We use this technique to analyse the recently measured global mean surface air temperature anomalies (GMTA)36 and various reconstructed external forcings covering the period from 1850 to 2005 (156 years)37. To introduce the method we calculate the information flow (IF) in nat (natural unit of information) per unit time [nat/ut] from the 156 years annual time series of global CO 2 concentration to GMTA as 0.348 ± 0.112 nat/ut and −0.006 ± 0.003 nat/ut in the reverse direction. Obviously, the former is significantly different from zero, while the latter, in comparison to the former, is negligible. This result unambiguously shows a one-way causality in the sense that the recent CO 2 increase is causing the temperature increase, but not the other way around. The results prove to be robust against detrending the data (SI, Table SI2), selecting shorter time periods as e.g. using only the last 100 years, or against using decadal means only (results not shown). It is difficult to achieve a similarly clear result when using Granger causality, as in this case the reverse causality between GMTA and CO 2 forcing is also significant whereas with CCM only the direction from GMTA to CO 2 is found to be significant (SI, Tables SI-1 and SI-2).

The atmospheric CO 2 content serves only as proxy for its radiative forcing and therefore we now examine in more detail the causal relations between the major climate forcings and GMTA. The correlation and the IF between the major reconstructed radiative forcings37 (for the used identifiers in37 see SI, Table SI-3) and the GMTA time series are given in Table 1, correlations and causations significant at the 95% level and that are larger than 0.1 nat/ut are in bold. The calculated significant IF from the total radiative forcing to GMTA (Table 1) is basically in agreement with results presented by28 (their Table 2, Model I), finding a significant one-directional Granger causality between these two variables. The calculated Granger causalities between the different forcing components and GMTA are also largely in agreement with the IF results (SI, Table SI-2). However the non-quantitative nature of Granger causality makes it difficult to disregard the significant reverse causalities from GMTA to anthropogenic and greenhouse gas forcing, as could be done in case of the very small reverse information flows.

Table 1 Correlation and information flow between observed global surface temperature and different external forcing’s and internal climate variations. Full size table

Table 2 Correlation and information flow between global surface temperature and different CMIP5 forcing’s and internal climate variations. Full size table

The values in Table 1 clearly confirm that the total greenhouse gases (GHG), especially the CO 2 , are the main drivers of the changing global surface air temperature. The radiative forcing caused by aerosols and aerosol-cloud interactions is also important, but significantly smaller (0.2 vs. 0.3 nat/ut). Neither solar irradiance nor volcanic forcing contributes in a significant manner to the long-term GMTA evolution. This is true in spite of short episodes of volcanic forcing that are clearly visible in the time series as they are of insufficient strength to make significant long-term contributions to the GMTA dynamics. Selecting only short data records around a volcanic eruption will however result in a significant causality relation (SI, Table SI-4) for that specific period. For the known major natural modes, the information flows between the Pacific Decadal Oscillation (PDO) and Atlantic Multidecadal Oscillation (AMO) from and to the global surface temperatures are close to 0.0, so essentially no causality relations could be identified here, in contrast to the significant correlation between AMO and GMTA time series (Table 1). This is a good real world example that illustrates the basic fact: correlation does not mean causation. It further questions the assumed fundamental role of the AMO for the global climate as speculated in38.

We also try to determine when human activities started to significantly influence the GMTA. Time dependent change in IF from CO 2 radiative forcing to GMTA since 1880 is presented in Fig. 1. Significant values larger than 0.1 nat/ut are observed only beginning from about 1960. That this is not an effect of the increasing time series length has been tested see SI, Figs SI-1 and SI-2. In this case a qualitative similar result could have been obtained by using Granger causality (SI Fig. SI-3).

Figure 1 Global information flow from radiative CO 2 forcing to GMTA. Shown is the time dependence of the information flow between CO 2 forcing and GMTA when calculating segments with increasing lengths beginning from 1850 to the actual displayed year. Statistically significant values are indicated by the dark squares in the lower part of the figure and the dashed horizontal line at 0.1 [nat/ut] indicates the threshold for relevant flows. Full size image

The same approach can be applied to investigate the IF between the different forcing components and model derived global surface temperature. As the models are governed by well-known physical equations we might expect even higher causality measures in this case. Indeed the correlation coefficients between the different forcings and the historical CMIP5 overall ensemble temperatures are all higher compared to the one between forcings and observed GMTA (Table 2). The IF from the total forcing to the simulated GMTA is indeed slightly increased, confirming the important influence of the external forcing on the GMTA. As expected, ensemble averaging has the effect of enhancing the relative importance of the external forcing component compared to internal model variability. However the IF from single forcing components to the simulated GMTA is always significantly smaller and in the case of aerosol forcing and aerosol-cloud interactions even becomes insignificant (Table 2) compared to the IF to the observed GMTA. As this result is in disagreement to the analysis based on observed temperatures it might point to differences with relation to the model specific implementations of aerosol and aerosol-cloud interactions in the CMIP5 models9,39.

