Evaluating of spatial hydraulic head distribution using Empirical Bayesian Kriging and ANFIS methods in Dogger Karst Aquifer

Abstract

In this study, Adaptive Neuro Fuzzy based Inference System (ANFIS) and Empirical Bayesian Kriging (EBK) are evaluated for assessing hydraulic head distribution in a karst aquifer. ANFIS uses three reduced centered preprocessed inputs, which are cartesian coordinates (XY) and the elevation (Z). All models are applied to the same case study: Dogger aquifer, which covers an area of 445 km2 in the south east of Poitiers, France. Models are tested on 100 random data subset of 20 data among 113, the remaining is used to train and validate the models. ANFISXYZ and EBK are then used to interpolate the hydraulic head on a 100 m square - grid covering the study area. Both EBK and ANFIS interpolations exhibit similar patterns, with the average values of RMSE = 5.2 m and R2 = 0.80. Combining these approaches can be an advanced option for interpolating hydraulic head in a more accurate way.

Keywords

• ANFIS
• Empirical Bayesian Kriging
• Hydraulic head
• Dogger
• Karst
• France

Karstik Dogger Akiferi’nde konumsal hidrolik yük dağılımının Ampirik Bayes Kriging ve ANFIS yöntemleriyle değerlendirilmesi

Abstract

Bu çalışmada, karstik bir akiferdeki hidrolik yük dağılımı, Bulanık mantıklı yapay sinir ağları (ANFIS) ve Ampirik Bayes Kriging (EBK) yöntemleri ile değerlendirilmiştir. ANFIS, önceden elde edilmiş kartezyen koordinatları (XY) ve yükseklik datasını (Z) giriş verisi olarak kullanır. EBK, giriş datalarından birçok semi-variogram modelini tahmin ederek ortaya çıkan hatayı hesaba katar ve enterpolasyonda kullanır. İki yöntem sonucunda çıkan modeller aynı çalışma alanındaki hidrolik yük dağılımını incelemede kullanılmıştır: Dogger akiferi, Fransa’nın Poitiers şehrinin güneydoğusunda yer alır ve 445 km2 genişliğinde bir alanı kaplamaktadır. Toplam 113 hidrolik yük verisinin içinden 20 verinin 100 adet rastgele veri alt kümesinde test edilerek modeller elde edilmiştir. Geriye kalan veriler ise modelleri eğitmek ve doğrulamak için kullanılmıştır. ANFISXYZ ve EBK daha sonra çalışma alanını kaplayan 100 m2 büyüklüğünde alana sahip hücrelere ayrılarak her hücredeki hidrolik yükü enterpole etmek için kullanılmıştır. Hem EBK hem de ANFIS enterpolasyonları, ortalama RMSE = 5.2 m ve R2 = 0.80 değerleri ile benzer enterpolasyon sonuçları göstermiştir. Bu iki yaklaşımı birleştirmek hidrolik yük dağılımını daha doğru enterpole etmek için gelişmiş bir seçenek olabilir.

