Critical Points of Uncertain Scalar Fields: With Applications to the North Atlantic Oscillation
In an era of rapidly growing data sets, information reduction techniques such as extracting and highlighting characteristic features, are becoming increasingly important for efficient data analysis. Particularly relevant features of scalar fields are their critical points since they mark locations i...
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| Format: | Doctoral or Postdoctoral Thesis |
| Language: | English |
| Published: |
2023
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| Online Access: | https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa2-917225 https://ul.qucosa.de/id/qucosa%3A91722 https://ul.qucosa.de/api/qucosa%3A91722/attachment/ATT-0/ https://ul.qucosa.de/api/qucosa%3A91722/attachment/ATT-1/ https://ul.qucosa.de/api/qucosa%3A91722/attachment/ATT-2/ https://ul.qucosa.de/api/qucosa%3A91722/attachment/ATT-3/ |
| Summary: | In an era of rapidly growing data sets, information reduction techniques such as extracting and highlighting characteristic features, are becoming increasingly important for efficient data analysis. Particularly relevant features of scalar fields are their critical points since they mark locations in the domain where a field's level set undergoes fundamental topological changes. There are well-established methods for locating and relating such points in a deterministic setting. However, many real-world phenomena studied in the computational sciences today are the result of a chaotic system that cannot be fully described by a single scalar field. Instead, the variability of such systems is typically captured with ensemble simulations, which generate a variety of possible outcomes of the simulated process. The topological analysis of such ensemble data sets, and uncertain data in general, is less well studied. In particular, there is no established definition for critical points of uncertain scalar fields. This thesis therefore aims to generalize the concept of critical points to uncertain scalar fields. While a deterministic field has a single set of critical points, each outcome of an uncertain scalar field has its own set of critical points. A first step towards finding an appropriate analog for critical points in uncertain data is to look at the distribution of all these critical points. In this work, different methods for analyzing this distribution are presented, which identify and track the likely locations of critical points over time, estimate their local occurrence probabilities, and eventually characterize their spatial uncertainty. A driving factor of winter weather in western Europe is the North Atlantic Oscillation (NAO), which is manifested by fluctuations in the sea level pressure difference between the Icelandic Low and the Azores High. Several methods have been developed to describe the strength of this oscillation. Some of them are based on certain assumptions, such as fixed positions of these ... |
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