์–ด๋ ค์šธ ๊ฒƒ์œผ๋กœ ํŒ๋‹จ๋œ๋‹ค.

2)ํ˜„์žฌ์˜ IDF ๊ณก์„ ์€ ์ผ๋ฐ˜์ ์œผ๋กœ ์ง€์ ๋นˆ๋„ํ•ด์„ ์ ˆ์ฐจ๋ฅผ ๊ธฐ์ค€์œผ๋กœ ์ˆ˜ํ–‰๋˜๊ณ  ์žˆ์œผ๋‚˜, ์œ ์‚ฌ์„ฑ์ด ์žˆ๋Š” ๊ฐ•์ˆ˜์ •๋ณด๋ฅผ ํ†ตํ•ฉ์ ์œผ๋กœ ํ™œ์šฉํ•˜๋Š” ๊ฒƒ์ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ €๊ฐ์‹œํ‚ฌ ์ˆ˜ ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ์•Œ๋ ค์ง€๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋Š” IDF ๊ณก์„ ์‹์˜ ๊ฐœ๋ฐœ์— ์žˆ์–ด์„œ๋„ ๋™์ผํ•˜๊ฒŒ ์ ์šฉ๋œ๋‹ค ํ•˜๊ฒ ๋‹ค. ์ฆ‰, ์œ ์‚ฌ์„ฑ์„ ๊ฐ€์ง€๋Š” ๊ฐ•์ˆ˜์ง€์ ์—์„œ์˜ Scaling ํŠน์„ฑ์„ ์ง€์—ญ์ ์œผ๋กœ ํ™•์žฅํ•˜๊ณ  ์ด๋ฅผ IDF๊ณก์„ ์‹ ๊ฐœ๋ฐœ๊นŒ์ง€ ์—ฐ๊ณ„ํ•˜๋Š” ๊ณผ์ •์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๊ฐ€ ์ƒ๋Œ€์ ์œผ๋กœ ๋ฏธ์ง„ํ•˜๋‹ค.

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ๋ฌธ์ œ์ ์„ ๊ฐœ์„ ํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฐœ๋…๊ณผ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ Scaling ํŠน์„ฑ์„ ํ†ตํ•ฉ์ ์œผ๋กœ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋Š” ํ•ด์„๋ฐฉ๋ฒ•์„ ๊ฐœ๋ฐœํ•˜๋Š”๋ฐ ๋ชฉ์ ์ด ์žˆ๋‹ค. ๋‹ค์‹œ ๋งํ•ด, ์œ ์‚ฌ์„ฑ์„ ๊ฐ€์ง€๋Š” ๋‹ค์ˆ˜์˜ ๊ฐ•์ˆ˜์ง€์ ์— ๋Œ€ํ•ด์„œ ๊ฐ ์ง€์ ๋ณ„ ํ™•๋ฅ ๋ถ„ํฌ ํŠน์„ฑ์„ ๊ณ ๋ คํ•จ๊ณผ ๋™์‹œ์— ์ง€์—ญ์  ํŠน์„ฑ์„ ๋ฐ˜์˜ํ•  ์ˆ˜ ์žˆ๋Š” ์ง€์—ญ๋นˆ๋„ํ•ด์„ ์ ˆ์ฐจ๋ฅผ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค. ์ด์™€ ํ•จ๊ป˜ ํ™•๋ฅ ๋ถ„ํฌํ˜•์˜ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ๋ถ„ํฌ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ Scaling ํŠน์„ฑ์„ ๋ช…ํ™•ํ•˜๊ฒŒ ๋ชจํ˜•์— ๋ฐ˜์˜ํ•˜๊ณ ์ž ํ•˜์˜€์œผ๋ฉฐ, ์ƒ๊ธฐ์— ๊ณผ์ •์„ ํ†ตํ•ฉ์ ์œผ๋กœ ์—ฐ๊ณ„ํ•œ ๋นˆ๋„ํ•ด์„ ๊ธฐ๋ฒ•์„ ๊ฐœ๋ฐœํ•˜๊ณ ์ž ํ•œ๋‹ค. ์ด๋ฅผ ํ†ตํ•ด ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ ์ •๋Ÿ‰ํ™”์™€ ๋”๋ถˆ์–ด ์‹ ๋ขฐ์„ฑ ์žˆ๋Š” ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰ ์ถ”์ •์— ์ฃผ์•ˆ์ ์„ ๋‘๊ณ  ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๊ณ„์ธต์  Bayesian ๊ธฐ๋ฒ•์„ ์ฃผ์š” ํ•ด์„ ๋ชจํ˜•์œผ๋กœ ๋„์ž…ํ•˜์˜€์œผ๋ฉฐ Scaling ํŠน์„ฑ์„ Bayesian GLM ๋ชจํ˜•๊ณผ ํ†ตํ•ฉํ•œ ์ด๋ก ์ ์ธ ๋ฐฐ๊ฒฝ์„ ๋‹ค์Œ ์ ˆ์— ์ œ์‹œํ•˜์˜€๋‹ค.

2.2 Bayesian GLM ๋ชจํ˜•

๋จผ์ € ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ž๋ฃŒํŠน์„ฑ์ด Gumbel ๋ถ„ํฌ๋ฅผ ๋”ฐ๋ฅธ๋‹ค๊ณ  ๊ฐ€์ •ํ•˜๊ณ  ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€๋‹ค. Gumbel ๋ถ„ํฌ์˜ ๊ฒฝ์šฐ ๋นˆ๋„ํ•ด์„์‹œ ์šฐ๋ฆฌ๋‚˜๋ผ์˜ ๋Œ€ํ‘œ๋ถ„ํฌํ˜•์œผ๋กœ ์ผ๋ฐ˜์ ์œผ๋กœ ํ™œ์šฉ๋˜๊ณ  ์žˆ๋Š” ํ™•๋ฅ ๋ถ„ํฌํ˜• ์ค‘ ํ•˜๋‚˜์ด๋‹ค. ์•„๋ž˜ Eqs. (1) and (2)๋Š” Gumbel ๋ถ„ํฌ์˜ ํ™•๋ฅ ๋ฐ€๋„ํ•จ์ˆ˜(probability density function)์™€ ๋ˆ„๊ฐ€ํ™•๋ฅ ๋ฐ€๋„ํ•จ์ˆ˜(cumulative density function)๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค.

