10. Zaidel Problem
One of the most challenging numerical cases for MODFLOW arises from drying-rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. This problem simulates a discontinuous water table configuration over a stairway impervious base and flow between constant-head boundaries at the left and right sides of the model domain. This problem is based on the problems that compared the analytical solution of (Zaidel, 2013) to MODFLOW-NWT (see Zaidel, 2013, fig. 6).
10.1. Example Description
Model parameters for the example are summarized in Table 10.1. The model consists of a grid of 200 columns, 1 row, and 1 layer and a bottom altitude of ranging from 20 to 0 m (Figure 10.1). The discretization is 5 m in the row direction and 1 m in the column direction for all cells. A single steady-stress period with a total length of 1 day is simulated.
Parameter |
Value |
|---|---|
Number of periods |
1 |
Number of layers |
1 |
Number of rows |
1 |
Number of columns |
200 |
Column width (\(m\)) |
5.0 |
Row width (\(m\)) |
1.0 |
Top of the model (\(m\)) |
25.0 |
Starting head (\(m\)) |
23.0 |
Cell conversion type |
1 |
Horizontal hydraulic conductivity (\(m/day\)) |
0.0001 |
Constant head in column 1 (\(m\)) |
23.0 |
A constant horizontal hydraulic conductivity of 0.0001 \(m/d\) was specified in all cells. An initial head of 23 \(m\) was specified in all model cells. Constant head boundary cells were specified in column 1 and 200. The constant head value in column 1 is 23 \(m\) and was used in all simulations. A constant head value of 1 and 10 \(m\) was specified in column 200 based on the values evaluated by (Zaidel, 2013).
Figure 10.1 Discontinuous water table configuration over a multistep impervious base. Simulated results for the case where the constant head in column 200 is equal to 1 meter is shown. The impervious model base and the location of constant head boundary cells is also shown.
10.2. Example Results
Simulated results for the case with the constant head in column 200 equal to 1 \(m\) and 10 \(m\) are shown in Figure 10.1 and Figure 10.2, respectively. Simulated results compare well with the results in (Zaidel, 2013).
Figure 10.2 Discontinuous water table configuration over a multistep impervious base. Simulated results for the case where the constant head in column 200 is equal to 10 meters is shown. The impervious model base and the location of constant head boundary cells is also shown.
10.3. References Cited
Zaidel, J. (2013). Discontinuous steady-state analytical solutions of the Boussinesq equation and their numerical representation by MODFLOW. Groundwater, 51(6), 952–959. https://doi.org/10.1111/gwat.12019
10.4. Jupyter Notebook
The Jupyter notebook used to create the MODFLOW 6 input files for this example and post-process the results is: