Topological descriptors of spatial coherence in a convective boundary layer

TL;DR

This paper introduces topological descriptors based on connectivity to better analyze and model the spatial coherence in turbulent convective boundary layers, addressing limitations of traditional bulk flow statistics.

Contribution

It presents a novel set of topological descriptors that capture spatial patterns in the CBL, improving analysis and modeling of surface forcing effects.

Findings

Topological descriptors effectively differentiate spatial patterns in the CBL.

Connectivity-based measures relate naturally to physical coherent structures.

Descriptors outperform bulk statistics in capturing surface forcing influences.

Abstract

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.