Skip to main content
SpringerLink
Log in

Elevating the possibilities of meshless groundwater flow modeling: a developed approach for parameter estimation and uncertainty quantification

  • Research Article - Hydrology and Hydraulics
  • Published:
Acta Geophysica Aims and scope Submit manuscript

Abstract

Groundwater modeling is often associated with uncertainties due to incomplete knowledge of the subsurface system or uncertainties arising from variability in model system processes and field conditions. So far, not much research has been conducted to investigate the uncertainty of the groundwater flow model. Studies in this field focus on statistical methods. Due to the need to investigate the uncertainty to obtain reliable results, this study presents an approach to evaluate the uncertainty parameters of the groundwater flow model. In this way, modified GLUE (MGLUE) method as the uncertainty assessment method is linked to the meshless local Petrov–Galerkin (MLPG) as the simulation model. The method (which is called MGLUE-MLPG) is applied to two aquifers. In the first aquifer, three parameters of the meshless flow model (parameters related to the numerical method e.g., sizes of the integration and weight subdomains and the amount of the penalty coefficient) are identified as uncertainty parameters. The results indicate that these three parameters have a high degree of uncertainty, so their coefficients of variation are 72.37, 19.92 and 51.55, respectively. In the second standard aquifer, in addition to the numerical parameters, the transmissivity coefficients (model parameters) in two different directions (horizontal and vertical directions) are taken into account in the uncertainty model. The results show more uncertainty for the numerical parameters and do not show many changes in the transmissivity coefficient parameter. This means that the box diagrams of these parameters are almost the same. After precise values have been reached, groundwater flow was simulated. The obtained results are so accurate as to indicate the importance of using this model for all aquifers. In the first aquifer, the root mean square error (RMSE) values for MGLUE-MLPG and finite element method (FEM) are 0.236 and 0.249 m, respectively. The second aquifer shows higher accuracy than the other numerical method, so the RMSE values for MGLUE-MLPG and PPCM are 0.0060 and 0.0121 m, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • KC Abbaspour CA Johnson MT Genuchten Van 2004 Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure Vadose Zone J 3 4 1340 1352

    Article  Google Scholar 

  • HA Afan A Ibrahem Ahmed Osman Y Essam AN Ahmed YF Huang O Kisi A El-Shafie 2021 Modeling the fluctuations of groundwater level by employing ensemble deep learning techniques Eng Appl Comput Fluid Mech 15 1 1420 1439

    Google Scholar 

  • SN Atluri S Shen 2002 The meshless local petrov-galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods CMES 3 1 11 51

    Google Scholar 

  • SN Atluri TL Zhu 1998 A new meshless local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling and simulation Comput Model Simul Engrg 3 187 196

    Google Scholar 

  • K Beven A Binley 1992 The future of distributed models: model calibration and uncertainty prediction Hydrol Process 6 3 279 298

    Article  Google Scholar 

  • K Beven J Freer 2001 Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology J Hydrol 249 11 29

    Article  Google Scholar 

  • T Cui L Peeters D Pagendam T Pickett H Jin RS Crosbie M Gilfedder 2018 Emulator-enabled approximate Bayesian computation (ABC) and uncertainty analysis for computationally expensive groundwater models J Hydrol 564 191 207

    Article  Google Scholar 

  • MD Dettinger JL Wilson 1981 First order analysis of uncertainty in numerical models of groundwater flow part: 1 Math Dev, Water Resour Res 17 1 149 161

    Article  Google Scholar 

  • Dupouit, J. 1863. Estudes theoriques et pratiques sur le mouvement desEaux, Paris: Dunod, Hydraulics, pp 304

  • J Freer K Beven B Ambroise 1996 Bayesian estimation of uncertainty in runoff prediction and the value of data: an application of the GLUE approach Water Resour Res 32 7 2161 2173

    Article  Google Scholar 

  • L Goliatt SO Sulaiman KM Khedher AA Farooque ZM Yaseen 2021 Estimation of natural streams longitudinal dispersion coefficient using hybrid evolutionary machine learning model Eng Appl Comput Fluid Mech 15 1 1298 1320

    Google Scholar 

  • BS Hamraz AP Akbarpour M Bilondi S Sadeghi Tabas 2015 On the assessment of ground water parameter uncertainty over an arid aquifer Arab J Geosci 8 10759 10773

    Article  Google Scholar 

  • A Jafarzadeh M Pourreza-Bilondi A Akbarpour A Khashei-Siuki M Azizi 2022 Sensitivity and stability analysis for groundwater numerical modeling: a field study of finite element application in the arid region Acta Geophys 71 1045 1062

    Article  Google Scholar 

  • MS Kahe S Javadi A Roozbahani K Mohammadi 2021 Parametric uncertainty analysis on hydrodynamic coefficients in groundwater numerical models using Monte Carlo method and RPEM Environ, Dev Sustain 23 8 11583 11606

    Article  Google Scholar 

  • MH Khorashadizadeh SA Monfared A Akbarpour M Pourreza Bilondi 2016 Uncertainty assessment of pollution transport model using GLUE method Iranian J Irrig Drainage 10 3 284 293 (In Persian)

