This study proposes a novel data-driven approach to causality analysis for complex stochastic differential systems, integrating the concepts of Liang-Kleeman information flow and linear inverse modeling (LIM). The method models environmental noise as either memoryless Gaussian white noise or memory-retaining Ornstein-Uhlenbeck colored noise, and allows for self and mutual causality.
The authors apply this approach to re-examine the causal relationships between the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), two major climate phenomena. The key findings are:
Regardless of the type of noise used, the causality between ENSO and IOD is mutual but asymmetric, with the causality map reflecting an ENSO-like pattern consistent with previous studies.
In the case of colored noise, the noise memory map reveals a hotspot in the Niño 3 region, which is further related to the information flow. This suggests that the proposed approach offers a more comprehensive framework and provides deeper insights into the causal inference of global climate systems.
The LIM-based approaches explicitly quantify the contribution of dynamics, which cannot be directly inferred by using the previous method. The different models can offer valuable and distinct insights into the same problem.
The Colored-LIM-based results tend to reveal stronger information flow, especially over the Niño 3 region, due to the enhanced deterministic damping force and coupling caused by the longer noise memory.
Overall, the study demonstrates that the LIM-based causality analysis framework can accommodate both white and colored noise, and provides a more realistic and comprehensive tool for understanding causal relationships in complex dynamical systems.
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