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.