Abstract

The identification of causal effects is a fundamental problem in climate change research. Here, a new perspective on climate change causality is presented using the central England temperature (CET) dataset, the longest instrumental temperature record, and a combination of slow feature analysis and wavelet analysis. The driving forces of climate change were investigated and the results showed two independent degrees of freedom —a 3.36-year cycle and a 22.6-year cycle, which seem to be connected to the El Niño–Southern Oscillation cycle and the Hale sunspot cycle, respectively. Moreover, these driving forces were modulated in amplitude by signals with millennial timescales.

Figure 1: The Driving force constructed using CET dataset and SFA with embedding dimension m = 13.

Causality analysis in climate change is an active and challenging research area that remains highly uncertain. The Intergovernmental Panel on Climate Change (IPCC)¹ advocates that human activity is the most important driving force of climate change, while some researchers have argued that natural forces might be the main cause. These different views are mainly due to a lack of methods to address the complexity of climate system and insufficiency in observational climate data.

Global circulation model (GCM) simulations are generally used to investigate the causality of climate change. However, due to the limited knowledge of the climate system, large uncertainties are still associated with GCMs; therefore, the improvement of current GCMs to meet the requirements for causality analysis is still an urgent issue. An alternative method to GCMs is to use long-term observational climate data to study the driving forces of climate change, a method that has recently benefited from the great progress made by physical and biological scientists in studying the driving forces in non-stationary time series. The main advantage of this approach is that observational data can be used to directly extract the driving forces of an unknown dynamical system. This can be achieved by two techniques. The first technique involves finding the driving forces by studying the connections among different physical factors. These types of relations cannot be established using general correlation analysis, but only in dynamical directional influences. Granger causality² is a pioneering approach for achieving this task. Mutual information and transfer entropy³ are used to identify cause-effect relationships between components which is equivalent to Granger causality in the linear case and some attempts have been made to extend Granger causality to the nonlinear case^4,5. Recently, Sugihara et al.⁶ presented another effective method known as convergent cross-mapping (CCM) to justify causality in some biological complex systems. Tsonis et al.⁷ used CCM to identify a causal relationship between cosmic rays and interannual variation in global temperature.

The second technique is to directly extract the driving force information behind the observational data. For example, cross-prediction error⁸ and slow feature analysis (SFA)⁹ have been successfully applied to extract slowly changing driving forces from non-stationary time series. To evaluate SFA, a modified logistic map has been used to test the ability of SFA to construct the driving forces from an observational time series, and the results showed that there is a good agreement between the constructed and the true driving forces with a correlation coefficient of 0.998¹⁰. This suggests that SFA is suitable for extracting the driving force from observational time series.

Using SFA and the wavelet transformation technique, Yang et al.¹¹(hereafter, Yang16) reconstructed and analyzed the driving forces for the monthly mean surface air temperature anomaly time series in the Northern Hemisphere, and found that the driving forces for this temperature climate system included two independent degrees of freedom that represented the effects of a 22-year solar cycle and the Atlantic Multidecadal Oscillation (AMO) on the climate system. Furthermore, they found that the driving forces are modulated in amplitude by signals with much longer time periods, this is, a long-term natural trend determined by the modulating amplitude signals.

The application of this method to climate change, which involves nonlinear and complex systems, is at a preliminary stage. The difficulties inherent in climate signal detection led us to further investigate the mechanism of the driving forces of the climate system. The present analysis for the temperature anomaly time series in the Northern Hemisphere needs to be verified and increased excavating and understanding of the causal effects directly from climatic observations is necessary with the longest instrumental record, the central England temperature (CET) dataset, which covers the Little Ice Age and some episodes of natural and anthropogenic warming of multidecadal duration.