Numerical Analysis of Water Movement in Agricultural Fields …
5
2.1 Soil Hydraulic Property Models
Since Richards equation is an open form equation, constitutive equations are required
to solve it. In the present study, the model proposed by van Genuchten and Nielsen
[12], which relates the independent parameter suction head with soil moisture and
hydraulic conductivity, was used.
2.2 Initial and Boundary Conditions
A hydrostatic condition with a suction pressure head of −2 m was assumed as the
initial condition. The upper boundary condition switches between prescribed flux
and constant head boundary conditions depending on the availability of water on the
surface. It is also assumed that any water beyond the maximum ponding depth will be
runoff and will not be considered in the analysis. No flow and free gravity drainage
boundary conditions were assumed at the walls and bottom boundary, respectively.
2.3 Generation of Flow Parameters and Choice of Domain
Size
Saturated hydraulic conductivity, K s , and van Genuchten pore size distribution
parameter, α, were treated as a continuous stochastic functions with multivariant
lognormal probability density function with mean values of 1.06 (cm/day) and −
1.48 (cm
−1 ), respectively. Three different sandy clay soil formations: a spatially
homogeneous media (σ
2
Y = 0) and two heterogeneous formations with two variances (σ
2
Y = 0.3 and σ
2
Y = 0.6), where Y = ln K s or ln α, were considered in the
simulations. The correlation length scales of the van Genuchten model parameters
were assumed to be equal to those of Y, which is taken from [13], i.e. I px = I py = 0.8 m
and I pz = 0.2 m. All the formations will have similar geometric mean of K s and α, and
the only parameter which will vary is the variance. Considering ergodic assumption
and single realization approach to be economical, the flow domain size was fixed to
be 10, 20, and 5 m along the x-, y-, and z-directions, respectively. Saturated moisture
content, θ s , was taken to be 0.4 (cm
3 /cm
3 ). Residual moisture content, θ r , and van
Genuchten pore size shape parameter, n, were considered to be 0.01 (cm
3 /cm
3 ) and
1.4, respectively.
5
2.1 Soil Hydraulic Property Models
Since Richards equation is an open form equation, constitutive equations are required
to solve it. In the present study, the model proposed by van Genuchten and Nielsen
[12], which relates the independent parameter suction head with soil moisture and
hydraulic conductivity, was used.
2.2 Initial and Boundary Conditions
A hydrostatic condition with a suction pressure head of −2 m was assumed as the
initial condition. The upper boundary condition switches between prescribed flux
and constant head boundary conditions depending on the availability of water on the
surface. It is also assumed that any water beyond the maximum ponding depth will be
runoff and will not be considered in the analysis. No flow and free gravity drainage
boundary conditions were assumed at the walls and bottom boundary, respectively.
2.3 Generation of Flow Parameters and Choice of Domain
Size
Saturated hydraulic conductivity, K s , and van Genuchten pore size distribution
parameter, α, were treated as a continuous stochastic functions with multivariant
lognormal probability density function with mean values of 1.06 (cm/day) and −
1.48 (cm
−1 ), respectively. Three different sandy clay soil formations: a spatially
homogeneous media (σ
2
Y = 0) and two heterogeneous formations with two variances (σ
2
Y = 0.3 and σ
2
Y = 0.6), where Y = ln K s or ln α, were considered in the
simulations. The correlation length scales of the van Genuchten model parameters
were assumed to be equal to those of Y, which is taken from [13], i.e. I px = I py = 0.8 m
and I pz = 0.2 m. All the formations will have similar geometric mean of K s and α, and
the only parameter which will vary is the variance. Considering ergodic assumption
and single realization approach to be economical, the flow domain size was fixed to
be 10, 20, and 5 m along the x-, y-, and z-directions, respectively. Saturated moisture
content, θ s , was taken to be 0.4 (cm
3 /cm
3 ). Residual moisture content, θ r , and van
Genuchten pore size shape parameter, n, were considered to be 0.01 (cm
3 /cm
3 ) and
1.4, respectively.