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Trend Analysis and Spatial Prediction of Groundwater Levels Using Time Series Forecasting and a Novel Spatio-Temporal Method

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Abstract

Overexploitation of groundwater in the Malayer Plain has resulted in a continuous decline of groundwater levels over recent years with associated risks to water security. Effective water resource management requires the identification of the most susceptible regions and periods to such risks and, hence, spatio-temporal prediction tools of groundwater levels. For this purpose, we use 27 years of groundwater level records (between 1984 and 2012) and apply time series forecasting models including seasonal Autoregressive Integrated Moving Average (ARIMA) and Holt-Winters Exponential Smoothing (HWES). The spatial variation of groundwater levels is investigated by a novel method known as Fixed Rank Kriging (FRK). The results demonstrate that ARIMA outperforms HWES in fitting the training data. In contrast, the 95% confidence bound of ARIMA predictions is wider than that of HWES and ARIMA’s predicted seasonal cycle is weaker. The time series forecasting by a stochastic simulation indicated that if the current situation continues, the level of groundwater is expected to decline from 1635 m to about 1605 m by 2022. The FRK showed that the amount of groundwater extraction in the western part of the aquifer was higher than that of the northern and central parts.

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References

  • Brockwell PJ, Davis RA (2002) Introduction to time series and forecasting, second edn. Springer, New York

  • Brown RG (1959) Statistical forecasting for inventory control. McGraw-Hill, New York

    Google Scholar 

  • Chen HU, Guoa S, Chong-Yu XU, Singh VP (2007) Historical temporal trends of hydro-climatic variables and runoff response to climate variability and their relevance in water resource management in the Hanjiang Basin. J Hydrol 344:171–184

    Article  Google Scholar 

  • Fouedjio F, Desassis N, Romary T (2015) Estimation of space deformation model for non-stationary random functions. Spat Stat-Neth 13:45–61

  • Gundogdu K, Guney I (2007) Spatial analysis of groundwater levels using universal kriging. J Earth Syst Sci 116:49–55

    Article  Google Scholar 

  • Holt CC (1957) Forecasting trends and seasonal by exponentially weighted averages. Int J Appl Forecast 20(1):5–10

    Article  Google Scholar 

  • Holtschlag DJ, Sweat MJ (1999) A temporal and spatial analysis of ground-water levels for effective monitoring in Huron County, Michigan. U.S. Geological Survey Report:98–629

  • Hurvich CM, Tsai C (1989) Regression and time series model selection in small samples. Biometrika 76(2):297–307

    Article  Google Scholar 

  • Hyndman RJ (2006) Another look at forecast-accuracy metrics for intermittent demand. Int J Appl Forecast 4:43–46

    Google Scholar 

  • Hyndman RJ, Koehler AB, Ord JK, Snyder RD (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer

  • Isaaks EH, Srivastava RM (1989) Applied geostatistics. Oxford University Press, New York

    Google Scholar 

  • Jalali M, Kolahchi Z (2008) Groundwater quality in an irrigated, agricultural area of northern Malayer, western Iran. Nutr Cycl Agroecosyst 80:95–105

    Article  Google Scholar 

  • Kumar V (2007) Optimal contour mapping of groundwater levels using universal kriging – a case study. Hydrol Sci J 52(5):1039–1049

    Article  Google Scholar 

  • Laio F, Baldassarre GD, Montanari A (2009) Model selection techniques for the frequency analysis of hydrological extremes. Water Resour Res 45:1–11

    Google Scholar 

  • Lewis CD (1997) Demand forecasting and inventory control. Wiley, New York 157pp

    Google Scholar 

  • Mirzavand M, Ghazavi R (2015) A Stochastic Modelling technique for groundwater level forecasting in an arid environment using time series methods. Water Resour Manag 29:1315–1328.

  • Montanari A, Rosso R, Taqqu M (1997) Fractionally dilferenced ARIMA models applied to hydrologic time series: identification, estimation. and simulation Water Resour Res 3:1035–1044

    Article  Google Scholar 

  • Moraes Takafuji EH, da Rocha MM, Manzione RL (2018) Groundwater Level Prediction/Forecasting and Assessment of Uncertainty Using SGS and ARIMA Models: A Case Study in the Bauru Aquifer System (Brazil). Nat Resour Res https://doi.org/10.1007/s11053-018-9403-6

  • Moritz S, Bartz-Beielstein T (2015). ImputeTS: Time Series Missing Value Imputation. R package version 2.6

  • Nakhaei M, Altafi Dadgar M, Amiri V (2016) Geochemical processes analysis and evaluation of groundwater quality in Hamadan Province, Western Iran. Arab J Geosci 9:384

    Article  Google Scholar 

  • Narany TS, Aris AZ, Sefie A, Keesstra S (2017) Detecting and predicting the impact of land use changes on groundwater quality, a case study in northern Kelantan, Malaysia. Sci Total Environ 599:844–853

    Article  Google Scholar 

  • Rossiter DG (2018). Tutorial: Time series analysis in R. http://www.css.cornell.edu/faculty/dgr2/teach/R/R_ts.pdf. Accessed 17 Sept 2016

  • Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

    Article  Google Scholar 

  • Singh CK, Katpatal YB (2017) A GIS based design of groundwater level monitoring network using multi-criteria analysis and geostatistical method. Water Resour Manag 31:4149–4163

    Article  Google Scholar 

  • Tabari H, Marofi S (2011) Changes of Pan evaporation in the west of Iran. Water Resour Manag 25:97–111

    Article  Google Scholar 

  • Valipour M, Banihabib ME, Behbahani SMR (2013) Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir. J Hydrol 476:433–441

    Article  Google Scholar 

  • Varouchakis EA (2017) Spatiotemporal geostatistical modelling of groundwater level variations at basin scale: a case study at Crete's Mires Basin. Hydrol Res 49:1131–1142

    Google Scholar 

  • Yang Q, Wang Y, Zhang J, Delgado J (2017) A comparative study of shallow groundwater level simulation with three time series models in a coastal aquifer of South China. Appl Water Sci 7:689–698

    Article  Google Scholar 

  • Zammit-Mangion, A.; Cressie, N. (2017). FRK: An R package for spatial and spatio-temporal prediction with large datasets, arXiv:1705.08105 Online; https://arxiv.org/abs/1705.08105. Accessed 13 Mar 2018

  • Zammit-Mangion A, Cressie N (2018). Fixed Rank Kriging: The R package. Online; https://cran.r-project.org/web/packages/FRK/index.html. Accessed 13 Mar 2018

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Acknowledgements

The authors would like to acknowledge the support of Hamedan Regional Water Authority (HRWA). This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Correspondence to Mohamed M. A. Mohamed.

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Sakizadeh, M., Mohamed, M.M.A. & Klammler, H. Trend Analysis and Spatial Prediction of Groundwater Levels Using Time Series Forecasting and a Novel Spatio-Temporal Method. Water Resour Manage 33, 1425–1437 (2019). https://doi.org/10.1007/s11269-019-02208-9

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