51
0 n (^nc-l,n ^nc,n) (Tnc-l,n+ Tnc,n)
+ 2 /Jwrx^pwrKpLnc dz^-i ~2
o n (^vnc-ljiT^vnc,!!) (^nc-l,n+ ^nc,n)
+ 2 cpvncDvnc j
+ dwnc ^nc,n (2-74)
The conservation relationships provide sufficient information to
determine three of the desired quantities for the soil profile leaving
a fourth remaining unknown. The constitutive relationship requiring
that the water in the liquid phase be in thermodynamic equilibrium with
the vapor phase was used to provide the remaining equation. Since the
surface node provides only an interface between the soil and the
atmosphere, this equilibrium condition was not necessary for the
surface node. Under atmospheric conditions, the soil may not become
completely dry (0 % volumetric water content), but will reach some
moisture content which is in equilibrium with the atmosphere. This is
typically taken to be the same as the permanent wilting point of the
soil (^= -150 m) and is the same as the residual water content
described by van Genuschten (1980). As the soil surface dries, the
soil reaches this equilibrium moisture content and is assumed to act as
an interface between the air and the wet soil below.
The system of equations (2-64) through (2-69)and (2-72) through
(2-74) along with equation (2-30) represent an explicit solution to the
differential equations, that is, the values of the state variables at
the next time step are functions of those at the previous time step.
Using the explicit representation allows a simple algorithm to be used