Usage of Particle Filter for Exact Estimation of Constant Head Boundaries in Unconfined Aquifer

Document Type : Research Article


1 Department of civil engineering

2 Associate Professor of Civil Engineering Department, University of Sistan and Baluchestan

3 Associate Professor in Hydraulic Structure, University of Sistan and Baluchestan Zahedan, Iran

4 Faculty of Engineering, University of Birjand


Having the exact values of boundary conditions is one of the effective ways to develop precise groundwater models. In the present study, the exact value of constant head boundaries in the Birjand aquifer is specified using particle filter linked to meshless groundwater model. Particle filter, known as one of the common data assimilation methods, applies to dynamic systems in order to improve performance. Meshless model, one of the numerical models that do not mesh the problem domain, enforces the governed equation to the nodes. Birjand aquifer, with an almost 269 km2 area, has 190 extraction and 10 observation wells. There are also nine inflow and one outflow regions with constant head boundary conditions, including 105 boundary nodes. In this research, after determining the lower and upper bounds of groundwater head for each node, the exact values of this parameter are computed. Finally, the simulated groundwater head was compared with observation data. The closeness of the achieved results to the observation data showed the performance of the engaged method, as the results indicated a significant decrease in RMSE occurs just with the usage of particle filter linked to the meshless model. RMSE value reduced to 0.386 m as its previous value was around 0.757 m. Results also showed that the model was more accurate when the number of particles in the particle filter was increased. The RMSE value for 500, 700 and 1000 particles were 0.484, 0.401 and 0.386m respectively.


