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:
- focus on processes,
- focus on high-performance numerical methods, and
- 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)
Physically correct representation of processes, illustrated with soil hydrology and scalar transport.
- fundamental processes, those that are understood quantitatively beyond reasonable doubt
- transitions between scales in dissipative systems and heuristic parameterizations
- the role of heterogeneities and boundaries.
- fluids and solutes in porous media
- architecture of terrestrial systems
- groundwater flow and transport
- soil hydrology
- land-atmosphere coupling
- patterned vegetation in arid regions
- inversion and data assimilation
FunCEP – Fundamentals of Computational Environmental Physics
(8 CP course in Masters curriculum, offered jointly with Prof. Bastian, IWR, in winter term)
Numerical solution of hard and large problems, illustrated with various environmental processes.
- formulation of models for different classes of processes (different types of PDEs)
- setup of appropriate numerical schemes
- operationally run and analyze large numerical simulations
- groundwater flow and scalar transport in heterogeneous 2- and 3-dimensional domains
- active transport (density- and viscosity-driven flow)
- fluid flow (turbulence)
CCEES – Chaotic, Complex, and Evolving Environmental Systems
(8 CP course in Masters curriculum, offered in summer term)
Self-organization, ranging from deterministic chaos to evolution (eco-evo-devo), illustrated with examples from our physical environment.
- hierarchy of chaos, complexity, and evolution
- fundamental causes, typical manifestations, and methods of analysis
- numerical simulations of generic systems
- nonlinear dynamical systems, their stability and bifurcations
- discrete and continuous chaotic systems
- discrete complex systems
- pattern formation and dynamics
- population dynamics
- fundamentals of evolution
- evolution of System Earth
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