**Combining Modern Statistical Methods and Thermodynamic Principles**

**for Dynamic System Analysis in Environmental Sciences**

Analysing complex and dynamic environmental systems often reaches technical and theoretical limits of statistical standard tools. This is the case as most classical statistical approaches fundamentally require assumptions about statistical independence and stationarity, which are especially problematic as soon as we deal with non-linearity and coevolution. Many promising approaches founded in scientific fields ranging from theoretical physics to information theory have been developed. Still, their application to applied climate and environmental sciences remains challenging.

This 4-day block course will introduce a set of modern tools for rigorous analyses of dynamic systems. Starting off with examples from geophysics and fluid mechanics the course will guide you during an excursion through stochastic physics, information theory, phase-state analyses and applications with big data and scaling. We especially invite you to bring own data and application questions to provide hands-on utilisation of the concepts and tools within your field of research.

**Programme**

**Day 1 – From fluid mechanics to dynamical systems**

The first day ensures a common basis for all participants. With fundamentals from classical fluid dynamics, thermodynamics, stability and scaling laws the foundation is laid.

The day will consist of four teaching units with practical analytical and numerical examples across the earth sciences.

**Day 2 – Coevolutionary dynamical systems**

The second day will extend the classical fluid dynamics with stochastic physics and information theory. With this, complexity will be rigorously treated in a sim- ple and coherent framework providing the physical background to coevolutiona- ry dynamics and organisation.

The day will consist of two teaching units and two real-world application cases.

**Day 3 – Mastering conjugated dimensions**

The third day will redefine the state-space system analyses with physical princi- ples and thermodynamic limits as true phase-state analyses towards dynamic system understanding without the requirement for single attractors, finite pha- ses and fixed scales. It also includes conjugated pairs and a new breed of non- paired conjugates.

The day will consist of two teaching units, one unit with real-world applications and one unit transferring the approaches to own analyses of the participants. Evening: Preparation of applications to own data.

**Day 4 – Presentations and frontier topics**

The fourth day will start with two units presenting first results of applications to own data. Subsequently frontier topics of scaling and big data applications will be tackled.

Evening: Discussion of possible collaboration and emerging aspects.

**Lecturer:** Dr. Rui Perdigão

**Schedule:** 27 February – 2 March, 2018

**Hosted by:**

GRACE – Graduate School for Climate and Environment

Engesserstr. 6, 76131 Karlsruhe – T+49-721-608-43676 – F+49-721-608-48475

Karlsruhe Institute of Technology (KIT)