z = 0 (2-32c)
The system defining the movement of water vapor, liquid water and
energy is defined by a system of partial differential equations (2-22,
2-25, 2-26) with boundary conditions (2-31a-c, 2-32a-c). The energy
equation is coupled to the continuity equations by the rate at which
the water is changed from liquid to vapor and through the movement of
sensible heat associated with the flux of water between zones of
differing temperatures. The conservation of water vapor is coupled to
the soil temperature indirectly in the calculation of saturated vapor
pressure. This coupling, along with the variation of the soil
properties with time and space, renders an analytical solution beyond
reach, therefore; a numerical solution was required.
Determination of Model Parameters
Solution of the governing equations for the energy and mass
balance for the soil requires knowledge of the properties relating to
the soils ability to diffuse heat, water, and water vapor. The other
parameters to be determined relate to the rate at which heat and water
vapor are dissipated from the soil surface to the air. In order to
determine a solution, relationships for determining thermal, hydraulic
and vapor diffusivities as well as the surface transfer coefficients
must be determined.
Diffusivity of Water Vapor
Diffusivity is the constant of proportionality relating flow to
the gradient in potential as stated in Fick's Law of molecular
diffusion. For the case of water vapor diffusing through air, the