Coupling functions in climate (1909.05096v2)

Abstract: We examine how coupling functions in the theory of dynamical systems provide a quantitative window into climate dynamics. Previously we have shown that a one-dimensional periodic non-autonomous stochastic dynamical system can simulate the monthly statistics of surface air temperature data. Here we expand this approach to two-dimensional dynamical systems to include interactions between two sub-systems of the climate. The relevant coupling functions are constructed from the covariance of the data from the two sub-systems. We demonstrate the method on two tropical climate indices; The El-Ni~{n}o--Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), to interpret the mutual interactions between these two air-sea interaction phenomena in the Pacific and Indian Oceans. The coupling function reveals that ENSO mainly controls the seasonal variability of the IOD during its mature phase. This demonstrates the plausibility of constructing a network model for the seasonal variability of climate systems based on such coupling functions.

• The paper introduces a two-dimensional stochastic model that uses coupling functions to capture interactions between ENSO and IOD.
• The authors derive the coupling functions from second-order statistical moments, providing a rigorous method for quantifying climate dynamics.
• Results reveal ENSO's stabilizing influence on IOD and illustrate the asymmetric interplay between these key climate phenomena.

Insights into Climate Dynamics through Coupling Functions

The paper "Coupling functions in climate" by Woosok Moon and John S. Wettlaufer explores the quantitative analysis of climate dynamics using coupling functions from the theory of dynamical systems. This work expands upon previous research that utilized a one-dimensional stochastic dynamical system to model surface air temperature data, broadening the application to two-dimensional systems. This approach enables the examination of interactions between different climate subsystems.

Key Contributions and Methodology

The authors present a method to construct coupling functions derived from the covariance of data between two climate subsystems, specifically focusing on the interactions between the El-Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). Their methodology extends the stochastic model to two dimensions, simulating and analyzing seasonal variability and interactions between these phenomena.

1. Two-Dimensional Stochastic Modeling: The paper introduces a two-dimensional periodic non-autonomous stochastic model using coupling functions to depict interactions between different climate variables, applied here to ENSO and IOD indices.
2. Analytical Derivation: The authors provide a rigorous methodology for determining the model coefficients from empirical data, relying on second-order statistical moments of observed variables. This involves equations and techniques that allow for the extraction of the system's intrinsic dynamics and the interaction terms that represent non-local effects.
3. Application to ENSO and IOD: By modeling ENSO and IOD interactions, the research highlights how ENSO predominantly controls the variability of the IOD during its mature phase. This model elucidates the asymmetric impact of these climate phenomena on each other, reflecting real-world observations.

Results and Analyses

The authors demonstrate that their model effectively reconstructs observed statistics of ENSO and IOD, including seasonal standard deviations and covariances. Key findings from the application of their model include:

• ENSO has a pronounced stabilizing influence on the IOD, significantly affecting its seasonal behavior, especially during the IOD's mature phase.
• The coupling functions indicate minimal influence of the IOD on ENSO during normal conditions, except during extreme IOD events.

Implications and Future Directions

This research provides a foundational step toward constructing a more comprehensive climate network model for predicting seasonal climate dynamics. By using coupling functions, the authors underscore the potential to better understand teleconnections within the climate system, laying groundwork for future studies that aim to incorporate multiple interacting subsystems.

The implications of this work suggest a new pathway for climate modeling, potentially enhancing predictability through the integration of stochastic dynamics and coupling functions. Future developments could extend this framework to more complex and high-dimensional systems, enabling insights into broader climate teleconnections and interactions on a global scale.

In conclusion, the paper demonstrates an innovative approach to climate modeling, elucidating the complex interplay between different climate phenomena and highlighting the utility of coupling functions in capturing these interactions. This stochastic model not only aligns with existing observational data but also sets the stage for further advancements in understanding and predicting climate dynamics.