Imputing missing data using grey system theory and the biplot method to forecast groundwater levels and yields
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Published:
May 26, 2022
Keywords:
groundwater management, groundwater source, forecasting
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Abstract
Groundwater management is one of today’s important tasks. It has become necessary to seek out increasingly reliable methods to conserve groundwater resources. Dependable forecasting of the amounts of groundwater that can be abstracted in a sustainable manner requires longterm monitoring of the groundwater regime (rate of abstraction and groundwater levels). Monitoring of the groundwater source for the town of Bečej, Serbia had been disrupted for multiple years. The objective of the paper is to assess the possibility of reinterpreting the missing data or, in other words, to reconstruct the operation of the groundwater source and its effect on groundwater levels. At the Bečej source, groundwater is withdrawn from three water-bearing strata comprised of fine- to coarse-grained sands. Historic data are used to reconstruct the operation of the Bečej source between 1st of October 1980 to 1st of May 2010. The monitored parameters are total source yield and piezometric head at seven observation wells and 14 pumping wells. A data reconstruction methodology was developed, which included the use of an autoregressive (AR) model, a grey model (GM), and the biplot method. The methodology is applied to fill the data gaps during the considered period. The paper also describes the criteria for evaluating the accuracy of the AR model, GM, and biplot method. The proposed data reconstruction approach yielded satisfactory results and the methodology is deemed useful for the Bečej source data, as well as other historic data not necessarily associated with groundwater sources, but also groundwater control and protection systems, as well as hydrometeorological, hydrological and similar uses.
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References
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KANG, M.G. & MAENG, SJ. (2016): Gray Models for Real-Time Groundwater-Level Forecasting in Irrigated Paddy-Field Districts.– Journal of Irrigation and Drainage Engineering. doi: 10.1061/(ASCE)IR.1943-4774.0000940
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MARTINS, W.O., PORSANI, M.J. & SILVA, M.G. (2016): Adaptive singular value decomposition filtering to enhance reflectors and geological structures in 3D seismic data.– Revista Brasileira de Geofısica, 34, 1–9. doi: 10.22564/rbgf.v34i2.797
MEHDIZADEH, S. (2020): Using AR, MA, and ARMA Time Series Models to Improve the Performance of MARS and KNN Approaches in Monthly Precipitation Modeling under Limited Climatic Data.– Water Resources Management (2020), 34, 263–282. doi: 10.1007/s11269-019-02442-1
MEIJAARD, J.P. (1993): Applications of the singular value decomposition in dynamics.- Computer Methods in Applied Mechanics and Engineering, 103, 161–173. doi: 10.1016/0045-7825(93)90044-X
MIRZAVAND, M. & GHAZAVI, R. (2015): A Stochastic Modelling Technique for Groundwater Level Forecasting in an Arid Environment Using Time Series Methods.– Water Resources Management, 29, 1315–1328. doi: 10.1007/s11269-014-0875-9
MOHAMMED, M., WATANABE, K. & TAKEUCHI, S. (2010): Grey model for prediction of pore pressure change.– Environmental Earth Sciences, 60, 1523–1534. doi: 10.1007/s12665-009-0287-y
MOHANTY, S., JHA, M.K., RAUL, S., PANDA, R. & SUDHEER, K. (2015): Using Artificial Neural Network Approach for Simultaneous Forecasting of Weekly Groundwater Levels at Multiple Sites.– Water Resources Management, 29, 5521–5532. doi: 10.1007/s11269-015-1132-6
NOURANI, V., MOGADDAM, A.A. & NADIRI, A.O. (2008): An ANN-based model for spatiotemporal groundwater level forecasting.– Hydrological Processes, 22, 5054–5066. doi: 10.1002/hyp.7129
POLOMČIĆ D., GLIGORIĆ Z., BAJIĆ D. & CVIJOVIĆ Č. (2017). A hybrid model for forecasting groundwater levels based on fuzzy C-mean clustering and singular spectrum analysis.– Water, 9/7, 541 (2017). doi: 10.3390/w9070541
POLOMČIĆ, D., BAJIĆ, D. & KRUNIĆ, O. (2014): Hydrodynamic analysis of the interaction of two operating groundwater source, case study: groundwater supply of Bečej.– Tehnika, 65, 597–603. doi: 10.5937/tehnika1404597P
POLOMČIĆ, D., KRUNIĆ, O. & RISTIĆ VAKANJAC, V. (2011): Hydrogeological and hydrodynamic characteristics of groundwater sources for the public water supply of Bečej (northern Serbia).– Annales Géologiques De La Péninsule Balkanique, 72, 143–157.
