The diabetic influence function accounted for the transfer of air
movement in the vertical direction due to density gradients caused by
temperature gradients and is a function of the Richardson number
(Figure 2-4). Fuchs et al. (1969) stated that the roughness height
varied from 0.2 to 0.4 mm for a bare soil surface and accounted for a
small variation in the calculated heat transfer coefficient.
Therefore, for the purposes of this study, a roughness length of 0.3 mm
will be used Fuchs et al. (1969) also noted that the height of zero
wind velocity (d) was zero for a bare soil surface. This term was
employed in the approximate wind profiles to account for the fact that
wind does not penetrate full vegetative canopies and for practical
purposes the surface where the wind velocity is zero occurs at some
finite height above the soil surface (Brutsaert, 1982; Sutton, 1953).
Fuchs et al. (1969) compared transfer coefficients calculated using
equation (2-50) to that determined from field data for a bare sandy
soil and obtained fairly close agreement.
For the purposes of this model, the approach used by Fuchs et al.
(1969) to determine the surface mass (Equation 2-50) and heat
(Equation 2-51) transfer coefficients was employed. The diabetic
influence function was utilized to account for atmospheric instability
as proposed by Fuchs et al. (1969). A roughness height (Zo) of 0.3 mm
was utilized. The equations used in the formulation of this model and
the determination of parameters are summarized in Table 2-2
Numerical solution
The partial differential equations used to describe the mass and
energy balance in the soil must be solved numerically since analytical
solutions are not possible for the coupled nonlinear equations. Many