    Google Scholar 

  • GR Liu YT Gu 2001 A point interpolation method for two-dimensional solid Int J Numer Methods Eng 50 937 951

    Article  Google Scholar 

  • GR Liu YT Gu 2005 An introduction to meshfree methods and their programming Springer Singapore

    Google Scholar 

  • M Mategaonkar TI Eldho 2011a Simulation of groundwater flow in unconfined aquifer using meshfree point collocation method Eng Anal Boundary Elem 35 700 707

    Article  Google Scholar 

  • M Mategaonkar TI Eldho 2011b Meshless point collocation method for 1D and 2D groundwater flow simulation ISH J Hydraulic Eng 17 1 71 87

    Article  Google Scholar 

  • A Mohtashami A Akbarpour M Mollazadeh 2017 Development of two dimensional groundwater flow simulation model using meshless method based on MLS approximation function in unconfined aquifer in transient state J Hydroinf 19 5 640 652

    Article  Google Scholar 

  • SMT Mustafa J Nossent G Ghysels M Huysmans 2020 Integrated bayesian multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling Environ Model Softw 126 10465

    Article  Google Scholar 

  • M Nayyeri SA Hosseini S Javadi A Sharafati 2021 Spatial differentiation characteristics of groundwater stress index and its relation to land use and subsidence in the varamin plain, iran Nat Resour Res 30 339 357

    Article  Google Scholar 

  • V Nourani K Khodkar M Gebremichael 2022 Uncertainty assessment of LSTM based groundwater level predictions Hydrol Sci J 67 5 773 790

    Article  Google Scholar 

  • YC Park D Leap 2000 Modeling groundwater flow with a free and moving boundary using the element-free Galerkin (EFG) method Geosci J 4 3 243 249

    Article  Google Scholar 

  • Pholl, G. Pohlmann, K. Hassan, A. Chapman, J. & Mihvec, T. 2002. Assessing groundwater model uncertainty for the central Nevada test area, Spectrum.

  • V Pisinaras CT Petalas V. A. & Zagana, E. A, 2007 Groundwater flow model for water resources management in the ismarida plain North Greece, Environmental Modeling and Assessment 12 75 89

    Article  Google Scholar 

  • R Rojas A Dassargues 2007 Groundwater flow modelling of the regional aquifer of the pampa del tamarugal, northern Chile Hydrogeol J 15 537 551

    Article  Google Scholar 

  • Romanowicz, R. Karamuz, E. Napiorkowski, J. & Senbeta, T. 2021. Effects of climate change and human interactions on water balance dynamics in the River Vistula basin, EGU General Assembly, pp. 19–30.

  • SVM Sharief TI Eldho AK Rastgoi 2008 Optimal pumping policy for aquifer decontamination by pump and treat method ISH J Civ Eng 14 2 1 17

    Google Scholar 

  • J Sladek V Sladek PH Wen 2020 The meshless analysis of scale-dependent problems for coupled fields Materials 13 25 1 20

    Google Scholar 

  • B Swathi TI Eldho 2014 Groundwater flow simulation in unconfined aquifers using meshless local Petrov-Galerkin method Eng Anal Boundary Elem 48 43 52

    Article  Google Scholar 

  • B Swathi TI, E. 2018 Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm Comput Geosci 22 3 657 675

    Article  Google Scholar 

  • Thomas, A. Eldho T. I. & Rastogi, A. K. 2012. Groundwater flow simulation using meshfree method and fem, Proceedings of National Conference on Hydraulics, Water Resources, Coastal and Environmental Engineering (HYDRO-2012), Bombay, India.

  • F Yang J Wu Y Zhang S Zhu G Liu G Chen Z Fan 2021 Improved method for identifying manning’s roughness coefficients in plain looped river network area Eng Appl Comput Fluid Mech 15 1 94 110

    Google Scholar 

  • OC Zienkiewicz RL Taylor JZ Zhu 2005 The finite element method: its basis and fundamentals Elsevier

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bozorgmehr University of Qaenat, Qaen, Iran

    Mahdi Khorashadizadeh

  2. Department of Environmental Engineering and Infrastructures, Politecnico di Torino, Turin, Italy

    Siavash Abghari

  3. University of Birjand, Birjand, Iran

    Abolfazl Akbarpour

  4. University of Sistan and Baluchestan, Zahedan, Iran

    Ali Mohtashami & Seyed Arman Hashemi Monfared

Authors
  1. Mahdi Khorashadizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Siavash Abghari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abolfazl Akbarpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ali Mohtashami
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Seyed Arman Hashemi Monfared
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahdi Khorashadizadeh.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Edited by Dr. Hossein Hamidifar (ASSOCIATE EDITOR) / Prof. Jochen Aberle (CO-EDITOR-IN-CHIEF).

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khorashadizadeh, M., Abghari, S., Akbarpour, A. et al. Elevating the possibilities of meshless groundwater flow modeling: a developed approach for parameter estimation and uncertainty quantification. Acta Geophys. (2024). https://doi.org/10.1007/s11600-024-01287-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11600-024-01287-6

Keywords

Search

Navigation