The planet's climate is shaped by many remote interactions: fluctuations in one region echo in another through atmospheric and oceanic currents. Global climate models reproduce these connections, but their complexity makes it hard to extract the dominant physical mechanisms at individual timescales. Alongside this work in the archive lie studies that also seek simple dynamical descriptions of climate signals: some predict El Niño a year and a half ahead, others separate weather noise from climate signal. The present article takes the next step: it does not merely describe a single index but builds a bridge between two indices through coupling functions.
The authors take monthly Nino3.4 and IOD indices from 1870 to 2018. For each index separately, they compute the seasonal stability a(t) and noise intensity N(t) from the second statistical moments of the data. They then extend the model to two equations, adding coupling functions b12(t) and b21(t) that describe the influence of one phenomenon on the other. These functions are also computed from data: from the covariances between indices in each month. The procedure requires no manual parameter fitting; all coefficients are derived analytically from observed statistics.
For El Niño, the coupling function b12(t), showing the influence of the Indian Ocean Dipole, hovers around zero throughout the year and only becomes slightly negative in August. This means the Indian Ocean Dipole has almost no effect on El Niño's seasonal variability, except for a possible weak stabilization in late summer. In the opposite direction, the picture differs: the function b21(t), describing El Niño's influence on the dipole, has a large amplitude and peaks in August. The total stability a2(t) - b21(t) for the dipole is close to the stability computed from IOD data alone, suggesting that El Niño contributes most to stabilizing the dipole in the seasonal cycle. Model simulations reproduce the monthly standard deviations and the covariance between indices, with the covariance maximum occurring in October, when the dipole reaches its peak variability.
The work shows that coupling functions provide a more informative picture of climate subsystem interactions than simple covariance. Unlike neighboring studies that focus on predicting a single index or separating signal from noise, here the directed influences between two tropical phenomena on a seasonal scale are quantitatively separated for the first time. This supports the hypothesis of El Niño's dominant role in shaping the Indian Ocean Dipole and agrees with results from global models.
The method naturally generalizes to a larger number of variables, allowing the construction of interaction networks for many climate indices. Such a network could serve as a basis for seasonal forecasting of anomalies in different regions based on a unified stochastic dynamics.
The results are important for seasonal climate forecasting in the tropics, especially for regions dependent on monsoons and the El Niño and Indian Ocean Dipole phenomena.
The next step will be to include additional indices in the model, such as the Atlantic Meridional Mode or the Pacific Decadal Oscillation, and to test the predictive skill of the network on independent data.
An open question in climatology is how to extract causal relationships from correlations in short and noisy observational records. This approach offers a way to extract directed interactions from second moments, directly addressing the problem of identifying teleconnections and building empirical dynamical models.
The names El Niño and La Niña are linked to Christmas: the warm phase often peaks in December, and Peruvian fishermen named it after the Christ child.