Improving Topological Detection of Weather Regimes in climate dynamical systems

Abstract: Weather regimes provide a useful framework for describing large-scale atmospheric variability and its impacts on regional weather. Despite extensive study, there is still no universally accepted definition or method for identifying weather regimes. Recent work has shown that weather regimes can be interpreted geometrically as topological structures in the phase space of the atmospheric system. In this approach, regimes are identified using a density--radius bifiltration combined with persistent homology, a well-established tool from Topological Data Analysis (TDA). This topological perspective provides a unifying view of regimes and, unlike traditional methods, does not require the number of regimes to be specified in advance. However, the method relies on density estimation techniques (typically Gaussian kernel density estimation), which can over--smooth weakly populated but dynamically important regions of the phase space.