Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 314

Actual Evaporation. Actual evaporation is computed
using the limiting function (Wilson et al., 1997a), written as
follows:

10. Calculate runoff R using Eq. 6.7 using the known
value of precipitation P AE, and net infiltration I at
ground surface.
11. Check the solution to see if the convergence has been
reached for hydraulic head h and temperature T .The
difference between iterations must be less than the
designated tolerances.
12. If the solution has not yet converged, repeat steps
6-11 until convergence is achieved.

PE u soil

u air
v

−

v

AE = (6.73)

u soil
v 0

− u air

v

where:

PE = potential evaporation, mm/day,

u soil
v

= vapor pressure in the soil at the ground surface

temperature, kPa,

6.3.19.4 Limiting Function for AE (Uncoupled
Solution)
The Limiting Function can be used in an uncoupled manner
when solving for AE. In this case, the following assumptions
are made:

u soil
v 0

= saturated vapor pressure in the soil at the ground

surface temperature, kPa, and

u air
v

= vapor pressure in the air above the soil surface,

kPa.

If the air and soil temperatures are assumed to be approx-
imately equal, Eq. 6.73 can be written as follows:

• Liquid flow and vapor flow through the soil are gov-
erned by hydraulic head gradients and vapor pressure
gradients.
• The soil temperature in the entire domain is assumed
to be the same and equal to the air temperature above
the soil surface (i.e., ground thermal flux is neglected,
Q g =

exp

10 δ ψgω v
γ w R 273 . 15

−

u ai v /u air

T s

−

v 0

+

AE = PE (6.74)

/u air
v 0

u air
v

1 −

0).
• The ground surface temperature is assumed to be equal
to the air temperature.
• The AE is calculated using the limiting function pro-
posed by Wilson et al. (1997a).

where:

ψ = total suction (i.e., matric suction plus osmotic suc-

tion), kPa, and

δ = dimensionless factor for the adjustment of suction.

Partial Differential Equation Governing Moisture
Flow. Moisture flow in one dimension beneath the soil
surface can be described using Eq. 6.50.
Initial Soil-Water Content. The initial water content
profile can be assigned using one of the procedures men-
tioned above.
Boundary Condition for Moisture Flow. The ground
surface boundary condition for moisture flow can be defined
using Eq. 6.65.
Actual Evaporation. The limiting function proposed by
Wilson et al., (1997a) can be used to calculate AE (i.e., Eq.
6.73 or 6.74).
Calculation Procedure.

Potential Evaporation. The PE can be determined in a
number of different ways, including using the following:

1. Measured data (e.g., pan evaporation)
2. The Penman (1948) equation 6.20
3. The Thornthwaite (1948) equation 6.19
4. The Priestley-Taylor (1972) equation 6.23
5. The Monteith (1965) equation 6.22
Calculation Procedure.

1. Initialize the water content profile.
2. Initialize the soil temperature profile.
3. Apply the moisture flux boundary conditions accord-
ing to Eq. 6.65.
4. Apply thermal boundary conditions at the ground sur-
face using Eq. 6.63 or 6.64.
5. Ensure the model domain is initialized.
6. Determine PE using measured data or calculate from
one of the above-mentioned equations.
7. Calculate the AE using Eq. 6.73 or 6.74 together with
Eq. 6.70.
8. Solve the moisture flow equation 6.50 and the thermal
flow equation 6.53 based on initial conditions and
boundary conditions.
9. Calculate net infiltration I at the soil surface. The net
infiltration flux at the ground surface is defined as
k∂h/∂y .

1. Initialize the water content profile.
2. Initialize soil temperatures with the air temperature.
3. Apply the seepage boundary condition (i.e., Eq. 6.65),
which might involve precipitation or evaporation.
4. Determine PE through either measurement or one
of the empirical methods previously discussed [e.g.,
Penman (1948) equation].
5. Calculate AE using Eq. 6.73 or 6.74.
6. Solve the moisture flow PDE (Eq. 6.50) and calculate
the soil temperature (Eq. 6.72) based on the initial
conditions and the specified boundary conditions.
7. Calculate net percolation I or infiltration at the

ground surface. The net infiltration is equal to

k∂h/∂y ,