Volumes in a dynamical system’s phase space can stretch, compress, fold or tear; the combination of these processes gives rise to a structure in its space. The topology of this structure is the signature of the mechanisms that act to shape the system’s flow in this phase space [1]. Our topological approach uses the novel concept of templex [2], which consists of finding a topological representation for the branched manifold approximated by a cell complex and a directed graph that prescribes the allowed connections between the highest dimensional cells of the complex as a function of the flow. The templex properties include the non-equivalent ways of circulating along the complex, which are essential to provide a complete description of the system’s dynamics. The templex provides the key features of the topological structure underlying a dynamical system. Weather extremes can be classified by two scalars: the instantaneous dimension and the persistence of a state of a dynamical system [3,4]. The computation of these asymptotic scalars for weather observables provides information on the rarity, and persistence of specific states. In this work, we present a first attempt to relate the instantaneous dimension and other local metrics to the topological properties of the templex of the system under study. References [1] M. Ghil, D. Sciamarella, Dynamical systems, algebraic topology and the climate sciences, Nonlinear Processes in Geophysics, 30(4), 399-434, (2023). [2] G. D. Charó, C. Letellier, D. Sciamarella, Templex: A bridge between homologies and templates for chaotic attractors, Chaos: An Interdisciplinary Journal of Nonlinear Science, 32.8 (2022). [3] D. Faranda, G. Messori, P. Yiou, Dynamical proxies of North Atlantic predictability and extremes, Scientific reports 7(1) 41278 (2017). [4] V. Lucarini, D. Faranda, A. C. M. Freitas, J. M. Freitas, M. Holland, T. Kuna, M. Nicol, M. Todd, S. Vaienti, Extremes and recurrence in dynamical systems, John Wiley & Sons (2016).