SCHRIFTENREIHE Institut für Pflanzenernährung und Bodenkunde ...

Simulations of soil water and heat flow were performed with HYDRUS-1D
(Šimůnek et al., 1998). HYDRUS-1D is a finite element model for simulating the
one-dimensional movement of water, heat, and multiple solutes in variably
saturated media. The program numerically solves the Richards’ equation for
saturated and unsaturated water flow and Fickian-based advection dispersion
equations for heat and solute transport. Variably saturated water flow is
described by the modified Richards’ equation:
∂h
∂T
[ ( h)
+ K ( h)
+ K ( h)
S
∂ ( h)
∂ = K ∂t
∂z
h ∂z
h
T ∂z
θ w ] −
[1]
where θw is the volumetric liquid water content, t is time, z is the spatial
coordinate positive upward, h is the pressure head, T is the temperature, and S
is a sink term usually accounting for root water uptake. Kh and KT donate
hydraulic conductivity due to a gradient in h and T, respectively. Soil hydraulic
properties are described by the following expressions (van Genuchten, 1980):
S ( h)
e
θ ( h)
−θ
1
w r = =
[2]
n m
θs
−θ
r [ 1+
αh
]
K ( h)
−
h
l
1/
m m 2
= K s × Se
( 1−
( 1 Se
) )
[3]
where Se is the effective saturation, θs and θr are the saturated and residual
water contents (L 3 L -3 ), respectively; the symbols α (L -1 ), n, and m=1-1/n are
empirical shape parameters, and the inverse of α is often referred to as the air
entry value or bubbling pressure; Ks is the saturated hydraulic conductivity (L
T -1 ), and L is a pore connectivity parameter which normally is set to 0.5. The Eq.
[2] was fitted to the measured water retention data (drying branch) using the
RETC code (van Genuchten et al., 1991).
The soil thermal regime is modeled with the conduction–convection heat
flow equation (e.g., Nassar et al., 1992):
∂T
∂T
[ λ(
] − C q C ST
∂ T ∂ C( ) = θ
t z w)
z w −
∂ ∂
∂
∂z
w
θ [4]
where C(θ) and Cw denote the volumetric heat capacity of the bulk soil and
liquid phase, respectively. C(θ) is determined according to De Vries (1963):
90
C( θ ×
6
θ ) ≈ ( 1.
92θ
m + 2.
51θ
o + 4.
18 w ) 10
[5]