Title: An efficient and robust algorithm for estimating parameters in a horizontal subsurface flow of a constructed wetland treating greywater

Authors: Ihsane Mouaouia; Abderrahim Charkaoui; Nour Eddine Alaa

Addresses: Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Marrakech, Morroco ' Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Marrakech, Morroco ' Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University, Marrakech, Morroco

Abstract: We establish a new method for estimating parameters in reaction-adsorption-diffusion systems modelling the greywater treatment through a horizontal subsurface flow of a constructed wetland. Two cost functions are presented to estimate the permeability coefficients, the initial concentration and the degradation of the phosphor in the considered model. A Lagrangian method is considered to compute the derivative of the cost functions with respect to the state variable. An iterative algorithm is illustrated with the reaction-adsorption-diffusion systems using optimisation techniques and the adjoint state model. We were able to estimate our parameters and our initial data. In addition, the performance of our algorithm is evaluated by perturbing the data with various levels of additive noise.

Keywords: constructed wetland; mathematical modelling; advection-dispersion-reaction equation; inverse problem; Lagrangian method; optimisation algorithm.

DOI: 10.1504/IJHST.2021.115490

International Journal of Hydrology Science and Technology, 2021 Vol.11 No.4, pp.422 - 438

Received: 20 Nov 2019
Accepted: 03 Feb 2020
Published online: 07 Jun 2021 *

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