Abstract
Discrete groundwater level datasets are interpolated often using kriging group of models to produce a spatially continuous groundwater level map. There is always some level of uncertainty associated with different interpolation methods. Therefore, we developed a new trend function with the mean groundwater level as a drift variable in the regression kriging approach to predict the groundwater levels at the unvisited locations. Groundwater level data for 29 observation wells in Adyar River Basin were used to assess the performance of the developed regression kriging models. The cross-validation results shows that the proposed regression kriging method in the spatial domain outperforms other physical and kriging-based methods with R2 values of 0.96 and 0.98 during pre-monsoon and post-monsoon seasons, respectively.
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Data availability statement
MATLAB scripts used for kriging and IDW models are available in the following GitHub repository: https://github.com/mohanasundaram1986/kriging
References
Adhikary PP, Dash CJ (2017) Comparison of deterministic and stochastic methods to predict spatial variation of groundwater depth. Appl Water Sci 7:339–348. https://doi.org/10.1007/s13201-014-0249-8
Ahmadi SH, Sedghamiz A (2008) Application and evaluation of kriging and cokriging methods on groundwater depth mapping. Environ Monit Assess 138:357–368. https://doi.org/10.1007/s10661-007-9803-2
Amini MA, Torkan G, Eslamian S, Zareian MJ, Adamowski JF (2019) Analysis of deterministic and geostatistical interpolation techniques for mapping meteorological variables at large watershed scales. Acta Geophys 67:191–203. https://doi.org/10.1007/s11600-018-0226-y
Arun PV (2013) A comparative analysis of different DEM interpolation methods. Egypt J Remote Sens Space Sci 16:133–139. https://doi.org/10.1016/j.ejrs.2013.09.001
Bierkens MFP, Knotters M, van Geer FC (1999) Calibration of transfer function-noise models to sparsely or irregularly observed time series. Water Resour Res 35:1741–1750. https://doi.org/10.1029/1999WR900083
Bierkens MFP, Knotters M, Hoogland T (2001) Space-time modeling of water table depth using a regionalized time series model and the Kalman Filter. Water Resour Res 37:1277–1290. https://doi.org/10.1029/2000WR900353
Chung JW, Rogers JD (2012) Interpolations of groundwater table elevation in dissected uplands. Ground Water 50:598–607. https://doi.org/10.1111/j.1745-6584.2011.00889.x
Clark I (1979) Practical geostatistics. Applied Science Publishers Ltd, London
Cooper RM, Istok JD (1988) Geostatistics applied to groundwater contamination. I: Methodology. J Hydraul Eng 114:270–286
Dash JP, Sarangi A, Singh DK (2010) Spatial variability of groundwater depth and quality parameters in the National Capital Territory of Delhi. Environ Manag 45:640–650. https://doi.org/10.1007/s00267-010-9436-z
Daya AA, Bejari H (2015) A comparative study between simple kriging and ordinary kriging for estimating and modeling the Cu concentration in Chehlkureh deposit, SE Iran 6003–6020. Doi:10.1007/s12517-014-1618-1
Delbari M, Motlagh MB, Amiri M (2013) Spatio-temporal variability of groundwater depth in the Eghlid aquifer in southern. Iran 17:105–114
Desbarats AJ, Logan CE, Hinton MJ, Sharpe DR (2002) On the kriging of water table elevations using collateral information from a digital elevation model. J. Hydrol. 255:25–38. https://doi.org/10.1016/S0022-1694(01)00504-2
Gong G, Mattevada S, O’Bryant SE (2014) Comparison of the accuracy of Kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas. Environ Res 130:59–69. https://doi.org/10.1016/j.envres.2013.12.005
Gundogdu KS, Guney I (2007) Spatial analyses of groundwater levels using universal kriging. J Earth Syst Sci. https://doi.org/10.1007/s12040-007-0006-6