Main Subjects

[1] M. Ghousehei, Groundwater balance computaion of Damghan aquifer, Kermanshah, 2011.
[2] A. Akbarpour, M. Azizi and M. Shirazi, Groundwater Management of Mokhtaran aquifer with using finite difference mathematical finite difference, Tehran, (2012) 1-12.
[3] A. P. Markopoulos, N. E. Karkalos and E. Papazoglou, Meshless Methods for the Simulation of Machining and Micro-machining: A Review, 1st ed., Archives of Computational Methods in Engineering, (2019).
[4] A. Mohtashami, A. Akbarpour and M. Mollazadeh, Modeling of groundwater flow in unconfined aquifer in steady state with meshless local Petrov-Galerkin, Modares Mechanical Engineering, 17(2) (2017) 393-403.
[5] B. Swathi, T. I. Eldho, Groundwater flow simulation in unconfined aquifers using meshless local Petrov-Galerkin method, Engineering Analysis with Boundary Elements, 48 (2017) 43-52.
[6] A. Mohtashami, A. Akbarpour and M. Mollazadeh, Development of two dimensional groundwater flow simulation model using meshless method based on MLS approximation function in unconfined aquifer in transient state, Journal of Hydroinformatics ,  19(5) (2017) 640-652.
[7] T. Pathania, A. Bottacin-Busolin, A. K. Rastogi, T. I. Eldho, Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method, Water Resources Management, 33 (2019) 2827–2845.
[8] M. Abedini, A. N. Ziai, M. Shafiei, B. Ghahraman, H. Ansari and J. Meshkini, Uncertainty Assessment of Groundwater Flow Modeling by Using Generalized Likelihood Uncertainty Estimation Method (Case Study: Bojnourd Plain), Iranian Journal of Irrigation and Drainage, 10(6) (2017) 755-769.
[9] G. Pohll, K. Pohlmann, A. E. Hassan, J. B. Chapman and T. Mihevic, Assessing Groundwater Model Uncertainty for the Central Nevada Test Area, Reno, Nevada, USA, (2002).
[10] M. D. Dettinger and J. L. Wilson, First order analysis of uncertainty in numerical models of groundwater flow part: 1. Mathematical development, Water Resource Research, 17(1) (1981) 149-161.
[11] M. Chitsazan, M. J. Abedini and M. Salek , The investigation and quantifying the uncertainty of groundwater models in Kazeroun aquifer with using statistic parameters, Journal of Irrigation Sciences and Engineering (JISE), 19 (2008) 17-33.
[12] A. Rasoulzadeh and S. A. A. Mousavi, Using inverse WTF uncertainty method in estimation of groundwater model parameters, Tehran, (2008).
[13] B. S. Hamraz, A. Akbarpour, M. Pourreza Bilondi and S. Sadeghi Tabas, On the assessment of ground water parameter uncertainty over an arid aquifer, Arabian Journal of Geosciences, 8 (2015) 10759-10773.
[14] X. Du, X. Lu, J. Hou, X. Ye, Improving the Reliability of Numerical Groundwater Modeling in a Data-Sparse Region, Water, 10(3) (2018) 289-304.
[15] S. M. Touhidul Mustafa, M. Moudud Hasan, A. Kumar Saha, R. Parvin Rannu, E. V. Uytven, P. Willems, M. Huysmans, Multi-model approach to quantify groundwater-level prediction uncertainty using an ensemble of global climate models and multiple abstraction scenarios, Hydrology and Earth System Sciences, 23 (2019) 2279-2303.
[16] J. Nossent, S. M. Touhidul Mustafa, G. Ghysels, M. Huysmans, Integrated Bayesian Multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling, Environmental Modelling and Software, 126 (2020) 104654-104671.
[17] S. Sadeghi tabas, S. Z. Samadi, A. Akbarpour and M. Pourreza Bilondi, Sustainable groundwater modeling using single-and multi-objective optimization algorithms, Journal of Hydroinformatics, 18(5) (2016) 1-18.
[18] S. Sadeghi Tabas, A. Akbarpour, M. Pourreza Bilondi and S. Z. Samadi, Application of Cuckoo Optimization Algorithm in Automatic Calibration of Aquifer Hydrodynamic Parameters using Mathematical Model, Iranian Journal of Irrigation and Drainage, 9(2) (2015) 345-356.
[19] S. R. Kambhampati, Target/Object Tracking Using Particle Filtering, Wichita: Wichita State University, (2008).
[20] P. Fearnhead and H. R. Kuensch, Particle Filters and Data Assimilation, Annual Review of Statistics and Its Application, 5(1) (2018) 421-449.
[21] R. Havangi, Increasing consistency of particle filter using the classic method and particle swarm algorithm, Computational Intelligence in Electrical Engineering, 7(2) (2016) 77-88.
[22] S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, tutorialon particle filters for Online nonlinear/nongaussian Bayesian tracking, IEEE Transaction Signal Process, 50(2) (2002) 174-188.
[23] B. Ristic, S. Arulampalam and N. Gordon, in Beyond Kalman Filter:Particle Filters Tracking Applicant, Boston: 1st ed, (2004).
[24] T. Li, M. Bolic and P. M. Djuric, Resampling Methods for Particle Filtering: Classification, implementation and strategies, IEEE Signal Processing Magazine, 32(3) (2015) 70-86.
