Climatologists have long built networks from time series to understand how distant regions influence each other. Alongside this work, the archive holds studies that search for connections in gene networks, predict droughts from weather data, and use artificial intelligence to analyze the cosmic web. All of them tackle a common problem: how to extract directed interactions from observations. This article belongs to that line of research but brings a tool from another field, neurophysiology, where the problem of noise and weak connections is especially acute.
The authors took two methods well established in brain signal analysis: renormalized partial directed coherence (rPDC) and directed partial correlation (DPC). Both rely on an autoregressive model that describes how the current value of a series depends on its past values and on the past values of another series. To account for the inevitable observation noise, the model is built in a state-space framework. For comparison, they also used the classical Granger causality estimator (GCE), which does not account for noise. The methods were first tested on synthetic data with known connection directions, then applied to real climate indices: NINO3.4 (sea surface temperature in the tropical Pacific) and All India Rainfall (precipitation over India), as well as data for the South Atlantic Convergence Zone.
On the synthetic example, rPDC and DPC clearly identified the direction of the connection, whereas GCE gave a spurious signal in the opposite direction due to noise. For the El Niño–monsoon pair, all three methods agreed: El Niño's influence on Indian rainfall is significantly stronger than the reverse. DPC additionally showed that the connection lags by one to two years. For the South Atlantic Convergence Zone, comparing DPC and GCE year by year revealed a high correlation (0.85) for the ocean-to-atmosphere direction, supporting the hypothesis that in some years the ocean indeed forces the atmosphere. In one year (1983), DPC detected a negative influence of the atmosphere on the ocean, something GCE cannot see in principle.
The work shows that methods designed for neural network analysis can be transferred to climate data without losing meaning. Unlike neighboring studies that either use simpler causality measures or focus on prediction, this is the first systematic application of an approach that accounts for observation noise and allows estimating the sign of the interaction. This gives climatologists a more refined tool for testing hypotheses about mechanisms, such as the sign of the feedback in the ocean–atmosphere system.
The rPDC and DPC methods could be applied to other pairs of climate indices, for example, connections between different ocean basins or between the atmosphere and sea ice. An important direction will be automatic selection of the autoregressive model order to eliminate subjectivity. Validation on surrogate data will also be needed to ensure that the detected connections are not artifacts.
The results will be useful for climatologists studying teleconnections and for specialists in time series analysis in geophysics. The methods may be adapted for other problems where the directionality of connections matters, such as in economics or ecology.
Conduct a detailed sensitivity analysis of the methods to the choice of model order and time series length. Verify the findings for the South Atlantic Convergence Zone on independent data and with surrogate tests.
An open question in climatology remains how to separate true causal connections from spurious correlations in short and noisy observational records. This work offers a path through accounting for noise in the model, but the problem of choosing the correct model dimension and nonlinear effects remains.
The NINO3.4 index used in the study is calculated from sea surface temperatures over an area roughly the size of Australia. The average temperature anomaly there changes by only a few tenths of a degree, yet that is enough to alter weather on the other side of the planet.