Various disciplines within the Earth sciences deal with measuring and representing the geometry of Earth’s land and sea surface, as well as atmospheric and oceanic conditions, to further our understanding of dynamic processes occurring on Earth.

All around the world, society and economy is becoming more and more vulnerable to changing weather. The recent extreme precipitation and flooding in western Germany and South Africa, the strong tornado in the Czech Republic, or dry spells leading to severe fires in Canada are just a few of many examples that illustrate how anthropogenic climate change is going to influence our weather. Climate describes the statistics of all-weather events and is typically predicted using physical models representing the relevant processes in the Earth system. Understanding these processes is paramount to anticipating and addressing the challenges posed by climate change today.

A key aspect of meteorological research and Earth sciences in general is to develop methods to turn atmospheric, oceanic, and terrestrial observations into regional information for weather and climate prediction. The observations are being collected with different types of sensors at increasing spatial and temporal resolution which poses computational challenges to meteorologists that cannot always be addressed with traditional methods. More and more observation systems (e.g., from commercial aircraft or new satellite series including radio occultation) but also opportunistic crowd-sourced measurements are currently exploited. In addition, there are ground-based remote-sensing networks for operational atmospheric profiling, which can shed light on small-scale processes such as turbulence and cloud physics that cannot be resolved in detail from satellites, but can be used to improve model parameterizations. Thus, on the horizon there is a wealth of new, voluminous observation systems providing unprecedented possibilities for improving weather and climate models through innovative and explorative approaches in the areas of data handling, data assessment, information extraction, and data assimilation.

The field of computational geometry is concerned with the design, analysis, and implementation of efficient algorithms for geometric and topological problems, which arise naturally in a wide range of application areas. Computational geometry is a vibrant and mature field of research, with several dedicated international conferences and journals and strong intellectual connections with other computing and mathematics disciplines. Within computer science and mathematics, computational geometry lies in the intersection of the theory of algorithms and combinatorial geometry. Despite its theoretical nature, the research in this field is strongly oriented towards and motivated by concrete practical problems that arise in various application areas that deal with geometric data. The related emerging field of geometric data analysis deals with the efficient statistical analysis of geometric data by providing sketches and data summaries with provable guarantees.

This Dagstuhl Seminar will bring together computational geometers and meteorologists and will provide a forum to discuss the unique computational challenges that meteorologists are dealing with and how the geometry underlying the input data can be exploited to obtain efficient algorithms. Concrete problem areas that could greatly benefit from synergies between the two research areas include (1) data assimilation of weather-related measurements for numerical simulation, (2) tracking and clustering of moving atmospheric features, and (3) the planning and optimization of sensor placements.

Creative Commons BY 4.0

Susanne Crewell, Anne Driemel, and Jeff M. Phillips