Abstract
Benchmarking of different numerical models simulating groundwater flow and contaminant mass transport is the aim of the present study, in order to determine criteria for the selection of numerical model(s) that could be better tailored to the needs of a specific region. This analysis aims at evaluating the performance of a finite difference-based numerical model (MODFLOW-ΜΤ3DMS), a finite element-based numerical model (FEFLOW), and a hybrid finite element-finite difference coupling numerical model (Princeton Transport Code-PTC), all developed to simulate groundwater flow and nitrate mass transport in an alluvial aquifer. The evaluation of the models’ performance is assessed based on statistical measures and graphical performance analysis of the model point predictions to the observed values. The outcome of the analysis showed that among the three groundwater simulation models, FEFLOW algorithm exhibited the best performance in simulating both groundwater level and nitrate mass distribution. All simulation algorithms were found to offer different advantages, so in principle the selection of the appropriate model(s) should be done in accordance with the problem’s characteristics and/ or in a complementary way in order to achieve accurate representation of the aquifer system and thus optimal groundwater resources management. Even though the selection of the most suitable groundwater simulation algorithm is case-oriented, however, fractional gross error (FGE) was proven to be a reliable indicator that could be used by modelers to select the most suitable groundwater algorithm based on the available groundwater data.
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References
Adamowski, J., & Chan, H. F. (2011). A wavelet neural network conjunction model for groundwater level forecasting. Journal of Hydrology, 407(1), 28–40.
Almasri, M. N., & Kaluarachchi, J. J. (2007). Modeling nitrate contamination of groundwater in agricultural watersheds. Journal of Hydrology, 343(3–4), 211–229.
Alhama Manteca, I. (2013). Simulation and consequences of successive anthropogenic activity in the Agua Amarga coastal aquifer (Southeast Spain). Hydrological Sciences Journal, 58(5), 1072–1087.
Anderson, M. P., Woessner, W. W., & Hund, R. J. (1992). Applied groundwater modeling. USA: Academic Press.
Appelo, C. A. J., & Postma, D. (2005). Geochemistry, groundwater and pollution. Amsterdam: Balkema Publishers.
Bear, J., & Verruijt, A. (1987). Modeling Groundwater Flow and Pollution. Holland: Kluwer Academic Publishers.
Bear, J., & Cheng, A. H. D. (2010). Modeling groundwater flow and contaminant transport. London: Springer.
Bennett, N. A., Croke, B. F. W., Guaris, G., et al. (2013). Characterising performance of environmental models. Environmental Modelling & Software, 40, 1–20.
Berkowitz, B., Dror, I., & Yaron, B. (2008). Contaminant geochemistry: Interactions and transport in the subsurface environment. Berlin: Springer.
Bezes, Κ. (1999). Hydrogeological study of artificial recharge in aquifers of Trizina in Pireaus prefecture. Athens: Ministry of Agriculture, Hydrogeological conditions report.
Calzolari, C., & Ungaro, F. (2012). Predicting shallow water table depth at regional scale from rainfall and soil data. Journal of Hydrology, 414–415, 374–387.
Celia, M. A., Bouloutas, E. T., & Zarba, R. L. (1990). A general mass-conservative numerical solution of the unsaturated flow equation. Water Resources Research, 26(7), 1483–1496.
Coppola, E., Szidarovszky, F., Poulton, M., et al. (2003). Artificial neural network approach for predicting transient water levels in a multilayered groundwater system under variable state, pumping, and climate conditions. Journal of Hydrologic Engineering, ASCE, 8(6), 348–360.
Cuello, C. (1976). Gastric cancer in Colombia: I. Cancer risk and suspect environmental agents. Journal of the National Cancer Institute, 57, 1015–1020.
Diersch, H.J.G., 2002. WASY Software® - FEFLOW: Finite Element Subsurface Flow & Transport Simulation System: Reference Manual [on line]. WASY Institute for Water Resources Planning and Systems Research Ltd.
