Obtaining reliable causal inference is crucial for understanding the climate system. Convergent Cross Mapping (CCM), a recently developed method to infer causal relationships from time series has been shown to be superior to previous methods which are based on linearity assumptions. However, CCM has so far been only tested on low-dimensional or bivariate models, while real-world systems, like the climate system, are high-dimensional and have many more interacting variables. Here, we demonstrate that standard CCM cannot reliably infer causal relations in high-dimensional chaotic systems. However, by using a hierarchy of conceptual models and observational data we show that time-lagged CCM reliably identifies causal relationships in contrast to standard CCM and Pearson correlation. Furthermore, we systematically demonstrate that time-lagged CCM is able to identify long-distance causal interactions. Moreover, we apply time-lagged CCM to detect causal relations in stratosphere-troposphere coupling, and demonstrate the downward causal chain induced by polar vortex activity.

获得可靠的因果推论对于理解气候系统至关重要。融合交叉映射（CCM）是一种最近开发的从时间序列推断因果关系的方法，它优于基于线性假设的先前方法。但是，到目前为止，CCM仅在低维或双变量模型上进行了测试，而现实世界的系统（如气候系统）是高维的，并且具有更多交互变量。在这里，我们证明了标准CCM不能可靠地推断高维混沌系统中的因果关系。但是，通过使用概念模型和观察数据的层次结构，我们证明了与标准CCM和Pearson相关性相比，时滞CCM能够可靠地识别因果关系。此外，我们系统地证明了时差CCM能够识别远距离因果关系。此外，我们应用时滞CCM来检测平流层-对流层耦合中的因果关系，并证明由极地涡旋活动引起的向下因果链。