Defining Topological Weather Regimes through Persistent Homology
Year: 2026
Type: preprint
Abstract: The chaotic dynamics of the mid-latitude atmospheric circulation is often described using the statistical concept of Weather Regimes. Recent applications have sought to define these regimes as non-trivial topological features extracted through Persistent Homology, to make the result independent of ad hoc choices such as the number of clusters. Here, this perspective is revisited in the light of the topological description of chaotic attractors as branched manifolds. We define Topological Weather Regimes as specific parts of these structures, rather than as any non-trivial topological feature. Depending on whether they lie in the high- or the low-density subset of the points in phase space, they are computed as zeroth- or first-order persistent homological features respectively. The statistical and topological protocols are applied independently, so that results can be compared. The approach is applied to two atmospheric datasets: the South-Atlantic and the North-Atlantic Polar-Front jets. The first one is characterized here for the first time within the weather-regime framework, while the second one has been thoroughly studied with clustering methods as well as with Persistent Homology. Each Topological Weather Regime is found to have its corresponding statistical match.
Source: Research Square
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220668420