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์ด๋•Œ PIC56D.gif๋Š” ์œ„์น˜๋งค๊ฐœ๋ณ€์ˆ˜(location parameter), PIC58E.gif๋Š” ๊ทœ๋ชจ๋งค๊ฐœ๋ณ€์ˆ˜(scale parameter)๋ฅผ ์˜๋ฏธํ•œ๋‹ค. ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜์˜ Scaling ํŠน์„ฑ๊ณผ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜๊ณ ์ž ํ•˜๋ฉฐ, ์ด๋ฅผ ๋ชจํ˜•ํ™” ํ•˜์˜€๋‹ค. ๋จผ์ € ๊ฐ•์šฐ์ง€์  PIC5BE.gif, ์‹œ๊ฐ„ PIC5FD.gif, ์ง€์†์‹œ๊ฐ„ PIC64C.gif์— ๋Œ€ํ•œ ์—ฐ์ตœ๋Œ€์น˜ ์ž๋ฃŒ PIC66C.gif๊ฐ€ ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด Gumbel ๋ถ„ํฌ๋ฅผ ๋”ฐ๋ฅธ๋‹ค๊ณ  ๊ฐ€์ •ํ•˜๋ฉด Eq. (3)๊ณผ ๊ฐ™์ด ๋‚˜ํƒ€๋‚ผ ์ˆ˜ ์žˆ๋‹ค. Eq. (3)์—์„œ PIC68D.gif๋Š” ์œ„์น˜๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ด๋ฉฐ, PIC6AD.gif๋Š” ๊ทœ๋ชจ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚˜๊ฒŒ ๋œ๋‹ค. ์œ„์น˜๋งค๊ฐœ๋ณ€์ˆ˜์™€ ๊ทœ๋ชจ๋งค๊ฐœ๋ณ€์ˆ˜๋Š” Eqs. (4) and (5)์™€ ๊ฐ™์ด ์ง€์†์‹œ๊ฐ„(PIC6CD.gif)์— ๋Œ€ํ•œ ํ•จ์ˆ˜๋กœ์„œ ์ •์˜ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์ด๋•Œ PIC6ED.gif๋Š” ๊ฐ ๊ฐ•์šฐ์ง€์  PIC6FE.gif์—์„œ์˜ Scaling ํŠน์„ฑ์„ Gumbel ๋ถ„ํฌํ˜•์— ํ†ตํ•ฉํ•˜๊ธฐ ์œ„ํ•œ ํšŒ๊ท€๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค. ์ฆ‰, ๋งค๊ฐœ๋ณ€์ˆ˜๋Š” GLM ํ˜•ํƒœ์˜ ๋ชจํ˜•์„ ๊ตฌ์„ฑํ•˜๋ฉฐ ๊ณ„์ธต์  Bayesian ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•˜์—ฌ ์ง€์ ๋ณ„ ์‚ฌํ›„๋ถ„ํฌ(posterior distribution)๋ฅผ ์ถ”์ •ํ•˜์˜€๋‹ค.

PIC75D.gif

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PIC82C.gif

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๊ฐ ๊ฐ•์šฐ์ง€์  PIC86C.gif์— ํšŒ๊ท€๋งค๊ฐœ๋ณ€์ˆ˜ PIC88D.gif๋Š” ์ •๊ทœ๋ถ„ํฌ๋ฅผ ๋”ฐ๋ฅด๋ฉฐ ๊ฐ ๋งค๊ฐœ๋ณ€์ˆ˜๋Š” ์ „์ฒด ๊ฐ•์šฐ์ง€์ ์„ ํฌ๊ด„ํ•˜๋Š” ์ƒ์œ„ ๋‹จ๊ณ„์˜ ํ‰๊ท ๊ฐ’ PIC8AD.gif์™€ ๋ถ„์‚ฐ PIC8CD.gif์„ ๊ฐ€์ง€๋Š” ์ •๊ทœ๋ถ„ํฌ ์˜ํ•ด์„œ ์กฐ์ •๋˜๋ฉฐ ์ด๋Š” Eq. (6)๊ณผ ๊ฐ™์ด ํ‘œํ˜„ํ•  ์ˆ˜ ์žˆ๋‹ค. ์ด๋•Œ PIC8ED.gif์™€ PIC90E.gif๋Š” Bayesian ๋ชจํ˜• ํ•˜์—์„œ ๊ณ„์ธต์  ๋…ธ๋“œ๋ฅผ ๊ฐ€์ง€๊ณ  Hyper-parameter์— ์˜ํ•ด์„œ ์กฐ์ •์ด ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ•˜์˜€์œผ๋ฉฐ, ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ํšŒ๊ท€๋ถ„์„์‹œ ์ถ”์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๊ฐ’์—์„œ ์–‘(+), ์Œ(-)์˜ ์ œํ•œ์ด ์—†์–ด์•ผ ํ•˜๊ธฐ ๋•Œ๋ฌธ์— ์ด๋Ÿฌํ•œ ๊ธฐ๋ณธ ์ด๋ก ์„ ๋งŒ์กฑํ•˜๊ณ ์ž ์ •๊ทœ๋ถ„ํฌ๋ฅผ ์‚ฌ์ „๋ถ„ํฌ๋กœ ํ™œ์šฉํ•˜์˜€๋‹ค. ์ด์™€ ๋”๋ถˆ์–ด Hyper-parameter PIC92E.gif, PIC94E.gif์˜ ๊ฒฝ์šฐ ๊ฐ๊ฐ ์ •๊ทœ๋ถ„ํฌ์™€ Gamma๋ถ„ํฌ๋ฅผ ๊ฐ–๋Š”๋‹ค๊ณ  ๊ฐ€์ •ํ•˜์˜€๋‹ค. Hyper-parameter ๋ถ„์‚ฐ์˜ ๊ฒฝ์šฐ ํ•ญ์ƒ ์–‘์˜ ๊ฐ’์„ ๊ฐ€์ ธ์•ผํ•˜๊ธฐ ๋•Œ๋ฌธ์— Gamma ๋ถ„ํฌ๋ฅผ ์‚ฌ์ „๋ถ„ํฌ๋กœ ํ™œ์šฉํ•˜์˜€๋‹ค. ์ฆ‰, ์ •๊ทœ๋ถ„ํฌ์˜ ๊ฒฝ์šฐ ๋ถ„ํฌ ํŠน์„ฑ์ƒ ์–‘(+), ์Œ(-)์„ ๋ชจ๋‘ ํฌํ•จํ•  ์ˆ˜ ์žˆ๋Š” ํ™•๋ฅ ๋ถ„ํฌํ˜•์ด๋ฉฐ, Gamma ๋ถ„ํฌ์˜ ๊ฒฝ์šฐ ์–‘(+)์˜ ๊ฐ’์„ ๋„์ถœํ•˜๊ธฐ ์œ„ํ•ด ์‚ฌ์šฉ๋˜๋Š” ํ™•๋ฅ ๋ถ„ํฌํ˜•์ด๋‹ค. ์ด๋•Œ ํšŒ๊ท€๋งค๊ฐœ๋ณ€์ˆ˜์— ์ž˜๋ชป๋œ ํ™•๋ฅ ๋ถ„ํฌํ˜•(ex. GEV, Gumbel ๋“ฑ)์„ ๋ถ€์—ฌํ•œ๋‹ค๋ฉด ์ถ”์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜๊ฐ€ ์–‘์˜ ๊ฐ’์œผ๋กœ๋งŒ ๋„์ถœ๋˜๊ธฐ ๋•Œ๋ฌธ์— ์ถ”์ •๋˜๋Š” ํ™•๋ฅ ๊ฐ•์šฐ๋Ÿ‰์ด ๋น„ํ˜„์‹ค์ ์œผ๋กœ ์ปค์งˆ ๊ฐœ์—ฐ์„ฑ์ด ์žˆ์œผ๋ฉฐ, ์ด๋Š” ๋‹ค์ˆ˜์˜ ๋…ผ๋ฌธ์—์„œ ์ œ์‹œ๋œ๋ฐ” ์žˆ๋‹ค(Gelman et al., 2004; Kwon and Myeong, 2011; Kim et al., 2014; Kim et al., 2016).

