# Frontiers in Mathematics Lecture Series

## Spring 2019

Date: | March 18, 2019 |

Time: | 4:00pm |

Location: | Blocker 117 |

Speaker: | Rupert Klein, Freie Universität Berlin |

Title: | Scales in Weather and Climate |

Abstract: | The science of weather and climate is challenging for many reasons, one being the multiscale nature of atmosphere-ocean flows. In this lecture I will first explain the notion of scales in this context through concrete examples, such as tropical hurricanes or the desertification of the Sahara some 8000 years ago. I will move on to discuss how mathematical formalization and solution techniques allow us to systematically unravel many, but far from all, of the underlying physical processes. An outline of remaining major challenges at the forefront of today’s weather and climate research will reveal that substantial progress can be expected only through intense interdisciplinary research involving the natural sciences as much as mathematics and computer science. |

Date: | March 19, 2019 |

Time: | 4:00pm |

Location: | Blocker 117 |

Speaker: | Rupert Klein, Freie Universität Berlin |

Title: | How Mathematics helps structuring climate discussions |

Abstract: | Mathematics in climate research is often thought to be mainly a provider of techniques for solving the continuum mechanical equations for the flows of the atmosphere and oceans, for the motion and evolution of Earth’s ice masses, and the like. Three examples will elucidate that there is a much wider range of opportunities. Climate modellers often employ reduced forms of Meteorologists define Modern climate research has joined forces with economy and the social sciences to generate a scientific basis for informed political decisions in the face of global climate change. One major type of problems hampering progress of the related interdisciplinary research consists of often subtle language barriers. The third example describes how mathematical formalization of the notion of |

Date: | March 21, 2019 |

Time: | 4:00pm |

Location: | Blocker 117 |

Speaker: | Rupert Klein, Freie Universität Berlin |

Title: | Multi-scale regimes of atmospheric motions |

Abstract: | Flows of the Earth’s atmosphere cover a very wide range of scales, from micrometer-sized raindrops to planetary-scale climate phenomena. The range of relevant time scales is equally broad. A central task of theoretical meteorology is to identify specific weather- or climate-related flow phenomena that are associated with particular length and time scales, and to construct simplified models describing these phenomena in terms of some reduced set of effective degrees of freedom. Textbooks on theoretical meteorology offer derivations of such reduced models from more comprehensive fluid dynamical governing equations through In the first part of the lecture I will introduce a systematization of reduced model equations of theoretical meteorology that is based on the principles of dimensional and asymptotic analysis. This approach allows one to re-derive a large number of reduced models of theoretical meteorology in a unified fashion from the full compressible flow equations via classical single-scale asymptotics.More importantly, this unified approach lends itself naturally to multiple scales analyses, i.e., to studies of how scale-dependent phenomena described by different reduced model equations are coupled across the scales. The second part of this lecture will cover examples of such multiscale interaction theories selecting from an asymptotic model for tropical storm intensification, the derivation and justification of |