Skip to main content
SpringerLink
Log in

Estimation of Hydrochemical Unsaturated Soil Parameters Using a Multivariational Objective Analysis

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Numerical experiment involving both moisture and solute transport predictions is performed to estimate the hydrochemical characteristics of unsaturated porous soil. The moisture and solute transport in the soil are described by the flow and advection–dispersion transport equations. These transport equations are solved by the spectral element method, which is based on Legendre–Gauss–Lobatto quadrature rule and the fully implicit time scheme using the modified Picard iterative procedure constructed with the standard chord slope approximation. The estimation of hydraulic and solute transport parameters has been conducted using the Levenberg–Marquardt method. The goals of the inverse problem were to develop soil hydrochemical characteristics estimation strategies based on combined two of the following functional cost measurements: moisture content, pressure head, hydraulic conductivity, cumulative outflow, and solute concentration. The performance of the inverse algorithm was evaluated using the coefficient of determination, the root-mean-square error, and the relative error analysis which provide an optimal scheme for parameters estimation. The spectral element method was shown to provide good results with negligible error when compared to analytical values. The obtained results indicate excellent agreement of the method for estimating hydraulic and transport parameters with negligible relative error when compared estimated parameters and true values. The choice and the order of combination of objective functions affect crucially the inverse solution especially in case of large hydrochemical parameters estimates.

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

Similar content being viewed by others

References

  • Abbasi, F., Jacques, D., Simunek, J., Feyen, J., van Genuchten, MTh: Inverse estimation of soil hydraulic and solute transport parameters from field experiments: heterogeneous soil. Am. Soc. Agric. Eng. 46(4), 1097–1111 (2003)

    Google Scholar 

  • Carbone, M., Brunetti, G., Piro, P.: Modelling the hydraulic behavior of growing media with the explicit finite volume solution. Water 7, 568–591 (2015)

    Article  Google Scholar 

  • Carmeliet, J., Descamps, F., Houvenagel, G.: A multi-scale network model for simulating liquid water and water vapour transfer properties of porous media. Transp. Porous Media 35, 67–88 (1999)

    Article  Google Scholar 

  • Chamkha, A.J.: Numerical modelling of contaminant transport with spatially-dependent dispersion and non-linear chemical reaction. Nonlinear Anal. Model. Control 12(3), 329–343 (2007)

    Google Scholar 

  • Chotpantarat, S., Limpakanwech, C., Siriwong, V., Siripattanakul, S., Sutthirat, C.: Effect of soil water characteristic curves on simulation of nitrate vertical transport in a Thai agricultural soil. Sustain. Environ. Res. 21(3), 187–193 (2011)

    Google Scholar 

  • De Smedt, F., Brevis, W., Debels, P.: Analytical solution for solute transport resulting from instantaneous injection in streams with transient storage. J. Hydrol. 315, 25–39 (2005)

    Article  Google Scholar 

  • Dehghan, M., Sabouri, M.: A Legendre spectral element method on a large spatial domain to solve the predator-prey system modeling interacting populations. Appl. Math. Model. 37(3), 1028–1038 (2013)

    Article  Google Scholar 

  • Filipović, V.: Numerical modeling of water flow and contaminant (Nitrates) transport in agriculture: review. Agric. Conspec. Sci. 78(2), 79–84 (2013)

    Google Scholar 

  • Huang, K., Mohanty, B.P., Leij, F.J., van Genuchten, M.T.: Solution of the nonlinear transport equation using modified Picard iteration. Adv. Water Resour. 21, 237–249 (1998)

    Article  Google Scholar 

  • Juncu, G., Nicola, A., Popa, C.: Nonlinear multigrid methods for numerical solution of the variably saturated flow equation in two space dimensions. Transp. Porous Med. 91, 35–47 (2012)

    Article  Google Scholar 

  • Komatistsch, D., Barnes, C., Tromp, J.: Wave propagation near a fluid solid interface: a spectral element approach. Geophysics 65(2), 623–631 (2000)

    Article  Google Scholar 

  • Konikow, L.F.: The secret to successful solute-transport modeling. Ground Water 49(2), 144–159 (2011)

    Article  Google Scholar 

  • Lee, D.H., Abriola, L.M.: Use of the Richards equation in land surface parameterizations. J. Geophys. Res. 104(D22), 27519–27526 (1999)

    Article  Google Scholar 

  • Li, W., Wei, C.: An efficient finite element procedure for analyzing three-phase porous media based on the relaxed Picard method. Int. J. Numer. Methods Eng. (2014). https://doi.org/10.1002/nme.4830

    Google Scholar 

  • Lu, X., Zhou, M., Wang, P.: Diurnal soil water flow and root water uptake/nitrogen dynamics in the wastewater irrigated pepper field. Commun. Soil Sci. Plant Anal. 47, 989–1005 (2016)

    Article  Google Scholar 

  • Mazaheri, M., Samani, J.M.V., Samani, M.V.: Analytical solution to one-dimensional advection diffusion equation with several point sources through arbitrary time-dependent emission rate patterns. J. Agric. Sci. Technol. 15, 1231–1245 (2013)