Hengl T, Heuvelink GBM, Stein A (2003) Comparison of Kriging with external drift and regression-Kriging. Technical note, ITC, Available on-line at https://www.itc.nl/library/Academicoutput/
Isaaks EH, Srivastava RM (1989) Applied geostatistics. Oxford University Press, New York
Kumar V (2007) Optimal contour mapping of groundwater levels using universal kriging: a case study. Hydrol Sci J 52:1038–1050. https://doi.org/10.1623/hysj.52.5.1038
Kumar D, Ahmed S (2003) Seasonal behaviour of spatial variability of groundwater level in a granitic aquifer in monsoon climate. Curr Sci 84(2): 188–196. Retrieved February 6, 2020, from www.jstor.org/stable/24108097
Kumar V, Remadevi (2006) Kriging of groundwater levels—a case study. J Spatial Hydrol 6:81–94
Landrum C, Castrignanó A, Zourarakis D, Mueller T (2016) Assessing the time stability of soil moisture patterns using statistical and geostatistical approaches. Agric Water Manag 177:118–127. https://doi.org/10.1016/j.agwat.2016.07.013
Ma T-S, Sophocleous M, Yu Y-S (1999) Geostatistical applications in ground-water modeling in south-central kansas. J. Hydrol. Eng 4(1):57
Marache, A., Lastennet, R., Breysse, D., (2016) Geostatistical investigations for suitable mapping of the water table: the Bordeaux case (France). Hydrogeol J 24:231–248. https://doi.org/10.1007/s10040-015-1316-4
Martínez-Murillo JF, Hueso-González P, Ruiz-Sinoga JD (2017) Topsoil moisture mapping using geostatistical techniques under different Mediterranean climatic conditions. Sci Total Environ 595:400–412. https://doi.org/10.1016/j.scitotenv.2017.03.291
Mhamad AJ (2019) Using regression Kriging to analyze groundwater according to depth and capacity of wells. UHD J. Sci. Technol. 3(1):39–47. https://doi.org/10.21928/uhdjst.v3n1y2019
Mohanasundaram S, Narasimhan B, Suresh Kumar G (2017) Transfer function noise modelling of groundwater level fluctuation using threshold rainfall-based binary-weighted parameter estimation approach. Hydrol Sci J 62(1):36–49. https://doi.org/10.1080/02626667.2016.1171325
Mohanasundaram S, Suresh Kumar G, Narasimhan B (2019) A novel deseasonalized time series model with an improved seasonal estimate for groundwater level predictions. H2Open J. 2:25–44. https://doi.org/10.2166/h2oj.2019.022
Nikroo L, Kompani-Zare M, Sepaskhah AR, Fallah Shamsi SR (2010) Groundwater depth and elevation interpolation by kriging methods in Mohr Basin of Fars province in Iran. Environ Monit Assess. https://doi.org/10.1007/s10661-009-1010-x
Plouffe CCF, Robertson C, Chandrapala L (2015) Comparing interpolation techniques for monthly rainfall mapping using multiple evaluation criteria and auxiliary data sources: a case study of Sri Lanka. Environ Model Softw 67:57–71. https://doi.org/10.1016/j.envsoft.2015.01.011
Rivest M, Marcotte D, Pasquier P (2008) Hydraulic head field estimation using kriging with an external drift: a way to consider conceptual model information. J Hydrol 361:349–361. https://doi.org/10.1016/j.jhydrol.2008.08.006
Rizo-Decelis LD, Pardo-Igúzquiza E, Andreo B (2017) Spatial prediction of water quality variables along a main river channel, in presence of pollution hotspots. Sci Total Environ 605–606:276–290. https://doi.org/10.1016/j.scitotenv.2017.06.145
Shirmohammadi B, Vafakhah M, Moosavi V, Moghaddamnia A (2013) Application of several data-driven techniques for predicting groundwater level. Water Resour Manag 27:419–432. https://doi.org/10.1007/s11269-012-0194-y
Shtiliyanova A, Bellocchi G, Borras D, Eza U, Martin R, Carrère P (2017) Kriging-based approach to predict missing air temperature data. Comput Electron Agric 142:440–449. https://doi.org/10.1016/j.compag.2017.09.033
