poster - International Conference of Agricultural Engineering

RE because it has the advantages over the other forms in applicability. However, the method
presented by Izumi et al. (2011) does not consider the effect of soil temperature on water
movement in soil.
The purpose of this paper, thus, is to develop an inverse modeling for the mixed form RE in
non-isothermal soil. Firstly, the governing equations (forward problem, FP) are described,
and SHPs which are model parameters included in the equations are parameterized. The
relative hydraulic conductivity (RHC) which is a major unknown parameter to be identified in
this study is described by a free-form parameterized function which is a sequence of
piecewise cubic spline functions over the whole effective saturation domain. For the
representation of the soil water retention curve (SWRC), van Genuchten model (VG model)
is employed due to being time-proven. Secondly, the inverse problem (IP) is defined as
minimizing errors between the observed and computed values of the pressure head. The
solution procedure is then described based on a simulation-optimization algorithm with the
aid of the Levenberg-Marqurdt method to determine the function shape of RHC. Finally, the
validity of the inverse modeling developed is examined through in-situ experiments in terms
of reproducibility for observed water movement.
2. Governing Equations
2.1 Water Movement Model
In order to obtain the mass-conservative numerical solutions, the mixed form of RE is
employed for the water movement. Additionally using the Boussinesq assumption to consider
the dependency of density and viscosity of water on soil temperature, the equation in onedimensional
vertical flow where the liquid phase is considerable magnitude, i.e. neglecting
the vapor fluxes, is described as follows (Huyakorn and Pinder, 1983);
∂S
ψ ⎛ ⎛ ρ ρ ⎞⎞
w
∂ ∂ ∂h
T
−
ρ
φ + WSwSs
= − − K ⎜ +
⎜
⎟
(1)
∂t ∂t ∂z ∂ ρ ⎟
⎝ ⎝ z
ρ ⎠⎠
with
⎧⎪ 1 ( ψ ≥ 0 ),
p
W = ⎨
Ss = ρρg( βs + φβw) , K = Kρ ( Se) KT ( Ts)
Ks,
h = + z = ψ + z (2)
⎪⎩ 0 ( ψ < 0 ),
ρρg
where φ is the porosity, S w the saturation, S s the specific storage, ψ the pressure head, K the
unsaturated hydraulic conductivity, h the hydraulic head, t the time, z the height defined as
positive upward, ρ T the water density at the soil temperature T s , ρ r the reference water density
at the reference soil temperature T r , g the gravitational acceleration, β s and β w the
compressibility coefficients of soil and water, respectively, K r the relative hydraulic
conductivity, K T the correction-factor function of soil temperature, K s the saturated hydraulic
conductivity, S e the effective saturation and p the water pressure.
2.2 Thermal Transport Model
The heat flux due to the water movement in soil is smaller than the heat conduction by the
solid soil and thus can be neglected. Accordingly, the heat conduction equation is employed
for the thermal transport, and described as follows;
∂ ( CT
h s)
∂ ⎛ ∂Ts
⎞
= − ⎜ −λ
∂ ∂ ∂ ⎟
(3)
t z⎝
z ⎠
with
0.5
( 1 φ) θ , λ θ θ
C = − c + c = r + r + r
(4)
h s w 1 2 3
where C h is the volumetric heat capacity of soil, θ the volumetric water content, c s and c w the
volumetric heat capacity of soil particles and that of water, respectively, and λ the thermal
conductivity of soil expressed by a simple empirical equation with the regression parameters
r 1 , r 2 and r 3 (Chung and Horton, 1987).