2.3. Numerical Modelling
For the simulation of vertical water flow, the one-dimensional Richards
equation (Eq. 6) was solved using the finite element code HYDRUS-1D
(Šimůnek et al., 2008; Šimůnek & van Genuchten, 2008):
\(\frac{\partial\theta}{\partial t}=\frac{\partial}{\partial z}\left[K_{(\theta)}\left(\frac{\partial h}{\partial z}+1\right)\right]-Q\)[6]
where z represents the vertical coordinate [cm], positive in
the downward direction, Q is the source/sink term, θ is
the volumetric water content [cm3cm-3], and K (θ) is the
unsaturated hydraulic conductivity [cm d-1] as a
function of water content.
A 200 cm soil profile was simulated, and the lower boundary condition of
the flow domain was defined as free drainage, which is typically used
when the ground water table is far below the soil surface. As a second
option, a fluctuating ground water table was prescribed as a Dirichlet
boundary condition. For the variable ground water table depth, a simple
sine curve of the ground water table fluctuations was generated by using
Eq. [7] for the 10988 days of climatic data (see end of this section
for a description of the model driving data):
\(y\left(t\right)=A_{s}\sin\left(2\text{πft}\right)\) [7]
where As is the amplitude of the sine curve,
which is defined as the maximum displacement of the function from its
centre position, and shows the height of the curve (fluctuation) (here,As = 100 cm), 2π is the natural period of the
sine curve, f is the frequency (here, f = 1/365
days-1), and t is the time period of the sine
curve (here, t = 1 to 10988 days).
The upper boundary condition in HYDRUS was set to an atmospheric
boundary with surface runoff. The domain was non-equally discretized
with 401 nodes, with finer discretization at the top to account for the
stronger flow dynamics close to the soil surface. Pressure head was used
for initialization of the soil profile with linearly decreasing
potentials between the bottom (0 cm) and the top (200 cm) node (i.e.,
hydrostatic equilibrium).
For the simulations, different setups were chosen with varying
complexity. A simple homogeneous soil profile without vegetation was
selected as the simplest case, to study the impact of the choice of
different PTFs. Complexity was increased by adding different vegetation
covers (grass and wheat). In both cases, growth was not simulated and
both crops covered the soil throughout the entire year. Potential
evapotranspiration, ET0 , was split into soil
evaporation, E , and transpiration, T , by setting Tto 75 % of ET0 . Also, rooting depth was assumed
to be the same (0-30 cm) for both vegetation covers with a linear
decrease in root density from the top soil layer to the maximum rooting
depth. The root water uptake reduction model of Feddes et al. (1978) was
used, based on the parameter values of Wesseling (1991) for both grass
and wheat vegetation, as taken from the HYDRUS embedded look up table
(see
Tab. 2). Therefore, the only difference between both vegetation
scenarios was the root water uptake. This simplification in terms of
growing season and rooting depth was done to simplify the comparison of
the simulation results, by ensuring that root water uptake will not be
from different soil layers when grass is replaced by wheat. In a next
step of increasing complexity, soil layering was introduced, whereby two
layering schemes were assumed. 1) Sandy loam over silt loam overlaying a
loamy sand and 2) silt loam over silty clay loam overlaying a silty
clay, respectively. For the layered profiles the first layer was set to
extend from 0 to 50 cm, the second layer from 50 – 100 cm, whereas the
third layer occupied the rest of the profile (100 – 200 cm). Again, the
same vegetation parameters as for the homogeneous soil were used.
Finally, the layered system covered by wheat with a fluctuating
groundwater table was simulated. Figure 2 shows a schematic view of the
seven model scenarios used in this study.
Thirty years (10988 days) of daily climatic data (comprising
precipitation and Penmen-Monteith potential ET) from 1982 to 2011 were
taken from North Rhine-Westphalia, Germany (mean NRW climatic data) as
used by Hoffmann et al. (2016) and Kuhnert et al. (2017). The climate is
humid temperate.