Topological descriptors of spatial coherence in a convective boundary layer
This work addresses a domain-specific problem in geosciences for researchers modeling atmospheric interactions, but it is incremental as it builds on existing topological methods by focusing on simpler connectivity descriptors.
The authors tackled the problem of modeling interactions between a turbulent convective boundary layer and land surfaces by developing topological descriptors based on connectivity to address the insufficiency of bulk flow statistics, showing these tools can analyze CBL structure and model responses to surface forcing differences.
The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which can describe it quantitatively. Commonly employed methods, such as bulk flow statistics, are known to be insufficient for this task, especially when land surfaces with equal aggregate statistics but different spatial patterns are involved. While geometrical properties of the surface forcing have a strong influence on flow structure, it is precisely those properties that get neglected when computing bulk statistics. Here, we present a set of descriptors based on low-level topological information (i.\,e. connectivity), and show how these can be used both in the structural analysis of the CBL and in modeling its response to differences in surface forcing. The topological property of connectivity is not only easier to compute than its higher-dimensional homological counterparts, but also has a natural relation to the physical concept of a coherent structure.