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๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ƒ๊ธฐ์™€ ๊ฐ™์€ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ถ”์ •ํ•˜๊ธฐ ์œ„ํ•ด Markov Chain Monte Carlo (MCMC) ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜๋“ค์˜ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ์ถ”์ •ํ•˜์˜€๋‹ค. ์ฆ‰, ๊ฐ ์‚ฌ์ „๋ถ„ํฌ์™€ ์šฐ๋„์™€์˜ ๊ด€๊ณ„๋ฅผ Bayesian ๋ชจํ˜•๋‚ด์—์„œ ์‚ฌํ›„๋ถ„ํฌ๊ฐ€ ์ถ”์ •์ด ๊ฐ€๋Šฅํ•œ ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€์œผ๋ฉฐ, ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” MCMC ๊ธฐ๋ฒ• ์ค‘ Gibbs Sampling์„ ํ™œ์šฉํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ถ”์ •ํ•˜์˜€๋‹ค. Bayes ์ด๋ก ์„ ๊ธฐ๋ฐ˜์œผ๋กœ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ์ •๋ฆฌํ•˜๋ฉด ๋‹ค์Œ Eq. (11)๊ณผ ๊ฐ™๋‹ค. ์ด๋•Œ PICC88.gif๋Š” ๋ฒกํ„ฐ์ž๋ฃŒ๋กœ์„œ ๊ฐ ๊ฐ•์šฐ๊ด€์ธก์ง€์ ์˜ ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€์น˜์ž๋ฃŒ๋ฅผ ์˜๋ฏธํ•œ๋‹ค.

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์—ฌ๊ธฐ์„œ, PICDB3.gif์œผ๋กœ์„œ PICDD3.gif์€ ํ•ด๋‹น์œ ์—ญ์˜ ๊ฐ•์ˆ˜ ์ง€์ ์˜ ์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค. PICE03.gif๋Š” ์‚ฌ์ „๋ถ„ํฌ๋ฅผ PICE42.gif๋Š” ์šฐ๋„ํ•จ์ˆ˜๋ฅผ ๋‚˜ํƒ€๋‚ด๋ฉฐ ๋‹ค์Œ Eq. (12)์™€ ๊ฐ™์ด ํ‘œํ˜„ํ•  ์ˆ˜ ์žˆ๋‹ค.

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์ตœ์ข…์ ์œผ๋กœ ๋ชจ๋“  ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ง์ ‘์ ์œผ๋กœ ์ถ”์ •ํ•˜๊ธฐ๋Š” ๋ถˆ๊ฐ€๋Šฅํ•˜๊ธฐ ๋•Œ๋ฌธ์— ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” MCMC ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•˜์—ฌ ๊ฐ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ์ถ”์ •ํ•˜์˜€๋‹ค. ์ด๋•Œ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์ˆ˜๋ ด์„ฑ์„ ํ™•์ธํ•˜๊ธฐ ์œ„ํ•ด Bayesian ๋ชจํ˜•๋‚ด์—์„œ 3๊ฐœ์˜ Chain์„ ๋…๋ฆฝ์ ์œผ๋กœ ์‹œํ–‰ํ•˜์˜€์œผ๋ฉฐ, 10,000๋ฒˆ ๋ชจ์˜ ๋ฐœ ์ƒ ์ค‘ 8,000๋ฒˆ์€ ์ œ๊ฑฐ(burn-in) ํ•˜๊ณ , ๋‚˜๋จธ์ง€ 2,000๊ฐœ์˜ Sample์„ ํ™œ์šฉํ•˜์—ฌ ๊ฐ ๋งค๊ฐœ๋ณ€์ˆ˜ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ์‚ฐ์ •ํ•˜์˜€๋‹ค.

3. ์ ์šฉ ๋ฐ ๊ณ ์ฐฐ

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๋Œ€์ƒ์œ ์—ญ ์ž๋ฃŒ๊ณ„์—ด์˜ Scaling ๊ฐ€๋Šฅ์„ฑ์„ ํŒŒ์•…ํ•˜๊ธฐ ์œ„ํ•ด ์ง€์ ๋ณ„ ๊ฐ•์ˆ˜๋Ÿ‰์— ๋Œ€ํ•ด ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ์ถ”์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜์— ๋Œ€ํ•ด์„œ ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ณ€ํ™” ์–‘์ƒ์„ Bayesian GLM ๊ธฐ๋ฒ•์„ ์ด์šฉํ•˜์—ฌ ํ•จ์ˆ˜ํ™” ํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ ๋ฐฉ๋ฒ•์— ๋Œ€ํ•œ ์š”์•ฝ์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

1)๋จผ์ € ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ „๋ผ๋ถ๋„ ์œ ์—ญ๋‚ด 6๊ฐœ ๊ด€์ธก์†Œ๋ฅผ ๋Œ€์ƒ์œผ๋กœ 1973~2014๋…„ ๊นŒ์ง€ ๊ด€์ธก๋œ ์‹œ๊ฐ„๊ฐ•์ˆ˜๋Ÿ‰ ์ž๋ฃŒ๋ฅผ ํ™œ์šฉํ•˜์—ฌ ์ง€์†์‹œ๊ฐ„๋ณ„(1, 2, 3, 4, 5, 6, ..., 24, 48, 72)๋กœ ์—ฐ์ตœ๋Œ€๊ฐ•์ˆ˜๋Ÿ‰ ์ถ”์ถœ ํ›„ Gumbel ํ™•๋ฅ ๋ถ„ํฌํ˜•์„ ๋Œ€ํ‘œํ™•๋ฅ ๋ถ„ํฌ๋กœ ๊ฐ€์ •ํ•˜์—ฌ ๋นˆ๋„ํ•ด์„์„ ์ง„ํ–‰ํ•˜์˜€๋‹ค.

