Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지
DOI QR코드

DOI QR Code

Development of Statistical Downscaling Model Using Nonstationary Markov Chain

비정상성 Markov Chain Model을 이용한 통계학적 Downscaling 기법 개발

  • Kwon, Hyun-Han (Water Resources Division, Korea Institute of Construction Technology) ;
  • Kim, Byung-Sik (Water Resources Division, Korea Institute of Construction Technology)
  • 권현한 (한국건설기술연구원 수자원연구실) ;
  • 김병식 (한국건설기술연구원 수자원연구실)
  • Published : 2009.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

A stationary Markov chain model is a stochastic process with the Markov property. Having the Markov property means that, given the present state, future states are independent of the past states. The Markov chain model has been widely used for water resources design as a main tool. A main assumption of the stationary Markov model is that statistical properties remain the same for all times. Hence, the stationary Markov chain model basically can not consider the changes of mean or variance. In this regard, a primary objective of this study is to develop a model which is able to make use of exogenous variables. The regression based link functions are employed to dynamically update model parameters given the exogenous variables, and the model parameters are estimated by canonical correlation analysis. The proposed model is applied to daily rainfall series at Seoul station having 46 years data from 1961 to 2006. The model shows a capability to reproduce daily and seasonal characteristics simultaneously. Therefore, the proposed model can be used as a short or mid-term prediction tool if elaborate GCM forecasts are used as a predictor. Also, the nonstationary Markov chain model can be applied to climate change studies if GCM based climate change scenarios are provided as inputs.

기존의 정상성 Markov Chain 모형은 자료 자체의 Markov 특성만을 고려하여 모의하는 기법으로서 수자원 설계에서 여러 가지 목적으로 이용되어 지고 있다. 그러나 일강수량의 천이확률 및 매개변수 등이 과거와 일정하다는 정상성을 기본 가정으로 하기 때문에 평균의 변동성 등과 같은 외부충격을 모형에 적용할 수 없다. 이러한 관점에서 본 연구의 가장 큰 목적은 기존일강수량 모형을 외부인자를 받아들일 수 있는 모형으로 개발하는 것이다. 즉, Markov Chain 모형의 매개변수인 천이확률과 확률분포형의 매개변수 등을 연결함수(link function)를 통해 외부인자와 연동하도록 하였으며 정준상관분석을 통해 매개변수를 추정하였다. 개발된 모형을 서울지방 1961-2006년까지의 일강수량 자료를 대상으로 검증하는 절차를 가졌다. 추정된 결과를 보면 계절강수량의 특성뿐만 아니라 일강수량의 특성 또한 적절하게 모의되는 것을 확인할 수 있다. 따라서 본 연구에서 개발된 모형은 GCM 예측결과를 입력자료로 활용한다면 일강수계열의 장단기 모의를 위한 downscaling 기법으로 사용될 수 있다. 또한, 기후변화 시나리오가 입력자료로 이용된다면 기후변화에 따른 수자원 영향 평가를 위한 downscaling 기법으로 활용이 가능할 것으로 판단된다.

Keywords

References

  1. 강경석 (2000). 다지점 일 강우모형에 의한 일 유출량의 모의발생, 인하대학교, 박사논문
  2. 권현한, 문영일, 최병규, 윤용남 (2004) '신뢰성 분석을 통한 기존 댐 재개발의 적정규모 결정의 관한 연구.' 한국수자원학회 논문집, 한국수자원학회, Vol. 38, No. 2, pp. 97-110 https://doi.org/10.3741/JKWRA.2005.38.2.097
  3. 김병식, 김형수, 서병하, 김남원 (2003). '전이함수모형과 일기발생모형을 이용한 유역규모 기후변화시나리오의 작성.' 한국수자원학회논문집, 한국수자원학회, Vol. 36, No. 3, pp. 345-363 https://doi.org/10.3741/JKWRA.2003.36.3.345
  4. 문영일, 차영일 (2004). '비동질성 마코프 모형을 이용한 일강수자료 모의발생 I-이론-.' 대한토목학회논문집, 대한토목학회, Vol. 24, No. 5B, pp. 431-435
  5. 유철상, 이동률 (2000). '기후변화에 따른 강수일수 및 강수강도의 변화연구.' 대한토목학회 논문집, 대한토목학회, Vol. 20, No. 4B, pp. 535-544
  6. 이창훈, 김승 (1995). '회귀분석에 의한 한국의 연.월평균 강수량의 추정,' 대한토목학회 논문집, 대한토목학회, Vol. 1, No. 5, pp. 1255-1266
  7. 정영훈, 이충성, 김형수, 심명필 (2005). '갑천 유역의 빈도별 갈수유량에 따른 필요유량 산정.' 대한토목학회 논문집, 대한토목학회, Vol. 25, No. 2B, pp.97-105
  8. 허준행 (1997). '수문통계학의 기초(V).' 한국수문학회지, 한국수문학회, 제30권, 제1호, pp. 88-95
  9. 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 https://doi.org/10.1029/WR012i003p00443
  10. Katz, R.W. (1996). 'Use of conditional stochastic models to generate climate change scenarios.' Clim. Change, Vol. 32, pp. 237–255 https://doi.org/10.1007/BF00142464
  11. Kim, B.S., Kim, H.S., Seoh, B. H., and Kim, N.W. (2007). 'Impact of climate change on water resources in Yongdam Dam basin, Korea.' Stochastic Environmental Research and Risk Assessment, Vol. 21, No. 4, pp. 355-357 https://doi.org/10.1007/s00477-006-0070-5
  12. Lall, U., Moon, Y.-I, and Bosworth, K. (1993). 'Kernel flood frequency estimators: bandwidth selection and kernel choice.' Water Resources Research, Vol. 29, No. 4, pp. 1003-1015 https://doi.org/10.1029/92WR02466
  13. Moon, Y.-I, Lall, U., and Bosworth, K. (1993). 'A comparison of tail probability estimators.' Journal of Hydrology, Vol. 151, pp. 343-363 https://doi.org/10.1016/0022-1694(93)90242-2
  14. Nord, J. (1975). 'Some applications of Markov chains,' Proceedings Fourth Conference on Probability and Statistics in Atmospheric Science, Tallahas, pp. 125-130
  15. Rajagopalan, B., Lall, U. and Tarboton, D. (1996). 'Nonhomogeneous Markov model for daily precipitation.' Journal of Hydrologic Engineering, Vol. 1, No. 1, pp. 33-40 https://doi.org/10.1061/(ASCE)1084-0699(1996)1:1(33)
  16. Wilks, D.S. (1992). 'Adapting stochastic weather generation algorithms for climate change studies.' Clim. Change, Vol. 22, pp. 67–84 https://doi.org/10.1007/BF00143344

