A development of stochastic simulation model based on vector autoregressive model (VAR) for groundwater and river water stages

Yoon Jeong Kwon; Chang-Hee Won; Byoung-Han Choi; Hyun-Han Kwon

doi:10.3741/JKWRA.2022.55.12.1137

All Issue

2022 Vol.55, Issue 12 Preview Page Next Page

Research Article

A development of stochastic simulation model based on vector autoregressive model (VAR) for groundwater and river water stages 벡터자기회귀(VAR) 모형을 이용한 지하수위와 하천수위의 추계학적 모의기법 개발

31 December 2022. pp. 1137-1147

PDF XML

Abstract

River and groundwater stages are the main elements in the hydrologic cycle. They are spatially correlated and can be used to evaluate hydrological and agricultural drought. Stochastic simulation is often performed independently on hydrological variables that are spatiotemporally correlated. In this setting, interdependency across mutual variables may not be maintained. This study proposes the Bayesian vector autoregression model (VAR) to capture the interdependency between multiple variables over time. VAR models systematically consider the lagged stages of each variable and the lagged values of the other variables. Further, an autoregressive model (AR) was built and compared with the VAR model. It was confirmed that the VAR model was more effective in reproducing observed interdependency (or cross-correlation) between river and ground stages, while the AR generally underestimated that of the observed.

Keywords

Autoregressive model (AR)

Vector autoregressive model (VAR)

Bayesian

Groundwater level

River water stage

Deviance information criterion (DIC)

하천수위와 지하수위는 수문학적 순환과정에서 나타나는 수문학적 요소로 상호 연관성이 높으며 이러한 수문학적 요소에 대해 확률적 시뮬레이션을 독립적으로 수행하는 경우 상호 관련 정보손실과 같은 문제가 발생할 수 있다. 하천수위와 지하수위는 수문학적·농업적 가뭄을 평가하는 중요한 지표로 활용되지만 하천수위의 경우 건기 중에는 정확한 관측을 얻기가 매우 어려우며, 지하수위의 경우 데이터 기간이 상대적으로 짧아 이를 활용한 가뭄지수 사용이 제한적이다. 이와 관련하여 손실 없이 자료를 최대한 이용하기 위해 본 연구는 각 변수의 시간 의존성을 고려하는 동시에 상호 연관된 변수의 시간 의존성을 고려하는 벡터자기회 모형VAR)을 구성했다. 하천수위와 지하수위 사이의 자기 상관 및 상관관계를 확인하고, 정보손실을 최소화하는 하천수위 및 지하수위를 예측할 수 있는지 여부를 결정하기 위해 벡터 자기 회귀 모델의 최적 순서 결정과 매개변수를 결정하였다. 또한, 두 변수 간의 상관관계를 반영하지 않는 자기회귀모형(AR)을 구축하고 모의에 대한 DIC와 상관계수를 VAR 모형과 비교하여 VAR 모형 더 적합함을 보이고 하천수위와 지하수위의 간의 상호관계성을 효과적으로 반영함을 확인하였다.

키워드

자기회귀모형(AR)

벡터자기회귀모형(VAR)

Bayesian

지하수위

하천수위

Deviance information criterion (DIC)

References

Kim, H.J., and Yeo, I.W. (2014). "Development of the autoregressive and cross-regressive model for groundwater level prediction at Muan coastal aquifer in Korea." Journal of Soil and Groundwater Environment, Vol. 19, No. 4, pp. 23-30. 10.7857/JSGE.2014.19.4.023

Kim, M.J., Gang, H.Y., and Park, J.S. (2017). "Drought status and prospects in '17." Water for Future, Vol. 50, No. 9, pp. 56-61.

Lee, I.M., Park, G.H., and Im, C.M. (1993). "Prediction of groundwater levels in hillside slopes using the autoregressive model." Geotechnical Engineering, Vol. 9, No. 3, pp. 67-76.

Liu, C., Pan, C., Chang, Y., and Luo, M. (2021). "An integrated autoregressive model for predicting water quality dynamics and its application in Yongding River." Ecological Indicators, Vol. 133, 108354. 10.1016/j.ecolind.2021.108354

Mirzavand, M., and Ghazavi, R. (2015). "A stochastic modelling technique for groundwater level forecasting in an arid environment using time series methods." Water Resources Management, Vol. 29, No. 4, pp. 1315-1328. 10.1007/s11269-014-0875-9

Nalbantis, I., and Tsakiris, G. (2009). "Assessment of hydrological drought revisited." Water resources management, Vol. 23, No. 5, pp. 881-897. 10.1007/s11269-008-9305-1

Pachauri, R.K., and Meyer, L.A. (2014). Climate change 2014: Synthesis report. Contribution of working groups I, II and III to the fifth assessment report of the intergovernmental panel on climate change. Intergovernmental Panel on Climate Change, Geneva, Switzerland.

Sims, C.A. (1980). "Macroeconomics and reality." Econometrica: Journal of the Econometric Society, Vol. 48, No. 1, pp. 1-48. 10.2307/1912017

Spiegelhalter, D.J., Best, N.G., Carlin, B.P., and Van Der Linde, A. (2002). "Bayesian measures of model complexity and fit." Journal of the royal statistical society: Series b (statistical methodology), Vol. 64, No. 4, pp. 583-639. 10.1111/1467-9868.00353

Sur, C., Park, S.Y., Kim, J.S., and Lee, J.H. (2020). "Prognostic and diagnostic assessment of hydrological drought using water and energy budget-based indices." Journal of Hydrology, Vol. 591, 125549. 10.1016/j.jhydrol.2020.125549

Vicente-Serrano, S.M., Beguería, S., and López-Moreno, J.I. (2010). "A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index." Journal of Climate, Vol. 23, No. 7, pp. 1696-1718. 10.1175/2009JCLI2909.1

Yi, M.J., Kim, G.B., Sohn, Y.C., Lee, J.Y., and Lee K.K. (2004). "Time series analysis of goundwater level data obtained from national groundwater monitoring station." Journal of the Geological Society of Korea, Vol. 40, No. 3, pp.305-329.

Yule, G.U. (1927). "VII. On a method of investigating periodicities disturbed series, with special reference to Wolfer's sunspot numbers." Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, Vol. 226, No. 636-646, pp. 267-298. 10.1098/rsta.1927.0007

Zanotti, C., Rotiroti, M., Sterlacchini, S., Cappellini, G., Fumagalli, L., Stefania, G.A., Nannucci, M.S., Leoni, B., and Bonomi, T. (2019). "Choosing between linear and nonlinear models and avoiding overfitting for short and long term groundwater level forecasting in a linear system." Journal of Hydrology, Vol. 578, 124015. 10.1016/j.jhydrol.2019.124015

Information

Publisher :KOREA WATER RESOURECES ASSOCIATION
Publisher(Ko) :한국수자원학회
Journal Title :Journal of Korea Water Resources Association
Journal Title(Ko) :한국수자원학회 논문집
Volume : 55
No :12
Pages :1137-1147
Received Date : 2022-11-08
Revised Date : 2022-12-04
Accepted Date : 2022-12-06
DOI :https://doi.org/10.3741/JKWRA.2022.55.12.1137

Journal of Korea Water Resources Association ISSN:2799-8746(Print) 2799-8754(Online) 한국수자원학회 논문집

All Issue