Separating cause from effect in the climate system is as old as climatology itself. Classical correlations are symmetric: they do not tell whether CO₂ warms the atmosphere or a warm atmosphere makes the ocean release more CO₂. Model-based approaches depend on how accurately the model represents real processes. Surrounding this work are studies that search for directed links between climate variables: some use Granger causality, others build graphical models, and still others limit themselves to pairwise comparisons. This paper stands apart from most of its neighbors because it is the first to bring together greenhouse gases, aerosols, solar activity, and internal ocean variability in a single analysis. The closest archive neighbors concern weather, quantum effects, or entropy in other contexts, so there is little direct overlap.
The authors took nine monthly series from 1984 to 2005: global mean temperature anomaly (GMTA), CO₂, CH₄, N₂O concentrations, stratospheric aerosol optical depth, El Niño index, total solar irradiance (TSI), ultraviolet flux in the 120–400 nm range, and cosmic ray flux from the Oulu neutron monitor. The series were interpolated to 10 samples per month, 20 points were discarded from each edge, and a moving average with a 20-month window was subtracted to remove trends and retain high-frequency fluctuations. Then, for each proxy–temperature pair, they estimated entropy transfer at lags from 0 to 10 months. Statistical significance was tested with a surrogate test: 100 random shuffles at the 5% level. To compare contributions from different drivers, they used normalized entropy transfer and a directionality index as the difference between flows in both directions.
Entropy transfer from CO₂, CH₄, aerosols, and ultraviolet to temperature was significantly higher than the reverse flow. This means the data behave as drivers, with temperature as the response. For El Niño, the picture is mixed: up to a lag of 3 months, the ocean leads temperature; after that, temperature leads the ocean. The integrated directionality index over 0–3 months gave the following shares of total information transferred to temperature: CO₂ about 24%, aerosols about 23%, CH₄ about 19%, El Niño about 12%, ultraviolet about 9%, and cosmic rays, N₂O, and TSI together less than 10%. The sum does not equal 100% of the total temperature variance: these are relative contributions only among the drivers considered. At a lag of 10 months, the results are qualitatively the same.
This work differs from archive neighbors by applying entropy transfer to a broad set of climate proxies at once, including volcanic aerosols, which rarely appear in such analyses. Neighboring studies either restrict themselves to greenhouse gases and solar radiation or consider other physical systems. Here, for the first time, it is quantitatively shown that volcanic aerosols compete on equal footing with CO₂ and methane during the studied period. This does not negate anthropogenic warming but clarifies that natural variability made a comparable contribution to short-term temperature fluctuations. The method requires no model assumptions and can serve as an independent check for climate models.
Entropy transfer can be applied to longer series, including paleoclimate reconstructions, to test whether the roles of drivers changed across different epochs. It would be interesting to study how GMTA affects El Niño at longer lags, since the feedback mechanism remains unclear. Additional proxies could be added: cloud cover, geomagnetic field, anthropogenic aerosols. Advances in information-based causal analysis, for instance accounting for delays and nonlinearities, would refine contribution estimates.
The results are useful for climate modeling: they provide independent quantitative constraints on the relative strength of drivers. The method can be applied in other Earth sciences where cause and effect need to be distinguished from time series.
Test the robustness of the estimates on longer series and with other probability estimation methods. Investigate in detail the two-way relationship between GMTA and El Niño, accounting for nonlinear interactions.
An unresolved question in climatology is the exact share of natural versus anthropogenic variability in observed warming. This work directly addresses that problem by offering an information-based criterion for separating driver contributions. The mechanism of global temperature's feedback on El Niño remains open, as does the long-term role of volcanic aerosols.
Nitrous oxide (N₂O) has a strong radiative effect per molecule and stays in the atmosphere for about 120 years, yet its contribution turned out to be marginal due to low concentration. Volcanic aerosols from the 1982 El Chichón and 1991 Pinatubo eruptions produced an optical depth spike that the method confidently identified as a temperature driver.
In Kim Stanley Robinson's novel The Ministry for the Future, climatologists try to separate natural fluctuations from the anthropogenic signal to justify geoengineering measures. The entropy transfer method from this paper resembles their tool for identifying causal links in climate data.