Cited by

  1. Assessment of the impact of climate change on the flow regime of the Han River basin using indicators of hydrologic alteration vol.25, pp.5, 2011, https://doi.org/10.1002/hyp.7856
  2. The Impact Assessment of Climate Change on Design Flood in Mihochen basin based on the Representative Concentration Pathway Climate Change Scenario vol.15, pp.1, 2013, https://doi.org/10.17663/JWR.2013.15.1.105
  3. Future Korean Water Resources Projection Considering Uncertainty of GCMs and Hydrological Models vol.44, pp.5, 2011, https://doi.org/10.3741/JKWRA.2011.44.5.389
  4. Development of Daily Rainfall Simulation Model Based on Homogeneous Hidden Markov Chain vol.33, pp.5, 2013, https://doi.org/10.12652/Ksce.2013.33.5.1861
  5. Outlook of Discharge for Daecheong and Yongdam Dam Watershed Using A1B Climate Change Scenario Based RCM and SWAT Model vol.44, pp.12, 2011, https://doi.org/10.3741/JKWRA.2011.44.12.929
  6. Development of Stochastic Downscaling Method for Rainfall Data Using GCM vol.47, pp.9, 2014, https://doi.org/10.3741/JKWRA.2014.47.9.825
  7. The Potential Effects of Climate Change on Streamflow in Rivers Basin of Korea Using Rainfall Elasticity vol.18, pp.1, 2013, https://doi.org/10.4491/eer.2013.18.1.009
  8. Effects of climate change on the thermal structure of lakes in the Asian Monsoon Area vol.112, pp.3-4, 2012, https://doi.org/10.1007/s10584-011-0233-3
  9. Evaluation of Hybrid Downscaling Method Combined Regional Climate Model with Step-Wise Scaling Method vol.46, pp.6, 2013, https://doi.org/10.3741/JKWRA.2013.46.6.585
  10. Large-Scale Slope Stability Analysis Using Climate Change Scenario (1): Methodologies vol.16, pp.3, 2013, https://doi.org/10.11108/kagis.2013.16.3.193
  11. Derivation of Flood Frequency Curve with Uncertainty of Rainfall and Rainfall-Runoff Model vol.46, pp.1, 2013, https://doi.org/10.3741/JKWRA.2013.46.1.59
  12. Development of Multi-Site Daily Rainfall Simulation Based on Homogeneous Hidden Markov Chain Model Coupled with Chow-Liu Tree Structures vol.46, pp.10, 2013, https://doi.org/10.3741/JKWRA.2013.46.10.1029
  13. Hydrological Assessment of Multifractal Space-Time Rainfall Downscaling Model: Focusing on Application to the Upstream Watershed of Chungju Dam vol.47, pp.10, 2014, https://doi.org/10.3741/JKWRA.2014.47.10.959
  14. Non-stationary Frequency Analysis for Extreme Precipitation based on Representative Concentration Pathways (RCP) Climate Change Scenarios vol.12, pp.2, 2012, https://doi.org/10.9798/KOSHAM.2012.12.2.231
  15. Evaluation of drought and flood risks in a multipurpose dam under climate change: a case study of Chungju Dam in Korea vol.73, pp.3, 2014, https://doi.org/10.1007/s11069-014-1164-x
  16. The Evaluation of Climate Change Impacts on the Water Scarcity of the Han River Basin in South Korea Using High Resolution RCM Data vol.43, pp.3, 2010, https://doi.org/10.3741/JKWRA.2010.43.3.295
  17. Assessment of future water resources and water scarcity considering the factors of climate change and social–environmental change in Han River basin, Korea vol.28, pp.8, 2014, https://doi.org/10.1007/s00477-014-0924-1
  18. Applicability of a Space-time Rainfall Downscaling Algorithm Based on Multifractal Framework in Modeling Heavy Rainfall Events in Korean Peninsula vol.47, pp.9, 2014, https://doi.org/10.3741/JKWRA.2014.47.9.839
  19. Effects of Climate Change on the Movement of Turbidity Flow in a Stratified Reservoir vol.29, pp.11, 2015, https://doi.org/10.1007/s11269-015-1047-2