Transactions of Atmospheric Sciences, Volume. 48, Issue 4, 626(2025)

Causal analysis of TWC information entropy using Liang-Kleeman information flow and wavelet coherence

WU Xianghua1,2,3, LI Yashao1, JIN Xinru1, REN Miaomiao1, and WANG Weiwei4
Author Affiliations
  • 1School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • 2Center for Applied Mathematics of Jiangsu Province, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • 3Jiangsu International Joint Laboratory on System Modeling and Data Analysis, Nanjing University of Information Science and Technology, Nanjing 210044, China
  • 4National Demonstration Center for Experimental Atmospheric Science and Environmental Meteorology Education, Nanjing University of Information Science and Technology, Nanjing 210044, China
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    Cloud microphysical processes are fundamentalto precipitation formation, involving complex interactions among cloud particles and their dynamic coupling with the surrounding atmosphere. Understanding the causal relationships underlying the information entropy of cloud microphysical quantities is crucial for elucidating the development of precipitating cloud systems and improving precipitation forecasting. This study investigates the multiscale causal relationships between the information entropy of total cloud water content (TWC) and that of relevant atmospheric variables, aiming to explore the self-organizational behavior and influencing mechanisms during cloud system evolution. A typical precipitating cloud event over northeastern China was selected for analysis. The degree of self-organization during the development of the cloud system was assessed through the information entropy of TWC, calculated based on the spatiotemporal distribution of cloud water content. This metric effectively captures the complexity and uncertainty of microphysical processes, where higher entropy values indicate greater disorder and lower values reflect more organized, potentially stable structures. To examine local coherence characteristics across different time scales, wavelet coherence analysis was employed to evaluate the nonlinear and timevarying relationships between TWC entropy and covariate entropies. Wavelet decomposition enabled the breakdown of information entropy time series into multiple scales, facilitating the identification of linear Granger causality relationships via a vector autoregression (VAR) model. The strength and direction of causal interactions were further quantified using the Liang-Kleeman information flow method.Results reveal that the TWC entropy increases initially and decreases as the cloud system matures, with a notable reduction during its mature stage, indicative of enhanced self-organization. On the 2-hour time scale, bidirectional Granger causality was observed between TWC entropy and all covariate entropies, suggesting mutual influence at this temporal resolution. At larger time scales (4 h and 8 h), the entropy of atmospheric precipitable water exerted the most substantial influence on TWC entropy, evidenced by the largest Liang-Kleeman information flow magnitude. Conversely, at shorter time scales (1 h and 2 h), the entropy of upward longwave radiation emerged as the dominnat driver. Radar reflectivity and vertical air velocity entropies also exhibited causal relationships with TWC entropy to varying degrees. In summary, atmospheric precipitable water and upward longwave radiation are key variables influencing changes in TWC information entropy across time scales. These findings offer new insights into the self-organization and evolution of precipitating cloud systems, emphasizing the necessity of multiscale and multi-variable approaches in studying cloud microphysics. Future work should focus on incorporating these casual insights into comprehensive cloud and precipitation models and exploring their applicability across different climatic regions.

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    WU Xianghua, LI Yashao, JIN Xinru, REN Miaomiao, WANG Weiwei. Causal analysis of TWC information entropy using Liang-Kleeman information flow and wavelet coherence[J]. Transactions of Atmospheric Sciences, 2025, 48(4): 626

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    Paper Information

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    Received: Feb. 4, 2024

    Accepted: Aug. 21, 2025

    Published Online: Aug. 21, 2025

    The Author Email:

    DOI:10.13878/j.cnki.dqkxxb.20240204002

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