Abstract
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.
Highlights
1 Introduction If the climate system is viewed as a complex dynamical system yielding a strange attractor, i.e., a highly complicated object around which all trajectories wind up (Lorenz, 1963), climate variability is linked to the statistical properties of such an attractor (Ghil and Childress, 1987)
A few properties of the climate attractor due to external forcings have been treated by Pierini et al (2016) and Drótos et al (2015), who focused on low-dimensional strange attractors and investigated qualitative changes of the attractors, all those studies are quantitative in many aspects
4 Time-varying dynamical system We focus on a time-varying dynamical system that mimics variability around a seasonal cycle, and a monotonic forcing that plays after a triggering time T
Summary
If the climate system is viewed as a complex dynamical system yielding a strange attractor, i.e., a highly complicated object around which all trajectories wind up (Lorenz, 1963), climate variability is linked to the statistical properties of such an attractor (Ghil and Childress, 1987). In addition to climate internal variability, external forcings (either natural or anthropogenic) perturb the climate system dynamics by introducing a time dependence of the attractor. This is the cause of non-stationary behavior of the climate system. Lucarini et al (2017) have recently used response theory (Ruelle, 2009) to quantify the modification of the dynamics submitted to a forcing
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