EASAC-European Academies Science Advisory Council, 2010. Groundwater in the Southern Member States of the European Union: an assessment of current knowledge and future prospects, Country report for Greece [on line]. Available from: http://www.easac.eu/home/reports-and-statements/detail-view/article/groundwater.html. [Accessed 1 November 2015].
EEA-European Environment Agency, 2000. CORINE Land Cover [on line]. Available from: http://www.eea.europa.eu/data-and-maps/figures/corine-land-cover-2000-by-country-3. [Accessed 1 November 2015].
EPA-United States Environmental Protection Agency, 2009. National primary drinking water regulations [on line]. Available from: http://www.epa.gov/dwregdev/drinking-water-regulations-and-contaminants#Primary [Accesed 1 November 2015].
EU-European Union Council Directive 98/83/EC of 3 November 1998 on the quality of water intended for human consumption.
Fraser, P., Chilvers, C., Beral, V., et al. (1980). Nitrate and human cancer: A review of the evidence. International Journal of Epidemiology, 9(1), 3–11.
Fytikas, M., Innocenti, F., & Mazzuoli, R. (1981). Geological map of Greece-“Methana” Sheet, 1:50,000. Athens: IGME.
Ghoraba, S. M., Zyedan, B. A., & Rashwan, I. M. H. (2013). Solute transport modeling of the groundwater for quaternary aquifer quality management in Middle Delta, Egypt. Alexandria Engineering Journal, 52(2), 197–207.
Goovaerts, P. (1997). Geostatistics for natural resources evaluation. New York: Oxford University Press.
Gray, W. G. (1984). Comparison of finite difference and finite element methods. In J. Bear Editor & M. Y. Coropcioglu Editor (Eds.), Fundamentals of transport phenomena in porous media (pp. 899–785), NATO ASI Series (Series E: Applied Sciences), Dordrecht: Martinus Nijhoff Publishers.
Gu, B., Ge, Y., Chang, S. X., Luo, W., & Chang, J. (2013). Nitrate in groundwater of China: Sources and driving forces. Global Environmental Change, 23(5), 1112–1121.
Guneshwor Singh, L., Eldho, T. I., & Vinod Kumar, A. (2016). Coupled groundwater flow and contaminant transport simulation in a confined aquifer using mesh free radial point collocation method (RPCM). Engineering Analysis with Boundary Elements, 66, 20–33.
Gupta, V. H., Clark, M. P., Vrugt, J. A., et al. (2012). Towards a comprehensive assessment of model structural adequacy. Water Resources Research, 48(8), W08301.
Jang, C. S., Chen, C. F., Liang, C. P., & Chen, J. S. (2016). Combining groundwater quality analysis and a numerical flow simulation for spatially establishing utilization strategies for groundwater and surface water in the Pingtung plain. Journal of Hydrology, 533, 541–556.
Jones, D., Jones, N., Greer, J., & Nelson, J. (2015). A cloud-based MODFLOW service for aquifer management decision support. Computers & Geosciences, 78, 81–87.
Hayhoe, H. N. (1978). Study of the relative efficiency of finite difference and Galerkin techniques for modeling soil-water transfer. Water Resources Research, 14(1), 97–102.
Huyakorn, P. S., & Pinder, G. F. (1983). Computational methods in subsurface flow. New York: Academic Press.
Isaaks, E. H., & Srivastava, R. M. (1989). An introduction to applied geostatisics. New York: Oxford University Press.
Lockhart, K. M., King, A. M., & Harter, T. (2013). Identifying sources of groundwater nitrate contamination in a large alluvial groundwater basin with highly diversified intensive agricultural production. Journal of Contaminant Hydrology, 151, 140–154.
Ma, L., & Shaffer, M. J. (2001). A review of carbon and nitrogen processes in nine U.S. soil N dynamics models. In M. J. Shaffer Editor, L. Ma Editor, & S. Hansen Editor (Eds.), Modeling carbon and nitrogen dynamics for soil management (pp. 55–102). Florida: CRC Press.
