Detecting changes in forced climate attractors with Wasserstein distance

Yoann Robin (1, 2) , Pascal Yiou (1, 2) , Philippe Naveau (1, 2)

1 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
2 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation

The climate system can been described by a dy-namical 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 Maha-lanobis 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 attrac-tor 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.

Domaines: Océan, Atmosphère; Interfaces continentales, environnement

Yoann Robin, Pascal Yiou, Philippe Naveau. Detecting changes in forced climate attractors with Wasserstein distance. Nonlinear Processes in Geophysics, 2017, 24 (3), pp.393 - 405. ⟨10.5194/npg-24-393-2017⟩. ⟨hal-01584241⟩