A mathematical backward problem which involves solving a mathematical model based on a one dimensional advection -diffusion process of solute transport in a homogeneous soil structure is considered. The diffusion coefficient and advection velocity in the governing unsteady non-linear partial differential equation (PDE) are varied from constant to linearly dependent on time. This is done to develop a mathematical understanding of the initial root causes and levels of acidification in priori because determination of analytic solution involves a lot of assumptions making the results unrealistic as opposed to the our numerical experiment approach which is cost effective and more reliable results are obtained. Flow domain is assumed semi infinitely deep and homogeneous and it Original Research ArticlePeer-review history: The peer review history for this paper can be accessed here: http://www.sciencedomain.org/review-history/26541