The proposed Linear Inverse Modeling (LIM)-based causality analysis framework can be extended to study the seasonal dependency of information flows between the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) by incorporating a cyclo-stationary approach. This involves utilizing the Cyclo-Stationary Linear Inverse Model (CS-LIM), which is designed to handle periodic systems by approximating the underlying dynamics over specific intervals. By segmenting the time series data into seasonal windows, the CS-LIM can capture the seasonal variations in the dynamics and noise characteristics of the climate system.
To implement this, one could analyze the seasonal data for ENSO and IOD, applying the CS-LIM to estimate the linear dynamics and noise correlation time for each season. This would allow for the identification of how the information flows between these two climate phenomena change throughout the year. Additionally, the seasonal dependency can be quantified by comparing the estimated information flows across different seasons, revealing patterns that may be critical for understanding the interactions between ENSO and IOD during specific climatic conditions.
Furthermore, the integration of seasonal data into the LIM framework would enhance the model's ability to account for the influence of seasonal climate drivers, such as monsoons or trade winds, on the causal relationships. This comprehensive approach would provide deeper insights into the temporal dynamics of the climate system, ultimately improving the understanding of how seasonal variations affect the coupling between ENSO and IOD.