Environmental systems are often exceedingly complicated – highly nonlinear, operating in and creating multiscale heterogeneous structures, and stochastically forced. So far, we typically lack a comprehensive representation of them and approach them along different routes. Three of these form the basis of our group's teaching efforts:

  1. focus on processes,
  2. focus on high-performance numerical methods, and
  3. focus on self-organization.

Operationally, traditional mathematics only reaches to the most simple systems. Hence, essential tools for us are numerical methods, those with numerical mathematics as their solid basis as well as the more heuristic approaches like cellular automata or agent-based simulations.


PoTS - Physics of Terrestrial Systems

(4 CP course in Masters curriculum, offered in winter term)

Focus

Soil hydrology, from physical processes and soil architecture to numerical simulation and data assimilation.

Key Aspects

  • physical processes at scales of soil pore, continuum, and field
  • multi-scale heterogeneities and complicated boundaries
  • numerical forward simulation, inversion, and data assimilation
  • simulation projects

Contents

  • physics of fluids in porous media
  • scale transitions and soil water flow
  • numerical simulation of partial differential equations
  • inversion, data assimilation, and knowledge fusion
  • architecture of near-surface geologic formations (aquifers and soils)
  • soil hydrology project (modeling, num. sim., analysis)
  • representation of vegetation
  • arid land project (modeling, num. sim., analysis)

Material


FunCEP – Fundamentals of Computational Environmental Physics

(8 CP course in Masters curriculum, offered jointly with Prof. Bastian, IWR, in winter term)

Focus

Numerical solution of hard and large problems, illustrated with various environmental processes.

Key Aspects

  • formulation of models for different classes of processes (different types of PDEs)
  • setup of appropriate numerical schemes
  • operationally run and analyze large numerical simulations

Contents

  • groundwater flow and scalar transport in heterogeneous 2- and 3-dimensional domains
  • active transport (density- and viscosity-driven flow)
  • fluid flow (turbulence)

Material


CCEES – Chaotic, Complex, and Evolving Environmental Systems

(8 CP course in Masters curriculum, offered in summer term)

Focus

Self-organization, ranging from deterministic chaos to evolution (eco-evo-devo), illustrated with examples from our physical environment.

Key Aspects

  • hierarchy of chaos, complexity, and evolution
  • fundamental causes, typical manifestations, and methods of analysis
  • numerical simulations of generic systems

Contents

  • nonlinear dynamical systems, their stability and bifurcations
  • discrete and continuous chaotic systems
  • discrete complex systems
  • pattern formation and dynamics
  • population dynamics
  • geomorphology
  • fundamentals of evolution
  • evolution of System Earth

Material


Seminars

MSc CCEES seminar

(6 CP seminar in Masters curriculum, offered in winter term)

Based on CCEES course with focus varying between years.

Some projects have been published:

BSc CCEES seminar

(3 CP seminar in Bachelors curriculum, offered irregularly)

Special topic from the field of CCEES with focus varying between years. In German.

  • WS15/16: Komplexe terrestrische Systeme

FP - advanced practical