Topological Methods for
the Planet’s Dynamics
TEMPLEX
Topological Methods for the
Planet’s Dynamics
TEMPLEX
This project attempts to ‘catch’ important changes in the evolving climate system or in any of its components in terms of a change in its topological structure. This is done on simplified, stochastically-forced low-order deterministic models that are aimed at mimicking the topological structure and changes therein found in climatic time-series (obtained from atmosphere, ocean or hydrology). To do this, a new concept -the templex-, recently developed by the team, will be employed. The templex dissects the phase-space structure into several identifiable components, connected at certain joints.
The project represents a truly multidisciplinary endeavour. It ranges from the further development of abstract conceptual theoretical models on the evolution of stochastically forced nonlinear dynamical systems (representing the influence of small-scale unresolved processes on the largerscale dynamics), to their application in large-scale atmosphere-ocean and hydrological models.
The proposed research is timely in view of the climate-change induced rapid changes taking place in the ocean, atmosphere and hydrological cycle. The intention to follow changes in any of the climate’s subsystems comprehensively is welcome as it may be helpful in the public debate on the required urgency of action or adaptation following certain future manifestations of climate change.
The methods proposed are suitable and feasible. They start with a new type of data (time series) analysis, followed by a topological characterisation in phase space, the subsequent detection of rapid changes of these characteristics, and the attempt to build a matching noise-driven, nonlinear low-order model capturing these features. The methods are relevant in that the software that will be developed can also be of use in other fields and thus have a great potential applicability.
ANR funded project:
«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.
- Topological properties provide detailed information about the fundamental mechanisms that act to shape a system’s flow in state space.
- Topological invariants help 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.
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.