Mapping of Groundwater Salinity Using Dual Reciprocity Boundary Element Method in Nuq Region, Rafsanjan

Document Type : Research Paper


1 Assoc. Prof., Dept., of Soil Science., College of Agriculture, Vali-e-Asr University of Rafsanjan

2 Assist. Prof., Dept., of Physics, Faculty of Sciences, Vali-e-Asr University of Rafsanjan


In this study, a new numerical method based on Dual Reciprocity Boundary Element Method (DRBEM) is presented to interpolate scattered data. For this purpose, water samples were taken from 120 wells in Nuq region, Rafsanjan, for salinity measurements. The proposed estimator was compared with respect to its precision with the conventional ones, i.e., ordinary kriging and inverse distance weighting (IDW) while the spatial mapping of ground water salinity was performed in the study area. Besides, a more revealing measure of performance was obtained by computing the mean rank of each interpolation method. Results revealed the superiority of DRBEM over the kriging and IDW methods due to its lower root mean square error (RMSE) and relative root mean square error (RMSE%) as well as its higher goodness of prediction index (G) . It was also found that DRBEM is the most accurate one when the mean rank and standard deviations of the ranks are used to avoid the outlier effects in assessing the prediction performance of the three methods. Nevertheless, further research is required before DRBEM could be properly combined with ancillary variables to improve the interpolation performance and to develop a user-friendly algorithm that can be implemented in a GIS package.


Main Subjects

1. Collins, F. C., and Bolstad, P. V. (1996). “A comparison of spatial interpolation techniques in temperature estimation.” Proceedings of the 3rd International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, NM, Santa Barbara, CA: National Center for Geographic Information and Analysis, Santa Barbara.
2. Hartkamp, A. D., De Beurs, K., Stein, A., and White, J. W. (1999). Interpolation techniques for climate variables, CIMMYT, Mexico, D.F.
3. Laslett, G. M., McBratney, A. B., Pahl, P. J., and Hutchinson, M. F. (1987). “Comparison of several spatial prediction methods for soil pH.” Journal of Soil Science, 38, 325-341.
4. Li, J., and Heap, A. D. (2008). A review of spatial interpolation methods for environmental scientists, Geoscience Australia, Record 2008/23.
5. Jaswan, M. A. (1963). “Integral equation methods in potential theory I.” Proceedings of the Royal Society, 275, 23-32.
6. Symm, G. T. (1963). “Integral equation methods in potential theory II.” Proceedings of the Royal Society, 275, 33-46.
7. Hess, J., and Smith, A. M. O. (1964). “Calculation of non-lifting potential flow about arbitrary three-dimension bodies.” J. of Ship Research, 8, 22-44.
8. Brebbia, C. A., and Dominguez, J. (1970). “Boundary element methods for potential problems.” Applied Mathematical Modelling, 1, 7.
9. Brebbia, C. A. (1978). The boundary element method for engineers, Pentech Press, London, UK.
10. Becker, A. A. (1992). The boundary element method in engineering, Berkshire: McGraw-Hill Education in Maidenhead, New York, USA.
11. Paris, F., and Canas, J. (1997). Boundary element method: Fundamentals and application, Oxford University Press, London, UK.
12. Gaspar, C. (2000). “Multi-Level Biharmonic and Bi-Helmholtz interpolation with application to the boundary element method.” Engineering Analysis with Boundary Elements, 24, 559.
13. Sovizi, M., and Esfandiarpour, I. (2013). “Scattered data interpolation based on dual reciprocity boundary element method with unknown boundary conditions.” Mathematical Sciences Letters, 2(3), 1-7.
14. Arfken, G. B., Weber, H. J., and Harris, F. E. (2012). Mathematical methods for physicists: A comprehensive guide, 7th Ed., Academic Press, Elsevier, The Netherlands.
15. Shi, W., Liu, J., Du, Z., Song, Y., Chen, C., and Yue, T. (2009). “Surface modelling of soil pH.” Geoderma, 150, 113-119.
16. Farifteh, J., Van der Meer, F., Atzberger, C., and Carranza, E. J. M. (2007). “Quantitative analysis of salt-affected soil reflectance spectra: a comparison of two adaptive methods (PLSR and ANN).” Remote Sensing of Environment, 110, 59-78.
17. Park, S. J., and Vlek, P. L. G. (2002). “Environmental correlation of three-dimensional soil spatial variability: A comparison of three adaptive techniques.” Geoderma, 109, 117-140.
18. Corstanje, R., Grunwald, S., Reddy, K. R., Osborne, T. Z., and Newman, S. (2006). “Assessment of the spatial distribution of soil properties in a Northern Everglades marsh.” J. of Environmental Quality, 35, 938-949.
19. Schloeder, C. A., Zimmerman, N. E., and Jacobs, M. J. (2001). “Comparison of methods for interpolating soil properties using limited data.” Soil Science Society of America Journal, 65, 470-479.
20. Odeh, I. O. A., McBratney, A. B., and Chittleborough, D. J. (1994). “Spatial prediction of soil properties from landform attributes derived from a digital elevation model.” Geoderma, 63, 197-214.
21. Triantafilis, J., Odeh, I. O. A., and McBratney, A. B. (2001). “Five geostatistical models to predict soil salinity from electromagnetic induction data across irrigated cotton.” Soil Science Society of America Journal, 65, 869-878.
22. Efron, B., and Stein, C. (1981). “The jackknife estimate of variance.” The Annals of Statistics, 9(3), 586-596.
23. Hengl, T., and Husnjak, S. (2006). “Evaluating adequacy and usability of soil maps in Croatia.” Soil Science Society of America Journal, 70, 920-929.
24. Obiefun, G. I., and Sheriff, A. (2011). “Assessment of shallow ground water quality of Pindiga Gombe Area, Yola Area, NE, Nigeria for irrigation and domestic purposes.” Research Journal of Environmental and Earth Sciences, 3(2), 131-141.
25. Weber, D. D., and Englund, E.J. (1992). “Evaluation and comparison of spatial interpolators.” Mathematical Geology, 24, 381-391.