    Google Scholar 

  • Moitsheki, R.J., Broadbridge, P., Edwards, M.P.: Symmetry solutions for transient solute transport in unsaturated soils with realistic water profile. Transp. Porous Media 61, 109–125 (2005)

    Article  Google Scholar 

  • Nassar, I.N., Horton, R.: Heat, water, and solute transfer in unsaturated porous media: I -theory development and transport coefficient evaluation. Transp. Porous Media 27, 17–38 (1997)

    Article  Google Scholar 

  • Ogden, F.L., Lai, W., Steinke, R.C., Zhu, J., Talbot, C.A., Wilson, J.L.: A new general 1-D Vadose zone flow solution method. Water Resour. Res. 51, 1–19 (2015)

    Article  Google Scholar 

  • Patera, A.T.: A spectral element method for fluid dynamics laminar flow in a channel expansion. J. Comput. Phys. 54, 468–488 (1984)

    Article  Google Scholar 

  • Ramos, T.B., Goncalves, M.C., Martins, J.C., van Genuchten, MTh, Pires, F.P.: Estimation of soil hydraulic properties from numerical inversion of tension disk infiltrometer data. Vadose Zone J. 5(2), 684–696 (2006)

    Article  Google Scholar 

  • Ritter, A., Hupet, F., Munoz-Carpena, R., Lambot, S., Vanclooster, M.: Using inverse methods for estimating soil hydraulic properties from field data as an alternative to direct methods. Agric. Water Manag. 59(2), 77–96 (2003)

    Article  Google Scholar 

  • Saito, H., Simunek, J., Mohanty, B.P.: Numerical analysis of coupled water, vapor, and heat transport in the vadoze zone. Vadose Zone J. 5, 784–800 (2006)

    Article  Google Scholar 

  • Shahraiyni, H.T., Ataie-Ashtiani, B.: Mathematical forms and numerical schemes for the solution of unsaturated flow equations. J. Irrig. Drain. Eng. 138(1), 63–72 (2012)

    Article  Google Scholar 

  • Shamsi, M.: Modified pseudo spectral scheme for accurate solution of Bang–Bang optimal control problems. Optim. Control Appl. Math. 32(6), 668–680 (2011)

    Article  Google Scholar 

  • Shen, J., Tang, T.: Spectral and High-Order Methods with Applications. Science Press, Bejing (2006)

    Google Scholar 

  • Simunek, J., van Genuchten, MTh: Estimating hydraulic soil properties from tension disc infiltrometer data by numerical inversion. Water Resour. Res. 32(9), 2683–2696 (1996)

    Article  Google Scholar 

  • Simunek, J., Jarvis, N.J., van Genuchten, MTh, Gardenas, A.: Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone. J. Hydrol. 272, 14–35 (2003)

    Article  Google Scholar 

  • Stagnitti, F., Li, L., Barry, A., Allinson, G., Parlange, J.-Y., Steenhuis, T., Lakshmanan, E.: Modelling solute transport in structured soils: performance evaluation of the ADR and TRM models. Math. Comput. Model. 34, 433–440 (2001)

    Article  Google Scholar 

  • Trefethen, L.N.: Spectral Methods in MATLAB. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000)

    Book  Google Scholar 

  • van Genuchten, M.T.: A closed form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Sci. Soc. Am. J. 44(5), 892–898 (1980)

    Article  Google Scholar 

  • Varado, N., Braud, I., Ross, P.J., Haverkamp, R.: Assessment of an efficient numerical solution of the 1D Richards equation on bare soil. J. Hydrol. 323, 244–257 (2006)

    Article  Google Scholar 

  • Yadav, S.K., Kumar, A., Jaiswal, D.K., Kumar, N.: One dimensional unsteady solute transport along unsteady flow through inhomogeneous medium. J. Earth Syst. Sci. 120(2), 205–213 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the Volkswagen Foundation with the grant number VW 89362 under the funding initiative Knowledge for Tomorrow-Cooperative Research Project in sub-Saharan Africa on Resource, their Dynamics, and Sustainability.

Author information

Authors and Affiliations

  1. Life and Industrial Systems Thermal Engineering-Team (LISTE-T), Unité de Recherche de Mécanique et de Modélisation des Systèmes Physiques (UR2MSP), Department of Physics/Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Ernest Léontin Lemoubou & Hervé Thierry Tagne Kamdem

  2. Department of Physics, H.T.T.C. Bambili, University of Bamenda, Bamenda, Cameroon

    Jean Roger Bogning

  3. Sustainable Intensification Program (SIP), International Maize and Wheat Improvement Center (CIMMYT) ICRAF House, United Nation, Avenue, Gigiri, Village Market, P. O. Box 1041, Nairobi, 00621, Kenya

    Edouard Henri Zefack Tonnang

Authors
  1. Ernest Léontin Lemoubou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hervé Thierry Tagne Kamdem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean Roger Bogning
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Edouard Henri Zefack Tonnang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ernest Léontin Lemoubou.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lemoubou, E.L., Kamdem, H.T.T., Bogning, J.R. et al. Estimation of Hydrochemical Unsaturated Soil Parameters Using a Multivariational Objective Analysis. Transp Porous Med 127, 605–630 (2019). https://doi.org/10.1007/s11242-018-1216-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-018-1216-x

Keywords

Search

Navigation