2)์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์œ„ํ•ด Scaling ํŠน์„ฑ๊ณผ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๊ณ„์ธต์  Bayesian๊ธฐ๋ฒ•์„ ๋„์ž…ํ•˜์—ฌ ํ†ตํ•ฉ ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€์œผ๋ฉฐ, ์ง€์  ๋ฐ ์ง€์—ญ์„ ๋Œ€ํ‘œํ•˜๋Š” IDF ๊ณก์„ ์„ ์‚ฐ์ •ํ•˜์˜€๋‹ค.

3)์ตœ์ข…์ ์œผ๋กœ Bayesian GLM ๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ ์‚ฐ์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ฐ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์ œ์‹œํ•˜์˜€๋‹ค.

3.1 ๋Œ€์ƒ์œ ์—ญ ๋ฐ Scaling ํŠน์„ฑ ๋ถ„์„ ๊ฒฐ๊ณผ

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ „๋ผ๋ถ๋„ ์œ ์—ญ์„ ์„ ์ •ํ•˜์˜€์œผ๋ฉฐ, ๊ธฐ์ƒ์ฒญ ์‚ฐํ•˜ 6๊ฐœ ๊ด€์ธก์†Œ(๊ตฐ์‚ฐ, ์ „์ฃผ, ๋ถ€์•ˆ, ์ •์, ๋‚จ์›, ์ž„์‹ค)๋ฅผ ๋Œ€์ƒ์œผ๋กœ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ๋Œ€์ƒ์œ ์—ญ์˜ ๊ฐ•์ˆ˜์ง€์ ์€ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์œ„ํ•œ ์ด์งˆ์„ฑ ์ฒ™๋„ ๋ฐ ๋™์งˆ์„ฑ ๊ฒ€์ฆ์€ Kwon et al. (2013)์— ์˜ํ•ด์„œ ์ˆ˜ํ–‰๋œ ๋ฐ” ์žˆ์œผ๋ฉฐ 6๊ฐœ ์ง€์  ๋ชจ๋‘ ๋™์งˆ์„ฑ์„ ๊ฐ€์ง€๋Š” ์ง€์ ์ด๋‹ค. ๋จผ์ € ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์•ž์„œ ๊ฐ€์ •ํ•œ Gumbel ๋ถ„ํฌํ˜•์˜ ์ ํ•ฉ์„ฑ์„ ํŒ๋‹จํ•˜๊ธฐ ์œ„ํ•ดFig. 1 ๊ณผ ๊ฐ™์ด ๊ตฐ์‚ฐ๊ด€์ธก์†Œ์— ๋Œ€ํ•ด์„œ ๋Œ€ํ‘œ์ ์œผ๋กœ Gumbel ๋ถ„ํฌ ํ™•๋ฅ ์ง€์— ๋„์‹œํ•˜์—ฌ ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€์ž๋ฃŒ๋ฅผ ํ™•์ธํ•˜์˜€๋‹ค. ๋˜ํ•œ ์ ํ•ฉ์„ฑ ํ‰๊ฐ€๋ฅผ PICED1.gif๊ฒ€์ •, KS๊ฒ€์ •, CVM๊ฒ€์ •, PPCC๋ฅผ ํ™œ์šฉํ•˜์—ฌ ์ˆ˜ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ์ ํ•ฉ์„ฑ ๊ฒ€์ •๊ฒฐ๊ณผ 6๊ฐœ ๊ด€์ธก์ง€์  ๋ชจ๋‘ ์œ ์˜์ˆ˜์ค€ 5%์—์„œ ์ ํ•ฉ์„ฑ์„ ํ†ต๊ณผํ•˜๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” Gumbel ๋ถ„ํฌ๋ฅผ ๋Œ€ํ‘œ ํ™•๋ฅ ๋ถ„ํฌํ˜•์œผ๋กœ ์‚ฌ์šฉํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€๋‹ค. Table 1 ์€ ๋ณธ ์—ฐ๊ตฌ์—์„œ ํ™œ์šฉํ•œ 6๊ฐœ ์ง€์ ์˜ ์ง€์†์‹œ๊ฐ„๋ณ„ ๊ธฐ๋ณธ ํ†ต๊ณ„์น˜๋ฅผ ์‚ฐ์ •ํ•œ ๊ฒฐ๊ณผ์ด๋‹ค.

Fig. 1

Goodness-of-fit Test Through Gumbel Probability Plot at Gunsan Station

Figure_KSCE_37_01_04_F1.jpg
Table 1. Basic Statistics of Annual Maximum Data According to Different Durations Over the Six StationsTable_KSCE_37_01_04_T1.jpg
Table 1. Basic Statistics of Annual Maximum Data According to Different Durations Over the Six Stations(Continue)Table_KSCE_37_01_04_T1_1.jpg

Fig. 2๋Š” ์ง€์†์‹œ๊ฐ„๋ณ„ ๊ทน์น˜์‹œ๊ฐ„์ž๋ฃŒ๊ณ„์—ด์˜ Scaling์„ ํŒŒ์•…ํ•˜๊ธฐ ์œ„ํ•ด Eqs. (4) and (5)๋ฅผ ํ™œ์šฉํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„์„ ์‚ฐ์ •ํ•œ ๊ฒฐ๊ณผ๋ฅผ ๋‚˜ํƒ€๋‚ธ ๊ฒƒ์ด๋‹ค. Fig. 2์—์„œ ํšŒ์ƒ‰์˜ ๊ตฌ๊ฐ„์€ Bayesian GLM ๋ชจํ˜•์„ ํ†ตํ•ด ๋„์ถœ๋œ ๊ฐ ์ง€์ ๋ณ„ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„(2.5, 97.5%)์„ ๋‚˜ํƒ€๋‚ด๋ฉฐ, ๋นจ๊ฐ„ ์‹ค์„ ์€ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„์˜ 50% Quantile์„ ์˜๋ฏธํ•œ๋‹ค. ์ด๋•Œ ๊ฒ€์€ ๋ณ„์€ ์ง€์†์‹œ๊ฐ„๋ณ„๋กœ ์ง€์ ๋ณ„ ๊ธฐ์กด ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๋ฐฉ๋ฒ•(Hosking et al., 1985)์„ ํ™œ์šฉํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์‚ฐ์ •ํ•œ ๊ฒฐ๊ณผ์ด๋‹ค. ๊ธฐ๋ฒ•๋ณ„ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋น„๊ตํ•ด ๋ณธ ๊ฒฐ๊ณผ ์ง€์  ๋ฐ ์ง€์†์‹œ๊ฐ„๋ณ„ ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ชจ๋‘ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„ ๋‚ด์— ๋‚ดํฌํ•˜๊ณ  ์žˆ์œผ๋ฉฐ, ์ง€์ ๋ณ„๋กœ ์ถ”์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜์™€ ํ•จ์ˆ˜๋กœ๋ถ€ํ„ฐ ์ถ”์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜๊ฐ€ ๊ฑฐ์˜ ์œ ์‚ฌํ•œ ๊ฑฐ๋™์„ ํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค.

