Journal of Wetlands Research (한국습지학회지)

Korean Wetlands Society (한국습지학회)
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Modelling and Residual Analysis for Water Level Series of Upo Wetland

우포늪 수위 자료의 시계열 모형화 및 잔차 분석

  • Kim, Kyunghun (Department of Civil Engineering, Inha University) ;
  • Han, Daegun (Department of Civil Engineering, Inha University) ;
  • Kim, Jungwook (Department of Civil Engineering, Inha University) ;
  • Lim, Jonghun (Department of Civil Engineering, Inha University) ;
  • Lee, Jongso (Urban Research Division, Korea Research Institute for Human Settlements) ;
  • Kim, Hung Soo (Department of Civil Engineering, Inha University)
  • Received : 2019.01.30
  • Accepted : 2019.02.22
  • Published : 2019.02.28
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Abstract

Recently, natural disasters such as floods and droughts are frequently occurred due to climate change and the damage is also increasing. Wetland is known to play an important role in reducing and minimizing the damage. In particular, water level variability needs to be analyzed in order to understand the various functions of wetland as well as the reduction of damage caused by natural disaster. Therefore, in this study, we fitted water level series of Upo wetland in Changnyeong, Gyeongnam province to a proper time series model and residual test was performed to confirm the appropriateness of the model. In other words, ARIMA model was constructed and its residual tests were performed using existing nonparametric statistics, BDS statistic, and Close Returns Histogram(CRH). The results of residual tests were compared and especially, we showed the applicability of CRH to analyze the residuals of time series model. As a result, CRH produced not only accurate randomness test result, but also produced result in a simple calculation process compared to the other methods. Therefore, we have shown that CRH and BDS statistic can be effective tools for analyzing residual in time series model.

기후변화로 인해 홍수나 가뭄과 같은 자연재난이 빈번하게 발생하고 있고, 이로 인한 피해 또한 커지고 있다. 습지는 이러한 피해를 저감하고 최소화하는데 중요한 역할을 하고 있는 것으로 알려져 있다. 특히, 자연재난으로 인한 피해 저감 뿐만 아니라 습지의 다양한 기능을 이해하기 위해서는 수위의 변동성을 분석할 필요가 있다. 따라서 본 연구에서는 경상남도 창녕군에 위치한 우포늪의 수위 자료에 적합한 시계열 모형을 도출하고 모형의 적절성을 확인하기 위해 잔차 분석을 수행하였다. 즉, ARIMA 모형을 구축하였고, 잔차 분석을 위해 기존의 비모수 통계기법, BDS 통계기법 및 CRH(Close Returns Histogram)를 통한 결과들을 비교 분석하였다. 특히, 본 연구에서는 시계열 모형의 잔차 분석을 위해 CRH의 적용 가능성을 제시하고자 하였다. 분석 결과, CRH는 정확한 무작위성 검정 결과를 도출하였을 뿐만 아니라 다른 방법들에 비해서 단순한 계산과정을 통해 쉽게 결과를 얻을 수 있었다. 따라서 시계열 모형의 잔차 분석을 위해 BDS 통계기법 뿐만 아니라 CRH를 이용한다면 보다 효과적인 분석을 할 수 있을 것으로 판단된다.

Keywords

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Fig. 1. CRP & CRH of Gaussian and Logistic data. (a) Gaussian white noise data, (b) Logistic data

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Fig. 2. Location of water gauges

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Fig. 3. Weekly water level data of Upo station 1 & 2

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Fig. 4. Box-Cox transformed Upo station 1 data(λ = 0.1603)

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Fig. 6. Model fit of Transformed Upo station 1 data and Upo station 2 data

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Fig. 5. ACF & PACF of Transformed Upo station 1 data and Upo station 2 data

Table 1. Statistic for the Gaussian and logistic series(Kim et al, 2003)

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Table 2. Result of CRH

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Table 3. statistics of water level data

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Table 4. Result of Stationary test

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Table 5. statistics of Box-Cox transformed Upo station 1 data

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Table 6. Compare AIC with several ARIMA model of Upo station 1 & station 2

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Table 7. The result of Nonparametric statistics of Residual data

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Table 8. BDS statistic result(Residual of Upo station 1)

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Table 9. BDS statistic result(Residual of Upo station 2)

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Table 10. The Randomness test result of CRH about Residual data

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Table 11. Randomness test result of (A) and (B) data

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