Further we apply this technique to analyse paleoclimatological air temperature (PAT)40 and CO 2 /CH 4 data from the EPICA Dome C ice cores41,42 from the last 800,000 years. Both time series are interpolated on the same time steps of 1000 years using the AICC201243,44 chronology. As already known the two data set are highly correlated with a correlation coefficient of 0.842 ± 0. By calculating the IF in nat per unit time from the 1000 year interpolated PAT time series to CO 2 concentration we get 0.123 ± 0.060 nat/ut and −0.054 ± 0.040 nat/ut in the reverse direction. Therefore we have on these long time scales a significant IF only from the temperature data to the CO 2 , but not in the other direction, exactly opposite to that seen in the data from the last 156 years. This result proves robust against using different ice age/gas age chronologies (SI, Tables SI-5 and SI-6 comparing EDC3 and AICC2012 chronology) and against using the recent corrected CO 2 data from Bereiter45 (SI, Table SI-7). The time step chosen for interpolation influences neither the strong correlation (always around 0.88 for the EDC3 chronology) nor the significant causation (SI, Table SI-8). This supports the hypothesis that on geological time scales air temperature changes are causing the subsequent changes in CO 2 concentration. This was already hypothesized by46, who claimed that CO 2 lagged Antarctic deglacial warming by 800 ± 200 years, during a specific deglaciation event (Termination III ~ 240,000 years ago). Recently Parrenin et al.47, did not find any significant asynchrony in the timing between atmospheric CO 2 and Antarctic temperature changes during the last deglaciation event (Termination TI). If we apply causality analysis only to data from event TI (22000–10000 years), we do get a bidirectional significant flow of 0.120 ± 0.074 nat/ut from PAT to CO 2 and 0.484 ± 0.168 nat/ut from CO 2 to PAT pointing to a synchronous behaviour or even a leading CO 2 signal (see Table SI-9). Using the old EDC3 chronology would have given a very different result, with CO 2 changes clearly causing PAT changes (Table SI-10). Because of the inherent nonlinear dynamics of the climate system, changes in correlation during single events could even be expected35. The causality analysis indicates that for the full 800,000 years time series PAT is indeed leading CO 2 because of the significant IF from PAT to CO 2 . This is in principal agreement with the conclusion from Nes et al.48 that has been derived using convergent cross mapping. However, when interpolating to time steps longer than 3000 years the IF decreases (Table SI-8). Because of this it is not possible to specify a time lag of maximal IF in contrast to the 6000 year time lag found by Nes et al.48. Data from another strong greenhouse gas, namely methane CH 4 , are also available from EPICA Dome C covering the same time period as the CO 2 data49. Again, as for CO 2 , we find a strong significant correlation between PAT and CH 4 of 0.777. The IF from PAT to CH 4 for the interpolated time series (1000 years time step) equals 0.393 ± 0.051 nat/ut and 0.007 ± 0.025 nat/ut in the reverse direction. Therefore the causal drive of temperature on the CH 4 dynamics is even stronger than for CO 2 . This supports the expectation that on paleoclimatological time scales changing temperature could be held responsible for following changes in greenhouse gas (CO 2 /CH 4 ) concentrations.

Another crucial research question that we can address with this new method is “where is the recently increasing anthropogenic forcing likely to cause the most pronounced consequences?”. In order to assess which regions of the earth are more ‘sensitive’ to anthropogenic forcings and where natural modes of variability contribute more to the temperature series, we applied the same type of causality analysis as used in29 to the globally-gridded GMTA product. Due to the historically sparse data availability we could use only data from 1950 onwards and excluded regions South and North of 70 degrees. Looking first at the natural climate modes we see that PDO mainly shows significant IF over the North Pacific (Fig. 2A) and AMO mainly over the North Atlantic (Fig. 2B). This kind of expected result provides an additional first order validation of the method when applied to climate data. When analysing the IF from the global anthropogenic forcing to the GMTA (Fig. 3), in the Northern Hemisphere, we identified several regions of significant high causality. For example, IF takes largest values in Europe, North America and China, densely populated and industrialized areas having shown strong recent warming2. On the other hand there are also regions with high causality like Siberia, the Sahel zone and Alaska that are not that much influenced by human activities. In the Southern Hemisphere, however, this IF distribution displays a most unexpected pattern, with high values in a large swath of the southern Atlantic, South Africa, parts of the Indian Ocean and Australia. This is true for both the total anthropogenic forcing (Fig. 3A) and the radiative forcing caused by CO 2 alone (Fig. 3B). Therefore, despite CO 2 being a globally well-mixed gas, the IF to surface temperature is regionally very different, showing sensitive areas. Indeed, most of these depicted sensitive regions have shown especially strong warming during the last 60 years see Fig. 4 of2. Analysis of the spatial distributions of the IFs between solar forcing and GMTA (Fig. 4A) and volcanic forcing and GMTA (Fig. 4B) shows that over the considered period these flows are basically insignificant, in agreement with the previous analysis with the global mean values.

Figure 2 Global information flow from internal climate variability to GMTA. Shown is the spatial distribution of the information flow between the Atlantic Multidecadal Oscillation (AMO) and the gridded global mean temperature anomalies (GMTA) (A) and the distribution of the information flow between the Pacific Decadal Oscillation (PDO) and the gridded global mean temperature anomalies (GMTA) (B). The maps were created by the authors using the m-map toolbox included in Matlab®. Full size image

Figure 3 Global information flow from anthropogenic forcing to GMTA. Shown is the spatial distribution of the information flow between the total anthropogenic forcing and the gridded global mean temperature anomalies (GMTA) (A) and the spatial distribution of the information flow between the radiative forcing caused by CO2 and the gridded global mean temperature anomalies (GMTA) (B). The maps were created by the authors using the m-map toolbox included in Matlab®. Full size image