# Numerical Modeling in Soil Physics

The practical course *F53: Numerical Modeling in Soil Physics* introduces the students to the basics of non-linear parameter estimation with the help of a soil hydraulic model.

Inversion methods are widely used to estimate model parameters in a large variety of applications. However, these methods are often applied via black boxes (origin, matlab, gnuplot, ...). In order to be able to successfully judge the quality of the resulting model parameters, it is beneficial to increase the understanding of these methods. Due to its high non-linearity, the soil hydraulic model is a perfect working horse for this goal.

The course basically consists of seven exercises with increasing complexity. Thus, the students finally approach current research questions with state-of-the-art research code. Additional knowledge in soil physics, electrodynamics, and optimization theory besides the content of the manual of the practical course is helpful but not necessarily required.

# First part: Soil Hydraulics

After having understood the handling of the software, the students simulate, discuss, and understand many soil hydraulic processes. Also the data from a real experiment with a fluctuating water table realized at the ASSESS site may be used as a working example. A simulation of the soil water distribution during this experiment is shown in this video.

# Second Part: Non-Linear Parameter Estimation

As the Levenberg-Marquardt algorithm is very popular for non-linear parameter estimation, advantages and disadvatanges of this algorithm are discussed in detail. This video shows a simple example, in which the Levenberg-Marquardt algorithm was applied to search the minimum of a surface in 2D.

Once the basic properties of the inversion algorithm are understood, the students learn to judge the quality of the resulting model parameters by closely analyzing the residuum. This video shows the covergence of the simulated data to the measurement data over the increasing number of iterations.

The main working tools are the Terminal, a text editor, and Paraview. As the time is short, there are no programming exercises in this course, meaning that all the necessary software will be provided. Nevertheless, the students are invited to write their own evaluation software (e.g., in python) for the analysis and visualization of their solution to the exercises.

The current version of the manual to the practical course can be downloaded here.

Questions, suggestions, and comments are most welcome - just contact me.

All the best,

Stefan