RAKHSHANDEHROO, G.R., VAGHEFI, M. & AGHBOLAGHI, M.A. (2012): Forecasting Groundwater Level in Shiraz Plain Using Artificial Neural Networks.– Arabian Journal for Science and Engineering, 37, 1871–1883. doi: 10.1007/s13369-012-0291-5
RISTIĆ VAKANJAC, V., ČOKORILO ILIĆ, M., PAPIĆ, P., POLOMČIĆ, D. & GOLUBOVIĆ, R. (2018): AR, CR and ARCR modeling for simulations and analyses of karst groundwater quality parameters.– Geoloski anali Balkanskog poluostrva, 79, 71–81. doi: 10.2298/GABP1879071R
TANG, Y.Q., CUI, Z.D., WANG, J.X., YAN, L.P. & YAN, X.X. (2008): Application of grey theory-based model to prediction of land subsidence due to engineering environment in Shanghai.– Environmental Geology, 55, 583–593. doi: 10.1007/s00254-007-1009-y
TERZIN, V. (1994): State Geological Map of SFRY, scale 1:100.000, Zrenjanin section (map and guide).– Federal Geological Survey, Belgrade.
WANG, C.N. & PHAN, V.T. (2016): An Improvement the Accuracy of Grey Forecasting Model for Cargo Throughput in International Commercial Ports of Kaohsiung.– Wseas transactions on business and economics, 11, 322–327. doi: 10.11648/j.ijber.20140301.11
WUNSCH, A., LIESCH, T. & BRODA, S. (2018): Forecasting groundwater levels using nonlinear autoregressive networks with exogenous input (NARX).– Journal of Hydrology, 567, 743–758. doi: 10.1016/j.jhydrol.2018.01.045
XIAOJUN, D., JIANJUN, L. & HUAYING Z. (2015): Application of AR Model in the Analysis of Preearthquake Ionospheric Anomalies.– Mathematical Problems in Engineering, ID 157184. doi: 10.1155/2015/157184
YAN, Q. & MA, C. (2016): Application of integrated ARIMA and RBF network for groundwater level forecasting.– Environmental Earth Sciences, 75/5, 1–13. doi: 10.1007/s12665-015-5198-5
YONGPING, C., MIN, G., SHUNQI, P., HAIDONG, P., XIAN, Z. & ZHENGJIN, T. (2020): Application of auto-regressive (AR) analysis to improve short-term prediction of water levels in the Yangtze estuary.– Journal of Hydrology, 590, 125386. doi: 10.1016/j.jhydrol.2020.125386
YU, P.S., CHEN, C.J., CHEN, S.J. & LIN, S.C. (2001): Application of grey model toward runoff forecasting.– Journal of the American Water Resources Association (JAWRA), 37, 151–166. doi: 10.1111/j.1752-1688.2001.tb05482.x
ZHANG, L., LIU, Y. & ZHAO, F. (2018): Singular value decomposition analysis of spatial relationships between monthly weather and air pollution index in China.– Stochastic Environmental Research and Risk Assessment, 32, 733–748. doi: 10.1007/s00477-017-1491-z
ZHAO, B.B. & CHEN, Y.Q. (2010): Singular value decomposition (SVD) for extraction of gravity anomaly associated with gold mineralization in Tongshi gold field, Western Shandong Uplifted Block, Eastern China.– Nonlinear Processes Geophysics, 18, 103–109. doi: 10.5194/npg-18-103-2011
ZHAO-HUI, H. & JING, L. (2016): The Non-equidistance and Non-homogeneous Multivariable Grey NNMGM(1,n) Model and its Application.– Journal of Residuals Science & Technology, 13, 23.1–23.8.