Keywords

• ANFIS
• Ampirik Bayes Kriging
• Hidrolik yük
• Dogger
• Karst
• Fransa

References

1. Kurtulus, B., Flipo, N., Goblet, P., Vilain, G., Tournebize, J., Tallec, G., (2011). Hydraulic head interpolation in an aquifer unit using anfis and ordinary kriging. In: Madani K et al. (eds) Computational intelligence. 1st edn,. P. 265–276. Berlin, Heidelberg, Springer. https://doi.org/10.1007/978-3-642-20206-3_18.
2. Flipo, N., Monteil, C., Poulin, M., Fouquet, C., Krimissa, M., (2012). Hybrid fitting of a hydrosystem model: Long term insight into the Beauce aquifer functioning (France). Water Resources Research 48(5). https://doi.org/10.1029/2011WR011092.
3. Amini, M., Abbaspour, K.C., Johnson, C.A., (2010). A comparison of different rule-based statistical models for modeling geogenic groundwater contamination. Environmental Modelling & Software 25(12): 1650-1657. https://doi.org/10.1016/j.envsoft.2010.05.014.
4. Yeganeh, B., Hewson, M.G., Clifford, S., Knibbs, L.D., Morawska, L., (2017). A satellite-based model for estimating PM2.5 concentration in a sparsely populated environment using soft computing techniques. Environmental Modelling & Software 88: 84-92, https://doi.org/10.1016/j.envsoft.2016.11.017.
5. Rivest, M., Marcotte, D., Pasquier, P., (2008). Hydraulic head field estimation using kriging with an external drift: A way to consider conceptual model information. Journal of Hydrology 361(3): 349–361. https://doi.org/10.1016/j.jhydrol.2008.08.006.
6. Perkins, S.P., Sophocleous, M., (1999). Development of a comprehensive watershed model applied to study stream yield under drought conditions. Ground Water 37(3): 418–426. https://doi.org/10.1111/j.1745-6584.1999.tb01121.x.
7. Flipo, N., Jeannée, N., Poulin, M., Even, S., Ledoux, E., (2007). Assessment of nitrate pollution in the Grand Morin aquifers (France): Combined use of geostatistics and physically-based modeling. Environmental Pollution 146(1):241–256. https://doi.org/10.1016/j.envpol.2006.03.056.
8. Flipo, N., Mourhi, A., Labarthe, B., Biancamaria, S., Rivière, A., Weill, P., (2014). Continental hydrosystem modelling : the concept of nested stream-aquifer interfaces. Hydrology and Earth System Sciences 18(8)3121–3149. doi:10.5194/hess-18-3121-2014.

