RTG Course: Differential Equations and Dynamical Systems in Climate Physics

Lecturer: Dirk Olbers

When: January 31 - February 1, 2023

Where: Bremen and online

The Earth system is one of the most complex systems presently investigated by scientists. The physical compartments -- atmosphere, hydrosphere and cryosphere -- are usually combined as 'climate system' and can be described by mathematical equations which result from fundamental physical laws. The other non-physical parts of the system, as e.g. the vegetation on land, the living beings in the sea and the plentitude of chemical substances relevant to climate and life, can be represented by mathematical evolution equations as well. Comprehensive models spanning this broad range of coupled compartments are so complex that they are mostly beyond a deep reaching mathematical treatment, in particular when asking for general analytical solutions. Solutions are obtained by numerical methods for specific boundary and initial conditions. Simpler models have helped to construct these comprehensive models, they are also valuable to train the physical intuition of the behavior of the system and guide the interpretation of the results of numerical models.

Simple models may be stand-alone models of subsystems, such as stand-alone general circulation models of the ocean or the atmosphere or coupled models, with reduced degrees of freedom and a reduced content of the physical processes. They exist in a wide range of structural complexity but even the simplest model may still be mathematically highly complicated due to nonlinearities of the evolution equations. This course presents a selection of such models from ocean and atmosphere physics. The emphasis is placed on a brief explanation of the physical ingredients and a condensed outline of the mathematical form.