Climate is like an orchestra without a conductor: each musician hears the others with a delay, and the score changes mid-concert. The ocean, atmosphere, ice, and land continuously exchange energy, and the slightest hiccup in one instrument can escalate into a shift of the entire melody. Traditional climate models based on physical equations are becoming more detailed, but their computational complexity grows, and our understanding of cause-and-effect relationships remains limited.

The authors of the review propose not to build yet another giant model, but to look at the data differently. Instead of trying to reproduce every cog in the system, they search for patterns in multi-decadal records: how precipitation, sea surface temperature, El Niño indices, and the North Atlantic Oscillation have changed. First, the autocorrelation function identifies significant periodicities, which are then modeled with Fourier series. The LASSO method selects the most important harmonics. The system's short-term memory is captured by a Granger causality model, which tests whether past values of one variable help predict the current value of another. Spatial correlation between stations is accounted for via a Gaussian process. This hybrid approach separates long-term trends, seasonal cycles, and fast interactions.

In the first study, on droughts in southwestern Australia, an analysis of 194 weather stations over 58 years revealed a precipitation periodicity of about 5.5 years. The correlation structure among the precipitation index, ocean temperature, the Indian Ocean Dipole, and El Niño changed over time: before 2008, the dipole directly influenced precipitation, but after 2009, this influence weakened and the dipole began to act indirectly through ocean temperature and El Niño. Models that included ocean temperature and spatial correction showed the lowest forecast error: 0.34 for the 12-month precipitation index.

In the second study, covering the North Atlantic from 1982 to 2019, a feedback loop was found among the North Atlantic Oscillation, sea surface temperature, and sea ice extent. Granger tests confirmed mutual causality among all pairs of variables. The negative skewness of the oscillation index distribution indicates the system is approaching critical instability, which could herald more frequent extreme cold spells in the region.

This work shows that statistical learning and time series analysis methods can complement physical climate models by uncovering hidden dependencies and precursors of abrupt changes. Unlike neighboring studies that often focus on forecasting a specific phenomenon, this one proposes a general methodological framework applicable to different climate subsystems. Detecting feedback loops and signs of instability is important for risk assessment: such systems can transition to new states faster than traditional models predict.

The orchestra without a conductor keeps playing, but now we can hear which instruments are out of tune and when the melody might change. The methodology can be extended to other regions and sets of variables, including data on greenhouse gases, vegetation, and anthropogenic factors. Combining statistical approaches with physical models holds promise for improving decadal forecasts. Machine learning methods could also be applied to automatically detect instabilities in real time.