9. Kurtulus, B., Flipo, N., (2012). Hydraulic head interpolation using anfis - model selection and sensitivity analysis. Computer & Geosciences 38(1): 43–51, https://doi.org/10.1016/j.cageo.2011.04.019.
10. Mouhri, A., Flipo, N., Rejiba, F., Fouquet, C., Bodet, L., Goblet, P., Kurtulus, B., Ansart, P., Tallec, G., Durand, V., Jost, A., (2013). Designing a multi-scale sampling system of stream-aquifer interfaces in a sedimentary basin. Journal of Hydrology 504: 194–206, https://doi.org/10.1016/j.jhydrol.2013.09.036.
11. Tóth, J., (2002). József Tóth: An autobiographical sketch. Ground Water 40(3): 320–324. https://doi.org/10.1111/j.1745-6584.2002.tb02661.x.
12. Cressie, N., (1990). The origins of kriging. Mathematical Geology 22(2): 239–252, https://doi.org/10.1007/BF00889887.
13. Rouhani, S., Myers, D.E., (1990). Problems in space-time kriging of geohydrological data. Mathematical Geology 22(5): 611–623, https://doi.org/10.1007/BF00890508.
14. Weber, D.D., Englung, E.J., (1994). Evaluation and comparison of spatial interpolators II. Mathematical Geology 26: 589–604, https://doi.org/10.1007/BF02089243.
15. Zimmerman, D., Pavlik, C., Ruggles, A., Armstrong, M.P., (1999). An experimental comparison of ordinary and universal kriging and inverse distance weighting. Mathematical Geology 31(4): 375–390, https://doi.org/10.1023/A:1007586507433.
16. Brochu, Y., Marcotte, D., (2003). A simple approach to account for radial flow and boundary conditions when kriging hydraulic head fields for confined aquifers. Mathematical Geology 35(2): 111–139, https://doi.org/10.1023/A:1023231404211.
17. Theodossiou, N., Latinopoulos, P., (2006). Evaluation and optimisation of groundwater observation networks using the kriging methodology. Environmental Modelling & Software 21(7): 991–1000, https://doi.org/10.1016/j.envsoft.2005.05.001.
18. Lyon, S.W., Seibert, J., Lembo, A.J., Walter, M.T., Steenhuis, T.S., (2006) Geostatistical investigation into the temporal evolution of spatial structure in a shallow water table. Hydrology and Earth System Sciences 10: 113–125.
19. Ahmadi, S.H., Sedghamiz, A., (2007). Geostatistical analysis of spatial and temporal variations of groundwater level. Environmental Monitoring and Assessment 129(1-3): 277–294, https://doi.org/10.1007/s10661-006-9361-z.
20. Abedini, M.J., Nasseri, M., Ansari, A., (2008). Cluster-based ordinary kriging of piezometric head in West Texas/New Mexico - Testing of hypothesis. Journal of Hydrology 351(3): 360–367, https://doi.org/10.1016/j.jhydrol.2007.12.030.
21. Renard, F., Jeannée, N., (2008). Estimating transmissivity fields and their influence on flow and transport: The case of Champagne mounts. Water Resources Research 44(11): 1–12, https://doi.org/10.1029/2008WR007033.
22. Ta’any, R.A., Tahboub, A.B., Saffarini, G.A., (2009). Geostatistical analysis of spatiotemporal variability of groundwater level fluctuations in Amman-Zarqa basin, Jordan: A case study. Environmental Geology 57(3): 525–535, https://doi.org/10.1007/s00254-008-1322-0.
23. Buchanan, S., Triantafilis, J., (2009). Mapping water table depth using geophysical and environmental variables. Ground Water 47(1): 80–96, https://doi.org/10.1111/j.1745-6584.2008.00490.x.
24. Pardo-Igúzquiza, E., Chica-Olmo, M., Garcia-Soldado, M.J., Luque-Espinar, J.A., (2009). Using semivariogram parameter uncertainty in hydrogeological applications. Ground Water 47(1): 25–34, https://doi.org/10.1111/j.1745-6584.2008.00494.x.
25. 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. Environmental Modelling & Software 24(10): 1163–1170, https://doi.org/10.1016/j.envsoft.2009.03.009
26. Plouffe, C.C., 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. Environmental Modelling & Software 67: 57-71,https://doi.org/10.1016/j.envsoft.2015.01.011.
27. Hoeksema, R.J., Clapp, R.B., Thomas, A.L., Hunley, A.E., Farrow, N.D., Dearstone, K.C., (1989) Cokriging model for estimation of water table estimation. Water Resources Research 25(3): 429–438, https://doi.org/10.1029/WR025i003p00429.
28. Boezio, M., Costa, J., Koppe, J., (2006), Accounting for extensive secondary information to improve watertable mapping. Natural Resources Research 15(1): 33–48, https://doi.org/10.1007/s11053-006-9014-5.
29. Pardo-Igúzquiza, E., Chica-Olmo, M., (2007). KRIGRADI: A cokriging program for estimating the gradient of spatial variables from sparse data. Computers & Geosciences 33(4): 497–512, https://doi.org/10.1016/j.cageo.2006.08.004.
30. Ahmadi, S.H., Sedghamiz, A., (2008). Application and evaluation of kriging and cokriging methods on groundwater depth mapping. Environmental Monitoring and Assessment 138(1): 357–368, https://doi.org/10.1007/s10661-007-9803-2.
