Determining the free surface in the horizontal model means calculating the unknown thickness. The thickness (m) of the unconfined aquifer must be determined in such a way that for the potential heads (h) calculated with this thickness:

m = h - u

where u is the lower boundary of the aquifer. The calculation is performed by iterating the thickness of the individual elements. The thickness of the aquifer is adjusted so that the following applies for each element:

m_i+1 = h_i - u.

with: i = iteration step

To avoid oscillations during iteration, the change in thickness from one iteration step to the next is given an attenuation factor of 0 < w < 1:

m_i+1 = m_i + w * ((h_i - u) - m_i).

At w=1.0 the iteration is not attenuated at all, at w=0. it is extremely damped. The default setting is usually an attenuation factor of 0.5. The starting thicknesses calculated in the model check are used as the initial state for the iteration.

The iteration is continued until either the differences in the calculated potential heads of two steps fall below an internal limit or the maximum number of iteration steps specified by the user is reached.

In the case of a confined aquifer, the groundwater surface is restricted in its upward expansion. This is taken into account during iteration in that the iterated thickness must not exceed the maximum (possible) thickness calculated in the model test.

In order to be able to iterate the thicknesses in a 2D model, it is always necessary to specify the lower boundary (attribute UNTE) of the aquifer.

Example:

If a calibration state is to be recalculated, the initial potential heads (attribute EICH) and the -lower boundary of the aquifer (attribute UNTE) from which the thicknesses are calculated are usually specified in the mesh file. However, these largely correspond to the initial thicknesses calculated during the model check. In this case, the iteration should converge very quickly even with an attenuation factor of w=1.0.

For further calculations, it is generally not the calibration state that should be calculated, but any other groundwater situation (e.g. changed extraction rates). In an area with changed extraction rates, the thickness will change compared to the initial thickness. In the case of large changes compared to the calibration state, it makes sense to dampen the iteration of the thickness in order to avoid oscillations.

Special feature of the module SITRA:

In the SITRA module, the thicknesses are saved as node values. Therefore, the starting thicknesses and maximum thicknesses from the model check must be averaged to node values, which may lead to a loss of accuracy.

Calculation of the free surface (vertical- or 3D model)