ARCINIEGAS-ALARCON, S., GARCIA-PENA, M., KRZANOWSKI, WJ. & DIAS, C.T.S. (2014): Imputing missing values in multi-environment trials using the singular value decomposition: An empirical comparison.– International journal of the faculty of agriculture and biology, 9, 54–70. doi: 10.1590/1984-70332016v16n2a13
CHAKRABORTY, S., DENIS, D.M. & SHERRING, A. (2009): Development of Time Series Autoregressive Model for prediction of rainfall and runoff in Kelo Watershed Chhattisgarh.– International Journal of Advances in Engineering Science and Technology, 2, 153–163.
CHITSAZAN, M., RAHMANI, G. & NEYAMADPOUR, A. (2015): Forecasting Groundwater Level by Artificial Neural Networks as an Alternative Approach to Groundwater Modeling.– Journal of the Geological Society of India, 85, 98–106. doi: 10.1007/s12594-015-0197-4
DAI, X., LIU, J. & ZHANG, H. (2015): Application of AR Model in the Analysis of Preearthquake Ionospheric Anomalies.– Mathematical Problems in Engineering, ID ID 157184. doi: 10.1155/2015/157184
DAOGONG, H.U., SHUREN, W.U. & CHENGXUAN, T.A.N. (1999): Grey Prediction of Seismic Activity in the Three Gorges Area of the Yangtze River.– Acta Geologica Sinica, 73, 294–299.
EMAMGHOLIZADEH, S., MOSLEMI, K. & KARAMI, G. (2014): Prediction the Groundwater Level of Bastam Plain (Iran) by Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS).– Water Resources Management, 28, 5433–5446. doi: 10.1007/s11269-014-0810-0
GAI, J. & HU, Y. (2018): Research on Fault Diagnosis Based on Singular Value Decomposition and Fuzzy Neural Network.– Shock and Vibration, ID 8218657. doi: 10.1155/2018/8218657
GONZALEZ CABRERA, J.M., FIDALGO MARTINEZ, M.R., MARTIN MATEOS, E.J. & VICENTE TAVERA, S. (2006): Study of the evolution of air pollution in Salamancam (Spain) along a five-year period (1994–1998) using HJ-Biplot simultaneous representation analysis.– Environmental Modelling & Software, 21, 61–68.
GULDAL, V. & TONGAL, H. (2009): Comparison of Recurrent Neural Network, Adaptive Neuro-Fuzzy Inference System and Stochastic Models in Egirdir Lake Level Forecasting.– Water Resources Management, 24, 105–128. doi: 10.1007/s11269-009-9439-9
GUZMAN, S.M., PAZ, J.O. & TAGERT, M.L.M. (2017): The Use of NARX Neural Networks to Forecast Daily Groundwater Levels.– Water Resources Management. 31, 1591–1603. doi: 10.1007/s11269-017-1598-5
HAO, Y., ZHANG, L., WEI, T. & WANG, X. (2010): Piecewise Analysis and Prediction of Spring Flow Based ON GM(1,1).– Advances in Grey Systems Research, doi: 10.1007/978-3-642-13938-3_14
JIANFEI, F., LUN, Z., ZHIGUO, L. & JIANYING, Y. (2012): Study on the Sustainable Utilization of Groundwater Resources in Hebei Plain.– Procedia Environmental Sciences, 12, 1071–1076. doi: 10.1016/j.proenv.2012.01.389
KANG, M.G. & MAENG, SJ. (2016): Gray Models for Real-Time Groundwater-Level Forecasting in Irrigated Paddy-Field Districts.– Journal of Irrigation and Drainage Engineering. doi: 10.1061/(ASCE)IR.1943-4774.0000940
KANG, M.S., KANG, M.G., PARK, S.W., LEE, J.J. & YOO, K.H. (2006): Application of grey model and artificial neural networks to flood forecasting.– Journal of the American Water Resources Association (JAWRA), 42, 473–486.
LIU, Q. & LUO, Y. (2010): The Non-equidistant Linear Weighting Grey Model NWGM (1,1) and Its Application.– International Journal of Simulation Systems, Science & Technology, doi: 10.5013/IJSSST.a.17.25.28
MAHMOD, W.E., WATANABE, K. & ZAHR-ELDEEN, A.A. (2013): Analysis of groundwater flow in arid areas with limited hydrogeological data using the Grey Model: a case study of the Nubian Sandstone, Kharga Oasis, Egypt.– Hydrogeology Journal, 21, 1021–1034. doi: 10.1007/s10040-013-0959-2
MALEŠEVIĆ, M. (1984): State Geological Map of SFRY, scale 1:100.000, Srbobran section (map and guide).– Federal Geological Survey, Belgrade.
MARTINS, W.O., PORSANI, M.J. & SILVA, M.G. (2016): Adaptive singular value decomposition filtering to enhance reflectors and geological structures in 3D seismic data.– Revista Brasileira de Geofısica, 34, 1–9. doi: 10.22564/rbgf.v34i2.797
MEHDIZADEH, S. (2020): Using AR, MA, and ARMA Time Series Models to Improve the Performance of MARS and KNN Approaches in Monthly Precipitation Modeling under Limited Climatic Data.– Water Resources Management (2020), 34, 263–282. doi: 10.1007/s11269-019-02442-1
MEIJAARD, J.P. (1993): Applications of the singular value decomposition in dynamics.- Computer Methods in Applied Mechanics and Engineering, 103, 161–173. doi: 10.1016/0045-7825(93)90044-X
MIRZAVAND, M. & GHAZAVI, R. (2015): A Stochastic Modelling Technique for Groundwater Level Forecasting in an Arid Environment Using Time Series Methods.– Water Resources Management, 29, 1315–1328. doi: 10.1007/s11269-014-0875-9
MOHAMMED, M., WATANABE, K. & TAKEUCHI, S. (2010): Grey model for prediction of pore pressure change.– Environmental Earth Sciences, 60, 1523–1534. doi: 10.1007/s12665-009-0287-y
MOHANTY, S., JHA, M.K., RAUL, S., PANDA, R. & SUDHEER, K. (2015): Using Artificial Neural Network Approach for Simultaneous Forecasting of Weekly Groundwater Levels at Multiple Sites.– Water Resources Management, 29, 5521–5532. doi: 10.1007/s11269-015-1132-6
NOURANI, V., MOGADDAM, A.A. & NADIRI, A.O. (2008): An ANN-based model for spatiotemporal groundwater level forecasting.– Hydrological Processes, 22, 5054–5066. doi: 10.1002/hyp.7129
POLOMČIĆ D., GLIGORIĆ Z., BAJIĆ D. & CVIJOVIĆ Č. (2017). A hybrid model for forecasting groundwater levels based on fuzzy C-mean clustering and singular spectrum analysis.– Water, 9/7, 541 (2017). doi: 10.3390/w9070541
POLOMČIĆ, D., BAJIĆ, D. & KRUNIĆ, O. (2014): Hydrodynamic analysis of the interaction of two operating groundwater source, case study: groundwater supply of Bečej.– Tehnika, 65, 597–603. doi: 10.5937/tehnika1404597P
POLOMČIĆ, D., KRUNIĆ, O. & RISTIĆ VAKANJAC, V. (2011): Hydrogeological and hydrodynamic characteristics of groundwater sources for the public water supply of Bečej (northern Serbia).– Annales Géologiques De La Péninsule Balkanique, 72, 143–157.
