Transport in Porous Media

, Volume 127, Issue 3, pp 605–630 | Cite as

Estimation of Hydrochemical Unsaturated Soil Parameters Using a Multivariational Objective Analysis

  • Ernest Léontin LemoubouEmail author
  • Hervé Thierry Tagne Kamdem
  • Jean Roger Bogning
  • Edouard Henri Zefack Tonnang


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.


Solute transport Multivariate analysis Hydrochemical parameters Unsaturated soil Spectral element method 



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.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 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 SciencesUniversity of DschangDschangCameroon
  2. 2.Department of PhysicsH.T.T.C. Bambili, University of BamendaBamendaCameroon
  3. 3.Sustainable Intensification Program (SIP)International Maize and Wheat Improvement Center (CIMMYT) ICRAF HouseNairobiKenya

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