Sun Y, Kang S, Li F, Zhang L (2009) Comparison of interpolation methods for depth to groundwater and its temporal and spatial variations in the Minqin oasis of northwest China. Environ Model Softw 24:1163–1170. https://doi.org/10.1016/j.envsoft.2009.03.009
Tankersley CD, Graham WD, Hatfield K (1993) Comparison of univariate and transfer function models of groundwater fluctuations. Water Resour Res 29:3517–3533. https://doi.org/10.1029/93WR01527
Theodoridou PG, Varouchakis EA, Karatzas GP (2017) Spatial analysis of groundwater levels using fuzzy logic and geostatistical tools. J Hydrol 555:242–252. https://doi.org/10.1016/j.jhydrol.2017.10.027
Theodossiou N, Latinopoulos P (2006) Evaluation and optimisation of groundwater observation networks using the Kriging methodology. Environ Model Softw 21:991–1000. https://doi.org/10.1016/j.envsoft.2005.05.001
Varouchakis EA, Corzo GA, Karatzas GP, Kotsopoulou A (2018) Spatio-temporal analysis of annual rainfall in Crete. Greece Acta Geophys 66:319–328. https://doi.org/10.1007/s11600-018-0128-z
Varouchakis EA, Hristopulos DT (2013) Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables. Adv Water Resour 52:34–49. https://doi.org/10.1016/j.advwatres.2012.08.002
Varouchakis EA, Hristopulos DT, Karatzas GP (2012) Improving Kriging of groundwater level data using nonlinear normalizing transformations: a field application. Hydrol Sci J 57(7):1404–1419. https://doi.org/10.1080/02626667.2012.717174
Vereecken H, Huisman JA, Pachepsky Y, Montzka C, van der Kruk J, Bogena H, Weihermüller L, Herbst M, Martinez G, Vanderborght J (2014) On the spatio-temporal dynamics of soil moisture at the field scale. J. Hydrol. 516:76–96. https://doi.org/10.1016/j.jhydrol.2013.11.061
Wagner PD, Fiener P, Wilken F, Kumar S, Schneider K (2012) Comparison and evaluation of spatial interpolation schemes for daily rainfall in data scarce regions. J Hydrol 464–465:388–400. https://doi.org/10.1016/j.jhydrol.2012.07.026
WRO (Water Resources Organization) (2007) Micro level study Chennai basin. Volume-I Institute of Water Studies, Taramani, Chennai
Wu T, Li Y (2013) Spatial interpolation of temperature in the United States using residual Kriging. Appl Geogr 44:112–120. https://doi.org/10.1016/j.apgeog.2013.07.012
Yin S, Xiao Y, Gu X, Hao Q, Liu H, Hao Z, Meng G, Pan X, Pei Q (2019) Geostatistical analysis of hydrochemical variations and nitrate pollution causes of groundwater in an alluvial fan plain. Acta Geophys 67:1191–1203. https://doi.org/10.1007/s11600-019-00302-5
Zhu K, Cui Z, Jiang B, Yang G, Chen Z, Meng Q, Yao Y (2013) A DEM-based residual Kriging model for estimating groundwater levels within a large-scale domain: a study for the Fuyang River Basin. Clean Technol Environ Policy. https://doi.org/10.1007/s10098-012-0563-5
Acknowledgement
We would like to acknowledge the State Ground and Surface Water Resources Data Centre (SGSWRDC), Institute of Water Studies (IWS), Taramani, for sharing the groundwater hydraulic head datasets for this research. We would also like to acknowledge and thank the departmental computer facility, department of civil engineering, IIT Madras, India, and Water Engineering and Management, Asian Institute of Technology, Pathum Thani, Thailand, for providing the high-end computer facility to carry out this research. We also would like to acknowledge the authors of this manuscript for technical suggestions and grammatical editing contributions.
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Mohanasundaram, S., Udmale, P., Shrestha, S. et al. A new trend function-based regression kriging for spatial modeling of groundwater hydraulic heads under the sparse distribution of measurement sites. Acta Geophys. 68, 751–772 (2020). https://doi.org/10.1007/s11600-020-00427-y
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DOI: https://doi.org/10.1007/s11600-020-00427-y