Simulation of fields of soil physical properties by generalized exponential density models

It is well known that soil physical properties such as transmissivity in saturated groundwater modelling show large spatial variation. As it is impossible to describe all variations deterministically, modellers often use a large number of stochastically generated fields of transmissivities and investigate the results of this variation on the results. The picture below (see next page) could be interpreted as such a field, dark balls being clay and light balls being sand for instance. These fields should have certain statistical properties: the mean sand

There are several statistical techniques to simulate such fields. Kriging is a very well known one. In the well known groundwater program MODFLOW another simulation technique known under the name ”TPROGS” is implemented and used for MSc thesis work.

The thesis will consist in investigating yet another technique: simulation by generalized exponential densities. These techniques originate historically in statistical physical models of gasses and crystals. The picture shows a so called Ising model where the dark balls are positive charged particles and the light balls negative charged ones. These techniques can also be justified from an information point of view, as done e.g. in the work of Jaynes, see e.g. on wikipedia.

This technique is very versatile, can handle many both discrete and continuous fields and can handle all kind of spatial dependencies. Moreover the simulation algorithm is not complex and can be easily implemented, e.g. in a statistical language as R.

The MSc student should:

• Give a brief description and justification of the simulation technique andcompare it to other available ones.

• Implement the generalized exponential fields technique for two dimensionalfields.
  

• Use the simulated fields as input to a MODFLOW model

• Analyse the variations in output of this model due to the variation of input fields
  

• Discuss the advantages and difficulties of this approach.

In order to be succesfull the MSc student should have some affinities with ground-
water modelling, statistical simulation.

≈ 36 ECTS, e.g.: HWM80436 or SEG80436

Supervisors:

• G. Bier (SEG)
• P. Torfs (HWM)