Fig. 2

Estimated Parameters of Gumbel Distribution using Bayesian GLM Model with Scaling Properties, Their Uncertainty for Each Station. The Black Stars Indicate at Site Estimates and the Red Line Indicates a Median Value Estimated from the Scaling Function

Figure_KSCE_37_01_04_F2.jpg

๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด Bayesian GLM ๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ด ๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆํ•˜๊ณ ์ž ํ•˜๋Š” Bayesian GLM ๋ชจํ˜•์˜ ์ ํ•ฉ์„ฑ์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ์ ํ•ฉ์„ฑ ํ‰๊ฐ€ ๋ฐฉ๋ฒ•์€ ์ผ๋ฐ˜์ ์œผ๋กœ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ์‚ฌ์šฉ๋˜์–ด์ง€๋Š” ์ตœ์šฐ๋„๋ฒ• ๋ฐฉ๋ฒ•๊ณผ Bayesian GLM ๋ชจํ˜•์„ ํ†ตํ•ด ๋„์ถœ๋œ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ด์šฉํ•˜์—ฌ ์ง€์†์‹œ๊ฐ„ ๋ฐ ๋นˆ๋„๋ณ„๋กœ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ •ํ•˜์˜€์œผ๋ฉฐ, ๋„์ถœ๋œ ์ง€์ ๋นˆ๋„ํ•ด์„๊ฒฐ๊ณผ๋Š” IDF ๊ณก์„ ์„ ํ†ตํ•ด Fig. 3์— ๋„์‹œํ•˜์˜€๋‹ค. Fig. 3์„ ์‚ดํŽด๋ณด๋ฉด ์ง€์ ๋ณ„๋กœ Bayesian GLM์„ ํ†ตํ•ด ๋ชจ์˜ํ•œ ๊ฒฐ๊ณผ์™€ ๊ฐ ์ง€์ ๋ณ„ IDF ๊ณก์„ ์ด ์œ ์‚ฌํ•œ ๊ฒฐ๊ณผ๋ฅผ ๋„์ถœํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ๋‹ค. ์ด์— ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” Bayesian GLM ๋ชจํ˜•์„ ํ†ตํ•ด ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ๊ธฐ์กด ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฒฐ๊ณผ์™€ ๋น„๊ตยท๋ถ„์„ํ•œ ์ •๋Ÿ‰์  ๊ฒฐ๊ณผ๋Š” Table 2์— ์ œ์‹œํ•˜์˜€๋‹ค. ์ง€์ ๋ณ„ ์•„๋ž˜ ๊ด„ํ˜ธ ์•ˆ์€ ์ง€์†์‹œ๊ฐ„์„ ์˜๋ฏธํ•œ๋‹ค.

Fig. 3

Comparison of IDF Curve between the Point Rainfall Frequency Analysis and the Scaling Function Based Regional Frequency Analysis, According to Duration and Return Period

Figure_KSCE_37_01_04_F3.jpg
Table 2. Design Rainfalls and Their Uncertainty Bound Estimated from Posterior Distribution Table_KSCE_37_01_04_T2.jpg

3.2 ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฒฐ๊ณผ

์•ž์„œ ๊ฒ€์ฆ๋œ ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ ์ „๋ผ๋ถ๋„ ์œ ์—ญ์„ ๋Œ€์ƒ์œผ๋กœ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ์˜ ์ฃผ์š” ๋ชจํ˜•์ธ ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์˜ ์žฅ์ ์€ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰ํ™”ํ•จ๊ณผ ๋™์‹œ์— ์—ฌ๋Ÿฌ ์ง€์ ์˜ ์ž๋ฃŒ ํŠน์„ฑ์„ ์ข…ํ•ฉ์ ์œผ๋กœ ๊ณ ๋ คํ•˜์—ฌ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์‚ฐ์ •ํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฒƒ์ด๋‹ค. ์ฆ‰, ๊ณ„์ธต์  Bayesian ๋ชจํ˜• ๋‚ด์—์„œ ์ง€์ ๋ณ„๋กœ ์‚ฐ์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜๋Š” ์ƒ์œ„ ๋‹จ๊ณ„์— Hyper-parameter๋ฅผ ํ†ตํ•˜์—ฌ ํ•˜๋‚˜์˜ ์ง€์—ญ๋งค๊ฐœ๋ณ€์ˆ˜๋กœ Shrinkage ๋˜๋ฉฐ, ๊ฐœ๋ณ„ ์ง€์ ๋ณ„๋กœ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ถ”์ •ํ•˜๋Š” ๊ฒƒ์— ๋น„ํ•ด ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ๊ฐ์†Œ์‹œํ‚ฌ ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์ด ์žˆ๋‹ค(Kwon et al., 2013, Kim et al., 2014). ์ด๋Š” ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์˜ ์žฅ์  ์ค‘ ํ•˜๋‚˜๋ผ๊ณ  ํ•  ์ˆ˜ ์žˆ์œผ๋ฉฐ, ์œ ์‚ฌํ•œ ์ •๋ณด๋ฅผ ๊ฐ€์ง€๋Š” ์ง€์ ๊ฐ„์˜ ๋นˆ๋„ํ•ด์„ ์ˆ˜ํ–‰ ์‹œ ๋ณด๋‹ค ์‹ ๋ขฐ์„ฑ ์žˆ๋Š” ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ • ํ•  ์ˆ˜ ์žˆ๋Š” ๊ฒƒ์ด๋‹ค. Fig. 4์—์„œ 6๊ฐœ์˜ ํŒŒ๋ž€์ƒ‰ ์„ ์€ ์ง€์ ๋ณ„ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ๋‚˜ํƒ€๋‚ด์—ˆ์œผ๋ฉฐ, ๋นจ๊ฐ„์ƒ‰ ์„ ์€ Bayesian GLM ๋ชจํ˜•์œผ๋กœ ๋„์ถœ๋œ ์ง€์—ญ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์‚ฌํ›„๋ถ„ํฌ๋ฅผ ๋‚˜ํƒ€๋‚ธ๋‹ค. Table 3์€ ๊ฐ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„์„ ์ •๋žต์ ์œผ๋กœ ์ œ์‹œํ•œ ๊ฒฐ๊ณผ์ด๋‹ค.