[25] G. Choe, T. Wang, F. Liu, S. Hyon and J. Ha, Particle filter with spline resampling and global transition model, IET Computer Vision, 19(2) (2015) 184-197.
[26] F. Ruknudeen and S. Asokan, Application Particle Filter to On-Board Life Estimation of LED Lights, IEEE Photonics Journal, 9(3) (2017) 1:17.
[27] G. Y. Zhang, Y. M. Cheng , F. Yang, Q. Pan and Y. Liang, Design of an Adaptive Particle Filter Based on Variance Reduction Technique, Acta Automatica Sinica, 36(7) (2010) 1020-1024.
[28] M. Ramgraber, C. Albert, M. Schirmer, Data Assimilation and Online Parameter Optimization in Groundwater Modeling using Nested Particle Filters, Water Resources Research, 55(11) (2019) 9724-9747.
[29] M. Ahmadizadeh, S. Marofi, Bayesian analysis and particle filter application in rainfall-runoff models and quantification of uncertainty, Journal of Water and Soil Conservation, 24(1) (2017) 251-264.
[30] G. Manoli, M. Rossi, D. Pasetto, R. Deiana, S. Ferraris, G. Cassiani, M. Putti, An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment, Journal of Computational Physics, 283 (2015) 37-51.
[31] G. Field, G. Tavrisov, C. Brown, A. Harris and O. P. Kreidl, Particle Filters to Estimate Properties of Confined Aquifers, Water Resources Management, 30 (2016) 3175-3189.
[32] T. Li, G. Yuan, W. Li, Particle filter with novel nonlinear error model for miniature gyroscope-based measurement while drilling navigation, Sensors, 16(3) (2016) 371-395.
[33] H. Moradkhani, K. L. Hsu, H. Gupta, S. Sorooshian, Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter, Water resources research, 41(5) (2005) 1-17.
[34] S. N. Atluri and T. Zhu, A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics, Computational Mechanics, 22(2) (1998) 117-127.
[35] J. Sladek, P. Stanak, Z.-D. Han, V. Sladek and S. N. Atluri, Applications of the MLPG Method in Engineering & Sciences: A Review, Computer Modelling in Engineering & Sciences, 92(5) (2013) 423-475.
[36] S. N. Atluri,  S. Shen, The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple & Less-costly Alternative to the Finite Element and Boundary Element Methods, CMES, 3(1) (2002) 11-51.
[37] G. R. Liu and Y. T. Gu, An introduction to Meshfree Methods and Their Programming, Singapore: Springer, (2005).
[38] G. R. Liu and Y. T. Gu, A point interpolation method for two-dimensional solid, International Journal of Numerical Methods in Engineering, 50 (2001) 937-951.
[39] S. Khankham, A. Luadsong and N. Aschariyaphotha, MLPG method based on moving kriging interpolation for solving convection–diffusion equations with integral condition, Journal of King Saud University - Science, 27(4) (2015) 292-301.
[40] B. Dai, J. Cheng, B. Zheng, A Moving Kriging Interpolation-Based Meshless Local Petrov–Galerkin Method for Elastodynamic Analysis, International Journal of Applied Mechanics, 5(1) (2013) 1350011-1350032.
[41] W. Feng, G. Lin, B. Zheng, Z. Hu, J. Liu, MLPG method based on moving kriging interpolation for structural dynamic analysis,  Journal of Vibration and Shock, 33(4) (2014) 27-31.
[42] L. Lucy, A numerical approach to testing the fission hypothesis, Astrophysics Journal, 82 (1977) 1013-1024.
[43] N. Thamareerat, A. Luadsong and N. Aschariyaphotha, The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations, Springerplus. 5(1) (2016) 417.
[44] J. Dupouit, Estudes Theoriques et Pratiques sur le Mouvement desEaux, Paris: Dud, (1863).
[45] H. F. Wang and M. P. Anderson, Introduction to groundwater modeling: finite difference and finite element methods, first ed., Academic Press, (1995).
[46] A. Mohtashami, S. A. Hashemi Monfared, G. Azizyan and A. Akbarpour, Determination the capture zone of wells by using meshless local Petrov-Galerkin numerical model in confined aquifer in unsteady state( Case study: Birjand Aquifer), Iranian journal of Ecohydrology, 6(1) (2019) 239-255.
[47] A. Mohtashami, S. A. Hashemi Monfared, G. Azizyan and A. Akbarpour, Determination of the optimal location of wells in aquifers with an accurate simulation-optimization model based on the meshless local Petrov-Galerkin, Arabian Journal of Geosciences, 13(2) (2020) 1-13.
[48] S. Sadeghi Tabas, A. Akbarpour, M. Pourreza-Bilondi, S. Samadi, Toward reliable calibration of aquifer hydrodynamic parameters: characterizing and optimization of arid groundwater system using swarm intelligence optimization algorithm, Arabian Journal of Geosciences, 9 (2016) 719-739.
[49] R. Havangi, An Improved Particle Filter based on Soft Computing with Application in Target Tracking, Journal of Soft Computing and Information Technology (JSCIT), 7(2) (2018) 16-28.