Topological Data Analysis of Northern Hemisphere SLP Anomalies: Identifying and Tracking the Structural Skeleton of Atmospheric Pressure Systems
We propose a novel framework based on Topological Data Analysis (TDA) to identify and track cyclonic and anticyclonic structures in the Northern Hemisphere. Using persistent homology applied to seven decades of daily sea-level pressure anomalies (1948--2023), we represent the atmospheric field as a cubical complex and compute sublevel- and superlevel-set filtrations. This approach allows us to identify 1-dimensional topological features (1-holes) that correspond to coherent pressure systems, which we term 1-cyclones and 1-anticyclones. The structural intensity of these features is quantified through their topological depth, while their dynamical evolution is followed using an optimal matching procedure based on the Wasserstein distance between consecutive persistence diagrams. Our results reveal robust seasonal patterns characterized by winter maxima and summer minima in total persistence, frequency, and spatial extent. We show that cyclonic activity is topologically more fragmented and intense, consistent with the seasonal deepening of the Icelandic Low, whereas anticyclones exhibit a heavier long-duration tail associated with persistent blocking episodes. Crucially, we demonstrate that TDA metrics can differentiate between distinct dynamical regimes of atmospheric blocking, distinguishing the quasi-stationary, ``frozen'' topology of the 2003 European heatwave from the more volatile and unstable configuration of the 2012 cold spell. Compared to classical geometric tracking algorithms, this framework provides an objective, multiscale, and noise-robust characterization of the atmospheric skeleton, offering a unified mathematical description of the organization and stability of mid-latitude circulation.