Defining Topological Weather Regimes through Persistent Homology
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.
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BibTeX
@misc{micieli2026defining,
title = {{Defining Topological Weather Regimes through Persistent Homology}},
author = {Marco Ezequiel Micieli and Marisol Osman and Gisela Daniela Charó and Davide Faranda and Denisse Sciamarella},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.21203/rs.3.rs-11120408/v1},
url = {https://hal.science/hal-05854227v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Defining Topological Weather Regimes through Persistent Homology
AU - Marco Ezequiel Micieli
AU - Marisol Osman
AU - Gisela Daniela Charó
AU - Davide Faranda
AU - Denisse Sciamarella
PY - 2026
DA - 2026/10/06
PB - HAL
DO - 10.21203/rs.3.rs-11120408/v1
UR - https://hal.science/hal-05854227v1
AB - 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.
ER -