31. Bargaoui, Z.K., Chebbi, A., (2008). Comparison of two kriging interpolation methods applied to spatiotemporal rainfall. Journal of Hydrology 365(1): 56-73, https://doi.org/10.1016/j.jhydrol.2008.11.025.
32. Desbarats, A.J., Logan, C.E., Hinton, M.J., Sharpe, D.R., (2002). On the kriging of water table elevations using collateral information from a digital elevation model. Journal of Hydrology 255(1): 25–38, https://doi.org/10.1016/S0022-1694(01)00504-2.
33. Tóth, J., (1962). A theory of groundwater motion in small drainage basins in Central Alberta, Canada. Journal of Geophysical Research 67(11): 4375–4387, https://doi.org/10.1029/JZ067i011p04375.
34. Pilz, J., Spöck, G., (2007). Why do we need and how should we implement Bayesian Kriging methods. Stochastic Environmental Research and Risk Assessment 22(5): 621-632, https://doi.org/10.1007/s00477-007-0165-7.
35. Pilz, J., Kazianka, H., Spöck, G., (2012). Some advances in Bayesian spatial prediction and sampling design. Spatial Statistics 1: 65-81, https://doi.org/10.1016/j.spasta.2012.03.003.
36. Finzgar, N., Jez, E., Voglar, D., Lestan, D., (2014). Spatial distribution of metal contamination before and after remediation in the Meza Valley, Slovenia. Geoderma 217-218: 135-143, https://doi.org/10.1016/j.geoderma.2013.11.011.
37. Maier, H.R., Jain, A., Dandy, G.C., Sudheer, K.P., (2010). Methods used for the development of neural networks for the prediction of water resource variables in river systems: Current status and future directions. Environmental Modelling & Software 25(8):891–909, https://doi.org/10.1016/j.envsoft.2010.02.003.
38. Sivapragasam, C., Vanitha, S., Muttil, N., Suganya, K., Suji, S., Selvi, M.T., Selvi, R., Sudha, S.J., (2014). Monthly flow forecast for Missisipi River basin using artificial neural networks. Neural Computing and Applications 24(7-8): 1785-1793, https://doi.org/10.1007/s00521-013-1419-6.
39. Kant, A., Suman, P.K., Giri, B.J., Tiwari, M.K., Chatterjee, C., Nayak, P.C., Kumar, S., (2013). Comparison of multi-objectie evolutionary neural network, adaptive neuro-fuzzy inference system and bootstrap-based neural network for flood forecasting. Neural Computing and Applications 23(1): 231-246, https://doi.org/10.1007/s00521-013-1344-8.
40. Rezaeianzadeh, M., Tabari, H., Yazdi, A.A., Isik, S., Kalin, L., (2014). Flood flow forecasting using ANN, ANFIS and regression models. Neural Computing and Applications 25(1): 25-37, https://doi.org/10.1007/s00521-013-1443-6.
41. Alvisi, S., Franchini, M., (2011). Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environmental Modelling & Software 26(4): 523-537, https://doi.org/10.1016/j.envsoft.2010.10.016.
42. Johannet, A., Ayral, P. & Vayssade, B., (2007). Modelling non measurable processes by neural networks: Forecasting underground flow case study of the Ceze basin (Gard - France). In: “Advances and innovation in systems, computing sciences and software engineering”, 1st edn., (K. Elleithy ed.), Springer, pp. 53–58, Dordrecht, https://doi.org/10.1007/978-1-4020-6264-3_10.
43. Kurtulus, B., Razack, M., (2007). Evaluation of the ability of an artificial neural network model to simulate the input-output responses of a large karstic aquifer, The La Rochefoucauld (Charente, France). Hydrogeology Journal 15(2): 241–254, https://doi.org/10.1007/s10040-006-0077-5.
44. Lallahem, S., Mania, J., (2003). A nonlinear rainfall-runoff model using neural network technique: example in fractured porous media. Mathematical and Computer Modelling 37(9-10): 1047–1061, https://doi.org/10.1016/S0895-7177(03)00117-1.
45. Minns, A. & Hall, M., (2004). Rainfall-runoff modelling. In: “Neural Networks For Hydrological Modeling”, 1st edn., (R. Abrahart et al. eds.), CRC Press, pp. 157–176, Leiden.
46. Takagi, T.M., Sugeno, M., (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man Cybernetics 15(1): 116–132, https://doi.org/10.1016/B978-1-4832-1450-4.50045-6.
47. Jang, J.S.R., (1993). ANFIS adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man Cybernetics 23(3): 665–685, https://doi.org/10.1109/21.256541.
48. Jang, J.S.R., (1995). Neuro-fuzzy modeling and control. Proc. IEEE 83(3): 378–406, https://doi.org/10.1109/5.364486.
49. Jang, J.S.R., (1996). Input selection for anfis learning. Proc IEEE Int Conf on Fuzzy Syst. 2(3): 1493–1499, https://doi.org/10.1109/FUZZY.1996.552396.
50. Celikyilmaz, A., Turksen, I.B. (2009). Modeling Uncertainty with Fuzzy Logic, Berlin, Springer Heidelberg, https://doi.org/10.1007/978-3-540-89924-2
