A one state groundwater open water model for a hillslope

Understanding and modelling the flow of water through hillslopes helps understanding the rainfall runoff process. In our group Arno Hilberts has investigated these models in the framework of a Phd thesis.

The saturated flow in the hill slope can be modelled by a the so called Boussinesq equations. In its most simple form, this means that the flux trough the soil is given by the following formula:

In this h is the groundwater level, k the conductivity and z_b the bottom. It may happen that during a runoff event the groundwater reaches the surface and part of the flow continuous as open water flow. The discharge for open water flow are in general much more complicated, but a justifiable simplification in this case is given by the formula:

In this h stands for the open water level, n for the friction, z_s for the surface elevation.

If one does accept there is hydrostatic pressure throughout a vertical, the state of the system can be described by the one level h and both formulas can be combined into one.

The MSc thesis will consists in investigating this formula and the corresponding hillslope flow. For this the MSc student should:

• Understand and describe the theory behind these formulas

• Solve this model by a numerical technique called Finite Volume. An existing code in which this can be implemented is available.
  

• Investigate different one dimensional examples (inspired by the Phd work of Hilberts) and discuss the advantages and disadvantages of this technique.
  

In order to be succesfull, the MSc student should:

• Have an interest in the runoff generation process

• Have a basic insight in open water and groundwater flow

• Show such insight in numerical techniques that the available Finite Volume code can be used
  

• Show creativity in designing and discussing examples of application.