Table 3. The Estimated Parameters and Their Uncertainty Bound for Each Station and Hyper-Parameter using a Hierarchical Bayesian Model Table_KSCE_37_01_04_T3.jpg
Fig. 4

Marginal Posterior Distribution of the Parameters Derived from the Hierarchical Bayesian Model Parameters. The Blue Lines Indicates a Marginal Posterior Distribution for Each Station and the Red Line Indicates a Hyper-Parameter (i.e. Regional Parameters)

Figure_KSCE_37_01_04_F4.jpg

์ตœ์ข…์ ์œผ๋กœ Bayesian GLM ๋ชจํ˜•๊ธฐ๋ฐ˜์˜ Scaling ํ•จ์ˆ˜๋ฅผ ํ†ตํ•ด ์ถ”์ •๋œ ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„(2.5, 50, 97.5%)์„ ํ™œ์šฉํ•˜์—ฌ ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•˜๊ณ , ์‚ฐ์ •๋œ ๊ฒฐ๊ณผ๋ฅผ IDF ๊ณก์„ ์œผ๋กœ ์ž‘์„ฑํ•˜์—ฌ Fig. 5์— ๋„์‹œํ•˜์˜€๋‹ค. Fig. 5์— ๋„์‹œ๋œ ๊ฒฐ๊ณผ๋ฅผ ์‚ดํŽด๋ณด๋ฉด ๋นˆ๋„๋ณ„๋กœ ์‚ฐ์ •๋œ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„์ด ํฌ์ง€ ์•Š๋Š” ๊ฒƒ์„ ํ™•์ธ ํ•  ์ˆ˜ ์žˆ๋Š”๋ฐ ์ด๋Š” ์ „๋ผ๋ถ๋„ ์œ ์—ญ๋‚ด ๊ธฐ์ƒ์ฒญ ๊ด€์ธก์†Œ ์ž๋ฃŒ๊ฐ€ ๋™์งˆ์„ฑ ๋ฐ ์ด์งˆ์„ฑ์˜ ํ™•๋ณด, ๋˜ํ•œ ์ž๋ฃŒ๊ฐ„์˜ ์ •๋ณด๊ณต์œ ๊ฐ€ ํšจ๊ณผ์ ์œผ๋กœ ์ด๋ฃจ์–ด์ง€๋Š” ๊ฒƒ์œผ๋กœ ํ•ด์„ํ•  ์ˆ˜ ์žˆ๋‹ค. ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด Bayesian ๊ธฐ๋ฒ•์€ ์œ ์‚ฌํ•œ ํ†ต๊ณ„์  ์„ฑ์งˆ์„ ์ง€๋‹Œ ์ง‘๋‹จ์˜ ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ๋ถˆํ™•์‹ค์„ฑ์„ ์ค„์—ฌ์ฃผ๋Š” ์žฅ์ ์ด ์žˆ์œผ๋ฉฐ(Gelman et al., 2004), ์ถ”์ •๋œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ ๊ตฌ๊ฐ„์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์ œ์‹œํ•จ์œผ๋กœ์จ ๋ณธ ์—ฐ๊ตฌ๊ฒฐ๊ณผ์˜ ์‹ ๋ขฐ์„ฑ์„ ํ™•๋ณดํ•˜์˜€๋‹ค(Table 4).

Fig. 5

The IDF Curve Based on Hierarchical Bayesian Model Based Regional Frequency Model using Scaling Function

Figure_KSCE_37_01_04_F5.jpg
Table 4. The Design Rainfalls and Their Uncertainties using the Scaling Function Based Regional Frequency Analysis Table_KSCE_37_01_04_T4.jpg

์ตœ์ข…์ ์œผ๋กœ Fig. 6์€ ๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์•ˆ๋œ ๋ฐฉ๋ฒ•์„ ํ†ตํ•ด ๋„์ถœ๋œ Hyper-parameter, ์ฆ‰ ์ง€์—ญ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ์‚ฌํ›„๋ถ„ํฌ๋กœ๋ถ€ํ„ฐ Monte-Carlo ๋ชจ์˜๋ฅผ ์‹ค์‹œํ•˜์˜€์œผ๋ฉฐ, ์ง€์ ๋ณ„ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ •ํ•œ ๊ฒฐ๊ณผ์ด๋‹ค. ๊ทธ ๊ฒฐ๊ณผ ์ „๋ผ๋ถ๋„ ์œ ์—ญ๋‚ด ๋ชจ๋“  ๊ด€์ธก์†Œ ์ง€์ ์—์„œ ์ถ”์ •๋œ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์ด Bayesian GLM ๋ชจํ˜•์„ ํ†ตํ•ด ์‚ฐ์ •๋œ ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฒฐ๊ณผ ๋ฒ”์œ„ ๋‚ด์— ์œ„์น˜ํ•˜๊ณ  ์žˆ๋Š” ๊ฒƒ์„ ํ™•์ธ ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ๊ฒฐ๊ณผ๋Š” ๋ณธ ์—ฐ๊ตฌ์—์„œ ์ œ์‹œ๋œ ํ•จ์ˆ˜๋ฅผ ํ†ตํ•ด ๋ฏธ๊ณ„์ธก ์œ ์—ญ ๋˜๋Š” ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ์ž๋ฃŒ๊ณ„์—ด์ด ์ถฉ๋ถ„ํ•˜์ง€ ์•Š์€ ์ง€์—ญ ๋“ฑ์— Scaling ํŠน์„ฑ์„ ํ™œ์šฉํ•œ ์„ค๊ณ„๊ฐ•์ˆ˜๋Ÿ‰ ์ถ”์ •์ด ๊ฐ€๋Šฅ์„ฑ์„ ๋ณด์—ฌ์ค€๋‹ค ํ•˜๊ฒ ๋‹ค. ์ด์™€ ๋”๋ถˆ์–ด Bayesian ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ๊ฐ ๋‹จ๊ณ„์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์‚ฐ์ •ํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค.

Fig. 6

A Monte-Carlo Simulation Result Based on a Set of Hyper-Parameters Estimated from Hierarchical Bayesian GLM Model. The Red-Dotted Line Indicates a Bayesian Credible Interval for the Design Rainfall for a Region

Figure_KSCE_37_01_04_F6.jpg

4. ๊ฒฐ๋ก  ๋ฐ ํ† ์˜

ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๊ฒฝ์šฐ ์ˆ˜์ž์›๋ถ„์•ผ์—์„œ ๋„๋ฆฌ ํ™œ์šฉ๋˜๊ณ  ์žˆ๋Š” ์ž๋ฃŒ ์ค‘ ํ•˜๋‚˜์ด๋ฉฐ, ์ˆ˜์ž์› ๋ถ„์„์— ์žˆ์–ด ๊ฐ€์žฅ ์ค‘์š”ํ•œ ์ž๋ฃŒ ์ค‘ ํ•˜๋‚˜์ด๋‹ค. ์ผ๋ฐ˜์ ์œผ๋กœ ์ง€์†์‹œ๊ฐ„๋ณ„ ์—ฐ์ตœ๋Œ€๊ฐ•์ˆ˜๋Ÿ‰ ์ž๋ฃŒ๋ฅผ ํ™œ์šฉํ•˜์—ฌ ์ด๋ฅผ ๋นˆ๋„ํ•ด์„์„ ํ†ตํ•ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ •ํ•˜์—ฌ ํ™œ์šฉ๋˜์–ด์ง€๊ณ  ์žˆ๋‹ค. ๋˜ํ•œ ๋ถ„์„์ƒ์˜ ํŽธ์˜๋ฅผ ์œ„ํ•ด IDF ๊ณก์„ ์œผ๋กœ ๋ณ€ํ™˜ํ•˜์—ฌ ํ™œ์šฉ๋˜์–ด ์ง€๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋Š” ํŠน์ • ์ง€์†์‹œ๊ฐ„์— ๋Œ€ํ•ด ์ถ”์ •ํ•œ ํ›„ ์ž„์˜์˜ ์ง€์†์‹œ๊ฐ„์— ํ•ด๋‹นํ•˜๋Š” ๊ฐ•์ˆ˜๋Ÿ‰์„ ํ™˜์‚ฐํ•˜์—ฌ ์‚ฌ์šฉํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์ด ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๋นˆ๋„ํ•ด์„์‹œ ์ž๋ฃŒํŠน์„ฑ์— ์ ํ•ฉํ•œ ํ™•๋ฅ ๋ถ„ํฌํ˜• ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์‹œ ์ตœ์šฐ๋„๋ฒ• ๋˜๋Š” L-๋ชจ๋ฉ˜ํŠธ ๋ฒ•์˜ ๊ฒฝ์šฐ ์™ธ๋ถ€์ธ์ž๋ฅผ ๊ณ ๋ คํ•˜๋Š”๋ฐ ์–ด๋ ค์›€์ด ์กด์žฌํ•˜๋ฉฐ, ๋งค๊ฐœ๋ณ€์ˆ˜ ๋ฐ ์ž๋ฃŒ์—์„œ ๊ธฐ์ธํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์‚ฐ์ •ํ•  ์ˆ˜ ์—†๋Š” ๋‹จ์ ์ด ์กด์žฌํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ๊ฐ•์šฐ์ž๋ฃŒ์˜ Scaling ํŠน์„ฑ๊ณผ Bayesian GLM ํ•จ์ˆ˜๋ฅผ ํ†ตํ•ฉํ•˜์—ฌ ์ง€์—ญ๋นˆ๋„ํ•ด์„์„ ์ˆ˜ํ–‰ํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค. ๋ณธ ์—ฐ๊ตฌ๊ฒฐ๊ณผ๋ฅผ ํ†ตํ•ด ๋„์ถœํ•œ ๊ฒฐ๊ณผ๋Š” ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค.

์ฒซ์งธ, ๊ธฐ์กด ์ง€์—ญ๋นˆ๋„ํ•ด์„์‹œ ์ถ”์ •๋˜๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ๊ณ ๋ คํ•  ์ˆ˜ ์—†๋Š” ๋‹จ์ ์ด ์กด์žฌํ•˜์˜€๋‹ค. ์ด๋Š” ์ž๋ฃŒ ๋ฐ ๋ชจํ˜•์—์„œ ๊ธฐ์ธํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์‚ฐ์ •ํ•˜์ง€ ๋ชปํ•˜๋Š” ๋ฌธ์ œ๊ฐ€ ๋ฐœ์ƒํ•˜์—ฌ ์ด๋Ÿฌํ•œ ๋ถˆํ™•์‹ค์„ฑ์„ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•๊ฐœ๋ฐœ์ด ํ•„์š”ํ•˜๋‹ค ํ•  ์ˆ˜ ์žˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ž๋ฃŒ ๋ฐ ๋งค๊ฐœ๋ณ€์ˆ˜์—์„œ ๊ธฐ์ธํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ์„ ์ •๋Ÿ‰์ ์œผ๋กœ ์‚ฐ์ •ํ•˜๊ธฐ ์œ„ํ•ด Bayesian ๊ธฐ๋ฒ•์„ ๋„์ž…ํ•˜์—ฌ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜์˜€์œผ๋ฉฐ, ๊ธฐ์กด ์—ฐ๊ตฌ๋ณด๋‹ค ์‹ ๋ขฐ์„ฑ ์žˆ๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ์‚ฐ์ •์ด ๊ฐ€๋Šฅํ•œ ๋ชจํ˜•์„ ๊ฐœ๋ฐœํ•˜์˜€๋‹ค.

