Data Reconstruction for a Disturbed Soil-Column Experiment Using an Optimal Perturbation Regularization Algorithm

Abstract

This paper deals with data reconstruction problem for a real disturbed soil-column experiment using an optimal perturbation regularization algorithm. A purpose of doing the experiment is to simulate and study transport behaviors of Ca²⁺, Na⁺, Mg²⁺, K⁺, ${\text{SO}}_{\text{4}}^{2-}$, ${\text{NO}}_{\text{3}}^{-}$, ${\text{HCO}}_{\text{3}}^{-}$, and Cl⁻ when they vertically penetrating through sandy soils. By data analysis to breakthrough data of the eight kinds of solute ions, two kinds of models describing their transport behaviors in the column are given. One is the advection-dispersion equation with time-dependent reaction terms suitable for three ions of ${\text{HCO}}_{\text{3}}^{-}$, ${\text{NO}}_{\text{3}}^{-}$, and K⁺, the other is the ordinary advection-dispersion equation suitable for the rest ions. Furthermore, all the unknowns in each model are determined by utilizing the optimal perturbation regularization algorithm, respectively, and then the breakthrough data for each considered ion are reconstructed successfully. The inversion results show that the advection-dispersion model with suitable time-dependent reaction terms can be utilized to describe the experimental process and reconstruct the experimental data.