RAKHSHANDEHROO, G.R., VAGHEFI, M. & AGHBOLAGHI, M.A. (2012): Forecasting Groundwater Level in Shiraz Plain Using Artificial Neural Networks.– Arabian Journal for Science and Engineering, 37, 1871–1883. doi: 10.1007/s13369-012-0291-5
RISTIĆ VAKANJAC, V., ČOKORILO ILIĆ, M., PAPIĆ, P., POLOMČIĆ, D. & GOLUBOVIĆ, R. (2018): AR, CR and ARCR modeling for simulations and analyses of karst groundwater quality parameters.– Geoloski anali Balkanskog poluostrva, 79, 71–81. doi: 10.2298/GABP1879071R
TANG, Y.Q., CUI, Z.D., WANG, J.X., YAN, L.P. & YAN, X.X. (2008): Application of grey theory-based model to prediction of land subsidence due to engineering environment in Shanghai.– Environmental Geology, 55, 583–593. doi: 10.1007/s00254-007-1009-y
TERZIN, V. (1994): State Geological Map of SFRY, scale 1:100.000, Zrenjanin section (map and guide).– Federal Geological Survey, Belgrade.
WANG, C.N. & PHAN, V.T. (2016): An Improvement the Accuracy of Grey Forecasting Model for Cargo Throughput in International Commercial Ports of Kaohsiung.– Wseas transactions on business and economics, 11, 322–327. doi: 10.11648/j.ijber.20140301.11
WUNSCH, A., LIESCH, T. & BRODA, S. (2018): Forecasting groundwater levels using nonlinear autoregressive networks with exogenous input (NARX).– Journal of Hydrology, 567, 743–758. doi: 10.1016/j.jhydrol.2018.01.045
XIAOJUN, D., JIANJUN, L. & HUAYING Z. (2015): Application of AR Model in the Analysis of Preearthquake Ionospheric Anomalies.– Mathematical Problems in Engineering, ID 157184. doi: 10.1155/2015/157184
YAN, Q. & MA, C. (2016): Application of integrated ARIMA and RBF network for groundwater level forecasting.– Environmental Earth Sciences, 75/5, 1–13. doi: 10.1007/s12665-015-5198-5
YONGPING, C., MIN, G., SHUNQI, P., HAIDONG, P., XIAN, Z. & ZHENGJIN, T. (2020): Application of auto-regressive (AR) analysis to improve short-term prediction of water levels in the Yangtze estuary.– Journal of Hydrology, 590, 125386. doi: 10.1016/j.jhydrol.2020.125386
YU, P.S., CHEN, C.J., CHEN, S.J. & LIN, S.C. (2001): Application of grey model toward runoff forecasting.– Journal of the American Water Resources Association (JAWRA), 37, 151–166. doi: 10.1111/j.1752-1688.2001.tb05482.x
ZHANG, L., LIU, Y. & ZHAO, F. (2018): Singular value decomposition analysis of spatial relationships between monthly weather and air pollution index in China.– Stochastic Environmental Research and Risk Assessment, 32, 733–748. doi: 10.1007/s00477-017-1491-z
ZHAO, B.B. & CHEN, Y.Q. (2010): Singular value decomposition (SVD) for extraction of gravity anomaly associated with gold mineralization in Tongshi gold field, Western Shandong Uplifted Block, Eastern China.– Nonlinear Processes Geophysics, 18, 103–109. doi: 10.5194/npg-18-103-2011
ZHAO-HUI, H. & JING, L. (2016): The Non-equidistance and Non-homogeneous Multivariable Grey NNMGM(1,n) Model and its Application.– Journal of Residuals Science & Technology, 13, 23.1–23.8.