๋‘˜์งธ, ์•ž์„œ ์–ธ๊ธ‰ํ•˜์˜€๋“ฏ์ด ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ง€์—ญ๋นˆ๋„ํ•ด์„ ๊ฐœ๋…๊ณผ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ Scaling ํŠน์„ฑ์„ ํ†ตํ•ฉ์ ์œผ๋กœ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ๋Š” ํ•ด์„๋ฐฉ๋ฒ•์„ ๊ฐœ๋ฐœํ•˜๋Š”๋ฐ ๋ชฉ์ ์ด ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ด์œ ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ Scaling ํŠน์„ฑ์„ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•ด Bayesian GLM ๋ชจํ˜•์„ ๋„์ž…ํ•˜์—ฌ ์ง€์†์‹œ๊ฐ„์„ ๊ณ ๋ คํ•œ ํ•จ์ˆ˜๋กœ ๊ฐœ๋ฐœํ•˜์˜€์œผ๋ฉฐ, ๊ณ„์ธต์  Bayesian ๋ชจํ˜•์„ ํ†ตํ•ด ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์˜ ๋ถˆํ™•์‹ค์„ฑ์„ ์ €๊ฐ์‹œํ‚ฌ ์ˆ˜ ์žˆ๋Š” ๋ชจํ˜•์œผ๋กœ ํ™•์žฅํ•˜์˜€๋‹ค. ๊ฐœ๋ฐœ๋œ ๋ชจํ˜•์„ ํ™œ์šฉํ•˜์—ฌ ์‚ฐ์ •ํ•œ ๊ฒฐ๊ณผ ์ „๋ผ๋ถ๋„ ์œ ์—ญ๋‚ด 6๊ฐœ ๊ธฐ์ƒ์ฒญ ์ง€์  ๋ชจ๋‘ Bayesian ๋ชจํ˜• ๋‚ด์—์„œ ๋ชจ๋‘ Shrinkage ๋˜๋Š” ๊ฒฐ๊ณผ๋ฅผ ํ™•์ธ ํ•  ์ˆ˜ ์žˆ์—ˆ์œผ๋ฉฐ, ์ด๋Š” ๊ธฐ์ƒ์ฒญ ์ง€์  ๋ชจ๋‘ ๋™์งˆ์„ฑ ํ™•๋ณด ๋ฐ ์ž๋ฃŒ ๊ณต์œ ๊ฐ€ ํšจ๊ณผ์ ์œผ๋กœ ์ด๋ฃจ์–ด์ง€๊ณ  ์žˆ๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค.

์ตœ์ข…์ ์œผ๋กœ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ์œ ์‚ฌ์„ฑ์„ ๊ฐ€์ง€๋Š” ์ง€์—ญ์— ๊ฐ•์ˆ˜์ง€์ ์— ๋Œ€ํ•ด์„œ ํ™•๋ฅ ๋ถ„ํฌ์˜ ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ๋™์‹œ์— ์ถ”์ •ํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ์•ˆ์„ ๊ฐœ๋ฐœํ•˜์˜€์œผ๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๊ฐœ๋ณ„ ์ง€์ ์„ ํฌ๊ด„ํ•˜๋Š” ์ง€์—ญ๋‹จ์œ„์— ๋งค๊ฐœ๋ณ€์ˆ˜๋ฅผ ์ถ”์ •ํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค. ๋ณธ ์—ฐ๊ตฌ๋กœ๋ถ€ํ„ฐ ๋„์ถœ๋œ ์ง€์—ญ์  IDF ๊ณก์„ ์€ ๋ฏธ๊ณ„์ธก์œ ์—ญ ๋ฐ ์ง€์†์‹œ๊ฐ„์— ๋”ฐ๋ฅธ ์ž๋ฃŒ๊ณ„์—ด์ด ์ถฉ๋ถ„ํ•˜์ง€ ์•Š์€ ์ง€์—ญ ๋“ฑ์— ๋Œ€ํ•ด์„œ ํšจ๊ณผ์ ์œผ๋กœ ์ด์šฉ์ด ๊ฐ€๋Šฅํ•  ๊ฒƒ์œผ๋กœ ์‚ฌ๋ฃŒ๋˜๋ฉฐ, Bayesian ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ๊ฐ ๋‹จ๊ณ„์—์„œ ๋ฐœ์ƒํ•˜๋Š” ๋ถˆํ™•์‹ค์„ฑ ๋˜ํ•œ ์ •๋Ÿ‰ํ™” ํ•  ์ˆ˜ ์žˆ๋Š” ์žฅ์ ์ด ์žˆ๋Š” ๊ฒƒ์œผ๋กœ ์‚ฌ๋ฃŒ๋œ๋‹ค.

๋ณธ ์—ฐ๊ตฌ ๊ฒฐ๊ณผ๋Š” ํ•˜์ฒœ๊ด€๋ฆฌ, ์ˆ˜๊ณต๊ตฌ์กฐ๋ฌผ ์„ค๊ณ„ ๋“ฑ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ๊ธฐ์ดˆ ์ž๋ฃŒ๋กœ ์ด์šฉ๋  ์ˆ˜ ์žˆ์„ ๊ฒƒ์œผ๋กœ ๊ธฐ๋Œ€๋˜๋ฉฐ, ์ด์™€ ๋”๋ถˆ์–ด ๋ฏธ๊ณ„์ธก ์œ ์—ญ์—์„œ๋„ ํ™•๋ฅ ๊ฐ•์ˆ˜๋Ÿ‰์„ ์‚ฐ์ •ํ•  ์ˆ˜ ๋ฐฉ์•ˆ์œผ๋กœ ํ™œ์šฉ๋  ์žˆ์„ ๊ฒƒ์œผ๋กœ ํŒ๋‹จ๋œ๋‹ค. ํ–ฅํ›„ ์—ฐ๊ตฌ๋กœ๋Š” ๋งค๊ฐœ๋ณ€์ˆ˜ ์ถ”์ •์— ์žˆ์–ด ์—ฐ๊ด€์„ฑ์„ ๋ณด๋‹ค ํšจ๊ณผ์ ์œผ๋กœ ๊ณ ๋ คํ•˜๊ธฐ ์œ„ํ•ด์„œ, ๋งค๊ฐœ๋ณ€์ˆ˜๊ฐ„์˜ ์ƒ๊ด€์„ฑ๊ณผ ๋”๋ถˆ์–ด ์ง€์ ๊ฐ„์˜ ์ƒ๊ด€์„ฑ์„ ์ข…ํ•ฉ์ ์œผ๋กœ ๊ณ ๋ คํ•œ ์—ฐ๊ตฌ๋ฅผ ์ง„ํ–‰ํ•˜๊ณ ์ž ํ•œ๋‹ค. ์ฆ‰, ๋Œ€์ƒ์œ ์—ญ๋‚ด ์ง€์ ๋“ค ์‚ฌ์ด์— ๋งค๊ฐœ๋ณ€์ˆ˜์˜ ๊ณต๋ถ„์‚ฐ์„ ๋ชจํ˜•๋‚ด์—์„œ ๋ช…ํ™•ํ•˜๊ฒŒ ๊ณ ๋ คํ•œ ๋ฐฉ์•ˆ์˜ ๊ฐœ๋ฐœ์ด ํ•„์š”ํ•˜๋‹ค ํ•˜๊ฒ ๋‹ค.

Acknowledgements

๋ณธ ์—ฐ๊ตฌ๋Š” ๊ตญํ† ๊ตํ†ต๋ถ€ ๋ฌผ๊ด€๋ฆฌ์‚ฌ์—…์˜ ์—ฐ๊ตฌ๋น„์ง€์›(14AWMP- B082564-01)์— ์˜ํ•ด ์ˆ˜ํ–‰๋˜์—ˆ์Šต๋‹ˆ๋‹ค.

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