Mandle, R. J. 2002. Groundwater modeling guidance. Michigan Department of Environmental Quality, GMP, draft, 1
Matiatos I., and Papadopoulou, P.M., 2012. In: 2nd Common Conference of Hellenic Hydrotechnical Association and Greek Committee for Water Resources Management-Integrated Water Resources Management for Sustainable Development, 11–13 October 2012 Patra. Patra: Hellenic Hydrotechnical association and Greek Committee for Water Resources Management, 1212–1225 (In Greek).
Matiatos, I., & Evelpidou, N. (2013). Assessment of groundwater quality contamination by nitrate leaching using multivariate statistics and geographic information systems. In B. Arheimer (Ed.), Understanding freshwater quality problems in a changing world (Vol. 361, pp. 183–190). Sweden: IAHS Pub.
Matiatos, I., Alexopoulos, A., & Godelitsas, A. (2014a). Multivariate statistical analysis of the hydro-geochemical and isotopic composition of the groundwater resources in northeastern Peloponnesus (Greece). Science of the Total Environment, 476-477, 577–590.
Matiatos, I., Varouchakis, E.A., and Papadopoulou, M.P., 2014b. Statistical sensitivity analysis of multiple groundwater mass transport models. In: 10th International Hydrogeological Congress of Greece, 8-10 October 2014Thessaloniki. Vol.1, 447–456.
Matiatos, I. (2016). Nitrate source identification in groundwater of multiple land-use areas by combining isotopes and multivariate statistical analysis: A case study of Asopos basin (Central Greece). Science of the Total Environment, 541, 802–814.
McGechan, M. B., & Wu, L. (2001). A review of carbon and nitrogen processes in European soil nitrogen dynamics. In M. J. Shaffer Editor, L. Ma Editor, & S. Hansen Editor (Eds.), Modeling carbon and nitrogen dynamics for soil management (pp. 103–171). Florida: CRC Press.
Meijerink, A.M.J., Bannert, D., Batelaan, O., et al., 2007. Remote Sensing Applications to Groundwater [on line]. Paris, UNESCO. Available from: http://sesremo.eu/downloads/teaching-material/gis-course_itc/ebooks/Remote%20Sensing%20applications%20to%20groundwater.pdf [Accessed 1 November 2015].
Mohanty, S., Jha, M. K., Kumar, A., & Panda, D. K. (2013). Comparative evaluation of numerical model and artificial neural network for simulating groundwater flow in Kathajodi–Surua inter-basin of Odisha, India. Journal of Hydrology, 495, 38–51.
Narasimhan, T. N. (1982). Numerical modeling in hydrogeology. In T. N. Narasimhan (Ed.), Recent trends in hydrogeology. Special paper (Vol. 189, pp. 273–296). Colorado: Geological Society of America.
Nash, J., & Sutcliffe, J. (1970). River flow forecasting through conceptual models part I-A discussion of principles. Journal of Hydrology, 10(3), 282–290.
Neuman, S. P., Feddes, R. A., & Bresler, E. (1975). Finite element analysis of two-dimensional flow in soils considering water uptake by roots: 1 theory. Soil Science Society of America Proceedings, 39, 224–230.
Ngo, A. Q. T., Bastian, P., & Ippisch, O. (2015). Numerical solution of steady-state groundwater flow and solute transport problems: Discontinuous Galerkin based methods compared to the streamline diffusion approach. Computer Methods in Applied Mechanics and Engineering, 294, 331–358.
Nikolos, I. K., Stergiadi, M., Papadopoulou, M. P., & Karatzas, G. P. (2008). Artificial neural networks as an alternative approach to groundwater numerical modeling and environmental design. Hydrological Processes, 22(17), 3337–3348.
Papadopoulou, M. P., Pinder, G. F., & Karatzas, G. P. (2003). Enhancement of the outer approximation method for the solution of concentration-constrained optimal-design groundwater-remediation problems. Water Resources Research, 39(7), 1185.
Papadopoulou, M. P., Pinder, G. F., & Karatzas, G. P. (2007). Flexible time-varying optimization methodology for the solution of groundwater management problems. European Journal of Operational Research, 180(2), 770–785.
