Tavg = average temperature [OK]
X = thermal conductivity of soil [W.m-l1.- 1]
Pva = mass oJ water vapor per unit volume of dry ambient air
[kg-m-J]
PvO = concentration of water vapor at the soil surface, z=0
[kg-m-3]
0 = volume of water per unit total soil volume [m3.m-3]
Ideally, for a semi-infinite medium, the flux of energy and mass
should be zero in the limit of depth (z) approaching infinity.
However, in anticipation of a numerical solution to the system of
partial differential equations, the boundary conditions were specified
at a depth of 1.5 meters. This depth was chosen by comparing the
error between the analytical and numerical solutions for conduction of
heat in a semi-infinite slab with constant uniform properties and a
uniform heat flux at the surface. This depth resulted in an error of
less than 0.1 OC at the lower boundary. The depth at which the
amplitude of the diurnal fluctuations in temperature is less than
0.1 OC is approximately 60 cm for a sandy soil (Baver et al., 1972).
The zero flux condition for the liquid and vapor continuity equations
represents an impermeable layer in the soil. This condition may or
may not physically exist in the field, but for most situations
encountered, the errors introduced into the solution at the depth of
chosen should be minimal. The boundary conditions used at the lower
boundary were
T- = 0 (2-32a)
az Zzo
800
o I = 0 (2-32b)
a zz0Z