### Abstract:

Gaseous transport through soil in the presence of soil
microorganisms has been investigated. More recently, modeling of
gaseous transport in the unsaturated zone has been investigated.
However, the problem of mathematical model of oxygen and carbon
dioxide transport through soil, as affected by the climatic
conditions, the transport of soil water, and the biological
activities, has not been studied.
The problem of time-dependent diffusion of oxygen and carbon
dioxide through plant canopy and soil system, as affected by the
infiltration and evaporation of soil water and the rate of
consumption of oxygen and production of carbon dioxide by plant
leaves and roots and soil microorganisms was studied, using a
one-dimensional mathematical model. This model consists of four sets
of non-linear partial differential field equations, which describe
the time-dependent simultaneous transport of water, heat, oxygen, and
carbon dioxide through the soils.
Finite difference methods were used to find the approximate
solutions for the four sets of non-linear partial differential field
equations. The field equations for the transport of water and heat
were approximated by using the implicit scheme. The field equations
for the transport of oxygen and carbon dioxide were approximated by
using the explicit scheme. A computer program was written in Fortran
code to conduct the simulations of the mathematical model.
Simultaneous transport of water, heat, oxygen, and carbon dioxide
through the unsaturated Indio loam soil, through the compacted and
the non-compacted soil during infiltration, redistribution, and
evaporation of soil water was evaluated. Diffusion of oxygen and
carbon dioxide within the canopy and soil system was examined.
Several different functions for the root elongation and the root
oxygen consumption rates were used. Root elongation rate was chosen
to depend on oxygen or carbon dioxide concentrations, in addition to
being a function of time. Root oxygen consumption rate was assumed
to be a function of root age, in addition to being a function of
oxygen or carbon dioxide concentrations. Results illustrate that the
behaviors of the simultaneous transport of water, heat, oxygen, and
carbon dioxide were well predicted by the model.