51. Wang, W.C., Chau, K.W., Cheng, C.T., Qiu, L., (2009). A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. Journal of Hydrology 374(3): 294–306, https://doi.org/10.1016/j.jhydrol.2009.06.019.
52. Sağir, Ç., Kurtuluş, B., (2017). Hydraulic head and groundwater 111 Cd content interpolations using empirical Bayesian kriging (EBK) and geo-adaptive neuro-fuzzy inference system (geo-ANFIS). Water SA 43(3): 509-519, http://dx.doi.org/10.4314/wsa.v43i3.16.
53. Nayak, P.C., Sudheer, K.P., Ragan, D.M., Ramasastri, K.S., (2004). A neuro-fuzzy computing technique for modeling hydrological time series. Journal of Hydrology 291(1): 52–66, https://doi.org/10.1016/j.jhydrol.2003.12.010.
54. El-Shafie, A., Taha, M.R., Noureldin, A., (2007) A neuro-fuzzy model for inflow forecasting of the Nile river at Aswan high dam. Water Resourches Management 21(3): 533–556, https://doi.org/10.1007/s11269-006-9027-1.
55. Fırat, M., (2008). Comparison of artificial intelligence techniques for river flow forecasting. Hydrology and Earth System Sciences 12(1): 123–139.
56. Pai, T.Y., Wan, T.J., Hsu, S.T., Chang, T.C., Tsai, Y.P., Lin, C.Y., Hu, H.C., Yu, L.F., (2009). Using fuzzy inference system to improve neural network for predicting hospital wastewater treatment plant effluent. Computers &Chemical Engineering 33(7): 1272–1278, https://doi.org/10.1016/j.compchemeng.2009.02.004.
57. Lin, G.F., Chen, L.H., (2004). A spatial interpolation method based on radial basis function networks incorporating a semivariogram model. Journal of Hydrology 288(3): 288–298, https://doi.org/10.1016/j.jhydrol.2003.10.008.
58. Kholghi, M., Hosseini, S.M., (2009). Comparison of groundwater level estimation using neuro-fuzzy and ordinary kriging. Environmental Modelling & Assessment 14(6): 729–737, https://doi.org/10.1007/s10666-008-9174-2.
59. Flipo, N., Kurtulus, B., 2011. Geo-Anfis: Application to piezometric head interpolation in unconfined aquifer unit. Proceedings of the FUZZYSS’11 Congress, November 2011, pp. 195-198, Ankara, Turkey.
60. Tapoglou, E., Karatzas, G.P., Trichakis, I.C., Varouchakis, E.A., (2014). A spatio-temporal hybrid neural network kriging model for groundwater level simulation. Journal of Hydrology 519: 3193-3203, https://doi.org/10.1016/j.jhydrol.2014.10.040.
61. Le Gal La Salle, C., Marlin, C., Savoye, S., Fontes, J.C., (1996). Geochemistry and 14C dating of ground waters from Jurassic aquifers of North Aquitaine Basin (France). Applied Geochemistry 11(3): 433-445, https://doi.org/10.1016/0883-2927(96)00016-9.
62. Riva, M., Guadagnini, A., Bodin, J., Delay, F., (2009). Characterization of the hydrogeological experimental site of Poitiers (France) by stochastic well testing analysis. Journal of Hydrology 369(1): 154-164, https://doi.org/10.1016/j.jhydrol.2009.02.040.
63. Audouin, O., Bodin, J., Porel, G., Bourbiaux, B., (2008). Flowpath structure in a limestone aquifer: multi-borehole logging investigations at the hydrogeological experimental site of Poitiers, France. Journal of Hydrology 16(5): 939-950, https://doi.org/10.1007/s10040-008-0275-4.
64. Journel, A.G., (1986). Geostatistics: Models and tools for the earth sciences. Mathematical Geology 18(1): 119–140, https://doi.org/10.1007/BF00897658.
65. Chilès, J.P., Delfiner, P. (1999). Geostatistics: Modeling Spatial Uncertainty, New York, John Wiley & Sons.
66. Isaaks, E., Srivastava, R. (1989). An Introduction to Applied Geostatistics, Oxford University Press.
67. Goovaerts, P. (1997). Geostatistics for Natural Resources Evaluation, New York, Oxford University Press.
68. Firat, M., Gungor, M., (2007). River flow estimation using adaptive neuro fuzzy inference system. Mathematics and Computers in Simulation 75(3): 87–96, https://doi.org/10.1016/j.matcom.2006.09.003.
69. Pratihar, D.K. (2008). Soft Computing, Oxford, Alpha Science International Ltd.
70. Erdem, G., Sagir, C., Canoglu, M.C., Kurtulus, B., 2016. Comparison of Empirical Bayesian Kriging and Geo Anfis methods for interpolating hydraulic head in a karst alluvium, 8th IEMSS Congress, 10-14 July 2016, Toulouse, France.
71. Zadeh, L., (1965). Fuzzy sets. Information and Control 8(3): 338–353.
72. BRGM, Bureau de Recherches Géologiques et Minères, (2020). https://www.geoportail.gouv.fr/donnees/cartes-geologiques is retrieved, Accessed Date: 15.01.2020.
73. Demuth, H., Beale, M. (2003). Neural Network Toolbox for Use with MATLAB, USA, The MathWorks Inc.
74. Li, J., Heap, A.D., (2014). Spatial interpolation methods applied in the environmental sciences: A review. Environmental Modelling & Software, 53: 173-189, https://doi.org/10.1016/j.envsoft.2013.12.008.