  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.
