{"title":"A Liang-Kleeman Causality Analysis based on Linear Inverse Modeling","authors":"Justin Lien","doi":"arxiv-2409.06797","DOIUrl":null,"url":null,"abstract":"Causality analysis is a powerful tool for determining cause-and-effect\nrelationships between variables in a system by quantifying the influence of one\nvariable on another. Despite significant advancements in the field, many\nexisting studies are constrained by their focus on unidirectional causality or\nGaussian external forcing, limiting their applicability to complex real-world\nproblems. This study proposes a novel data-driven approach to causality\nanalysis for complex stochastic differential systems, integrating the concepts\nof Liang-Kleeman information flow and linear inverse modeling. Our method\nmodels environmental noise as either memoryless Gaussian white noise or\nmemory-retaining Ornstein-Uhlenbeck colored noise, and allows for self and\nmutual causality, providing a more realistic representation and interpretation\nof the underlying system. Moreover, this LIM-based approach can identify the\nindividual contribution of dynamics and correlation to causality. We apply this\napproach to re-examine the causal relationships between the El\nNi\\~{n}o-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), two\nmajor climate phenomena that significantly influence global climate patterns.\nIn general, regardless of the type of noise used, the causality between ENSO\nand IOD is mutual but asymmetric, with the causality map reflecting an\nENSO-like pattern consistent with previous studies. Notably, in the case of\ncolored noise, the noise memory map reveals a hotspot in the Ni\\~no 3 region,\nwhich is further related to the information flow. This suggests that our\napproach offers a more comprehensive framework and provides deeper insights\ninto the causal inference of global climate systems.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"55 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06797","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Causality analysis is a powerful tool for determining cause-and-effect
relationships between variables in a system by quantifying the influence of one
variable on another. Despite significant advancements in the field, many
existing studies are constrained by their focus on unidirectional causality or
Gaussian external forcing, limiting their applicability to complex real-world
problems. 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. Our method
models environmental noise as either memoryless Gaussian white noise or
memory-retaining Ornstein-Uhlenbeck colored noise, and allows for self and
mutual causality, providing a more realistic representation and interpretation
of the underlying system. Moreover, this LIM-based approach can identify the
individual contribution of dynamics and correlation to causality. We apply this
approach to re-examine the causal relationships between the El
Ni\~{n}o-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), two
major climate phenomena that significantly influence global climate patterns.
In general, 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. Notably, in the case of
colored noise, the noise memory map reveals a hotspot in the Ni\~no 3 region,
which is further related to the information flow. This suggests that our
approach offers a more comprehensive framework and provides deeper insights
into the causal inference of global climate systems.