Topological Methods for the Planet's dynamics – TeMPlex

"Templex" is an innovative concept emerging from a transversal development within an interdisciplinary team devoted to the study of climate and its impacts. Its principle is rooted in major contributions of Henri Poincaré, who first described the way in which a dynamical system’s properties depend upon its topology. Topological properties provide detailed information about the fundamental mechanisms that act to shape a system’s flow in state space. These mechanisms — stretching, squeezing, tearing, folding, twisting — constitute a bridge between dynamics and topology. Topological invariants hence allow us to determine whether two dynamics are equivalent, or whether a particular model is an adequate representation of the dynamics underlying an observational or numerically simulated time series. Consequently, an accurate topological characterization can be used to select the suitable reduced models that capture the right dynamics producing the data: this is particularly useful when there is no prior knowledge of the equations governing the observational dynamics. In Earth and environmental sciences, there is a great variety of models of different complexity and resolution. Although all are based on the equations that govern continuous media, they differ in several aspects: the modeling of clouds, ice or mixed-layer dynamics, among other processes. It is therefore important to establish to what extent a model correctly represents a given dynamics. This project proposes fingerprinting a model’s or system’s nonlinear behavior by the study of time evolving datasets, using the novel templex concept. The approach will be applied to atmosphere, ocean and hydrology datasets, provided by observations or by numerical simulations, under the guidance of a consortium of leading experts in each of these fields.