# A New method for identifying possible causal relationships between CO2, total solar irradiance and global temperature change

## Abstract

We apply a novel method based upon “before” and “after” relationships to investigate and quantify interconnections between global temperature anomaly (GTA), as response variable, and greenhouse gases (CO2) and total solar irradiance (TSI) as candidate causal variables for the period 1880 to 2010. The most likely interpretations of our results for the 6 to 8 years cyclic components of the variables are that during the period 1929 to 1936, CO2 significantly leads GTA. However, during the period 1960–2003, GTA apparently leads CO2, that is, the peaks (and troughs) in GTA are in front of, and close to, the peaks (and troughs) in CO2. For time windows outside these periods, we did not find significant before or after-relations. An alternative interpretation is that there is a shift between short (≈1.5 year) and long (≈5 years) durations between cause and effect. Relationships between GTA and TSI suggest that “inertia” of the global sea, land, and atmosphere system leads to delays longer than half their common cycle length of about 10 years. Based on the interaction patterns between the variables GTA, CO2, and TSI, we suggest the possibility that a new regime for how the variables interact started around 1960. From trend forms, and not considering physical mechanisms, we found that the trend in CO2 contributes ≈ 90 %, and the trend in TSI ≈ 10 %, to the trend in GTA during the last 130 years.

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## Notes

1. 1.

It can be implemented in Excel format: with v1 = (A1,A2,A3) and v2 = (B1,B2,B3) in an Excel spread sheet, the angle is calculated by pasting the following Excel expression into C2: = SIGN((A2-A1)*(B3-B2)-(B2-B1)*(A3-A2))*ACOS(((A2-A1)*(A3-A2) + (B2-B1)*(B3-B2))/(SQRT((A2-A1)2 + (B2-B1)2)*SQRT((A3-A2)2 + (B3-B2)2))).

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## Acknowledgments

We would like to thank Robert McNown for pointing out important literature for this study and for help in developing the leading-lagging ideas for climate studies. We thank Hans Martin Seip for pointing out relevant literature and for giving us useful comments and advices and Jostein-Riiser Kristiansen for providing the reference to Kjeldseth-Moe and Wedenmeyer-Böhm (2009). We would also like to thank two anonymous referees for constructive criticism and helpful comments. All data are available from the sources cited in the materials section of the paper, but are also supplied in Excel format as supporting information.

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Correspondence to Knut L. Seip.

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Seip, K.L., Grøn, Ø. A New method for identifying possible causal relationships between CO2, total solar irradiance and global temperature change. Theor Appl Climatol 127, 923–938 (2017). https://doi.org/10.1007/s00704-015-1675-8

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