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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 24, 393-405, 2017
https://doi.org/10.5194/npg-24-393-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
31 Jul 2017
Detecting changes in forced climate attractors with Wasserstein distance
Yoann Robin, Pascal Yiou, and Philippe Naveau Laboratoire des Sciences du Climat et de l'Environnement, UMR8212 CEA-CNRS-UVSQ, Institut Pierre-Simon Laplace & Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France
Abstract. The climate system can been described by a dynamical system and its associated attractor. The dynamics of this attractor depends on the external forcings that influence the climate. Such forcings can affect the mean values or variances, but regions of the attractor that are seldom visited can also be affected. It is an important challenge to measure how the climate attractor responds to different forcings. Currently, the Euclidean distance or similar measures like the Mahalanobis distance have been favored to measure discrepancies between two climatic situations. Those distances do not have a natural building mechanism to take into account the attractor dynamics. In this paper, we argue that a Wasserstein distance, stemming from optimal transport theory, offers an efficient and practical way to discriminate between dynamical systems. After treating a toy example, we explore how the Wasserstein distance can be applied and interpreted to detect non-autonomous dynamics from a Lorenz system driven by seasonal cycles and a warming trend.

Citation: Robin, Y., Yiou, P., and Naveau, P.: Detecting changes in forced climate attractors with Wasserstein distance, Nonlin. Processes Geophys., 24, 393-405, https://doi.org/10.5194/npg-24-393-2017, 2017.
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Short summary
If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called an attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well-known attractors, coherent with the size of data available.
If climate is viewed as a chaotic dynamical system, its trajectories yield on an object called...
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