Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 316

5. Ensure the model domain is initialized.
6. Determine PE using pan evaporation data that are
measured or calculated using one of

Empirical Experimental-Based Equation for AE.
The AE is obtained through use of

the empirical ex-

the above- perimental-based equation 6.75.

Potential Evaporation. The PE can be either measured
or calculated using one of several empirical methods [e.g.,
Penman (1948), Eq. 6.20; Thornthwaite (1948), Eq. 6.19;
Priestley-Taylor

mentioned methods.
7. Calculate the AE using Eq. 6.75.
8. Solve the moisture flow equation 6.50 and the thermal
flow equation 6.53, based on initial conditions and
designated boundary conditions.
9. Calculate net infiltration I at ground surface. The net
infiltration flux at the ground surface is defined as
k∂h/∂y .
10. Calculate runoff R using Eq. 6.7 using the known
value of precipitation P , AE, and net infiltration NP
at the ground surface.
11. Check the solution to see if the convergence has been
reached for both seepage head and soil temperature,
T soil . The difference in the calculated variables
between the last two iterations must be less than the
designated convergence tolerances.
12. If the solution has not yet converged, repeat steps
6-11 iteratively until the convergence is achieved.

(1972), Eq. 6.23; or Monteith (1965),

Eq. 6.22].
Calculation Procedure.

1. Initialize the water content profile.
2. Apply the moisture flux boundary condition according
to Eq. 6.65.
3. Determine PE using either measured pan evaporation
or one of the above-mentioned PE equations.
4. Calculate AE using Eq. 6.75.
5. Solve the moisture flow equation 6.50 and the soil tem-
perature equation 6.72 based on the initial conditions
and the boundary conditions.
6. Calculate net percolation I at the ground surface. The
net infiltration flux at the ground surface is defined as
k∂h/∂y .
7. Calculate runoff R using Eq. 6.7. At this time, AE and
I are known.
8. Check the solution to determine whether convergence
has been achieved with respect to hydraulic head. The
difference between the last two iterations must be less
than the designated convergence tolerance. If the solu-
tion has not converged, repeat steps 3-8 iteratively
until convergence is achieved.

6.3.19.6 Experimental-Based Relationship between AE
and PE (Uncoupled Solution)
The experimental-based solution is the same as the pre-
viously presented solution except that the thermal regime
partial differential equation for conductive and convective
flow is not solved. The following assumptions can be made
when performing the uncoupled solution that utilizes the
experimental-based relationship (i.e., Eq. 6.75):

6.3.20 Example Calculations of AE
Measurements of actual evaporation from a soil column
were presented by Wilson (1990). The results serve as
benchmark data for comparison with numerical model
calculations. Figure 6.45 compares the measured evap-
oration rates with computed results obtained with an
uncoupled analysis using SVFlux (SoilVision, 2010). The
uncoupled analyses were performed using three procedures:
(i) Wilson-Penman model (Wilson et al., 1994) (ii) limiting
function model (Wilson et al., 1997a), and (iii) experi-
mental-based model (Wilson et al., 1997a). Also shown
are the PE and AE measurements by Wilson (1990).
Figure 6.45 shows that the measured evaporation rates
are similar to the computed evaporation rates obtained
when using the three uncoupled models. The results from
the three uncoupled models are also quite similar to the
measured results.
Figure 6.46 shows the actual evaporation calculations
performed using a coupled mode with SVFlux and SVHeat
(SoilVision, 2010). The coupled analyses were performed
using: (i) Wilson-Penman model (Wilson et al., 1994)
(ii) limiting function model (Wilson et al., 1997a), and
(iii) experimental-based model (Wilson et al., 1997a). Once
again, the three models show similar amounts of computed

• Moisture flow (i.e., liquid and vapor) in the soil is driven
by hydraulic head and vapor pressure gradients.
• The soil temperature throughout the model domain is
constant and is assumed to be equal to the air tempera-
ture above the soil surface. In other words, the ground
thermal flux can be neglected (i.e., R g =

0).
• The soil surface temperature is assumed to be equal to
the air temperature.
• The actual evaporation can be calculated using the
empirical experimental-based equation proposed by
Wilson et al., (1997a).

Partial Differential Equation Governing Moisture
and Heat Flow. The moisture flow governing equation is
Eq. 6.50 and the soil temperature is computed using Eq. 6.72.
Initial Water Content Conditions. The initial water
content profile must be initialized.
Initial Temperature Conditions. The soil temperatures
throughout

the soil profile can be initialized to the air

temperature.
Boundary Condition for Moisture Flow. The ground
surface boundary condition for moisture flow can be defined
using Eq. 6.65.