Papadopoulou, M. P., Varouchakis, E. A., & Karatzas, G. P. (2009). Simulation of complex aquifer behavior using numerical and geostatistical methodologies. Desalination, 237(1–3), 42–53.
Pinder, G. F., & Gray, W. G. (1977). Finite element simulation in surface and subsurface hydrology. New York: Academic Press.
Pinder, G. F. (2002). Groundwater modeling using geographical information system. USA: John Wiley and Sons.
Pope, R. J., Chipperfield, M. P., Savage, N. H., Ordóñez, C., Neal, L. S., Lee, L. A., Dhomse, S. S., Richards, N. A. D., & Keslake, T. D. (2015). Evaluation of a regional air quality model using satellite column NO2: Treatment of observation errors and model boundary conditions and emissions. Atmospheric Chemistry and Physics., 15(10), 5611–5626.
Rao, S. V. N., Sreenivasulu, V., Murty Bhallamudi, S., et al. (2004). Planning groundwater development in coastal aquifers / Planification du développement de la ressource en eau souterraine des aquifères côtiers. Hydrological Sciences Journal, 49(1), 155–170.
Reilly, T. E., & Harbaugh, A. W. (2004). Guidelines for evaluating ground-water flow models. Scientific Investigations Report, 2004-5038, 37.
Rushton, K. R. (2003). Groundwater Hydrology: Conceptual and Computational Models. England: John Wiley and Sons.
Siemos, N., & Michalakakis, I. (2009). Evaluation of water resources in Attica region and the Islands of Argosaronic Gulf, Strategic Resources, (H.D. 06, Dep. 03)-Field measurements (Hydrological-Physical-Chemical). Athens: IGME.
Simpson, M. J., & Clement, T. P. (2003). Comparison of finite difference and finite element solutions to the variably saturated flow equation. Journal of Hydrology, 270(1–2), 49–64.
Singh, A. (2014). Groundwater resources management through the applications of simulation modeling: A review. Science of the Total Environment, 499, 414–423.
Singhal, B. B. S., & Gupta, R. P. (2010). Applied hydrogeology of fractured rocks. New York: Springer.
Spitz, K., & Moreno, J. (1996). A practical guide to groundwater and solute transport modeling. USA: John Wiley and Sons.
Van der Perk, M. (2006). Soil and water contamination: From molecular to catchment scale. Leiden: Taylor and Francis.
Varouchakis, E. A., Karatzas, G. P., & Giannopoulos, G. P. (2015). Impact of irrigation scenarios and precipitation projections on the groundwater resources of Viannos Basin at the island of Crete, Greece. Environmental Earth Sciences, 73(11), 7359–7374.
Varouchakis, E. A., & Hristopulos, D. T. (2013). Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables. Advances in Water Resources, 52, 34–49.
WHO-World Health Organisation, 2004. Rolling Revision of the WHO Guidelines for Drinking-Water Quality. Nitrates and Nitrites in Drinking Water [on line]. WHO. Available from: http://www.who.int/water_sanitation_health/dwq/chemicals/en/nitratesfull.pdf. [Accessed 1 November 2015].
WWAP-United Nations World Water Assessment Programme, 2015. The United Nations World Water Development Report 2015: Water for a Sustainable World [on line]. Paris, UNESCO. Available from: http://unesdoc.unesco.org/images/0023/002318/231823E.pdf [Accessed1 November 2015].
Yoon, H., Jun, S. C., Hyun, Y., Bae, G. O., & Lee, K. K. (2011). A comparative study of artificial neural networks and support vector machines for predicting groundwater levels in a coastal aquifer. Journal of Hydrology, 396(1–2), 128–138.
Zheng, C., & Bennett, G. D. (1995). Applied contaminant transport modeling. USA: Wiley.
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Matiatos, I., Varouchakis, E.A. & Papadopoulou, M.P. Performance Evaluation of Multiple Groundwater Flow and Nitrate Mass Transport Numerical Models. Environ Model Assess 24, 659–675 (2019). https://doi.org/10.1007/s10666-019-9653-7
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DOI: https://doi.org/10.1007/s10666-019-9653-7