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Detecting changes in forced climate attractors with Wasserstein distance

机译：利用Wasserstein距离检测强迫气候吸引子的变化

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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.
机译：气候系统可以用动力系统及其相关的吸引子来描述。这种吸引子的动力取决于影响气候的外部强迫。这种强迫可能会影响平均值或方差，但很少会吸引子的区域也会受到影响。衡量气候吸引器如何应对不同的强迫是一项重要的挑战。目前，欧氏距离或类似的测量方法如马哈拉诺比斯（Mahalanobis）距离已被偏爱用于测量两种气候情况之间的差异。这些距离没有自然的构建机制来考虑吸引子动力学。在本文中，我们认为源于最优输运理论的Wasserstein距离提供了一种区分动力系统的有效且实用的方法。处理玩具示例后，我们探索如何应用Wasserstein距离并进行解释，以检测受季节周期和变暖趋势驱动的Lorenz系统的非自主动力。

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