Reconstruction of driving forces from nonstationary time series including stationary regions and application to climate change

A new method based on cross-prediction errors is proposed for the rebuilding of the driving forces exerting influence on nonstationary systems. This method can retrieve driving force from nonlinear nonstationary time series including stationary regions. The numerical tests show that the method is very accurate. Generally, the correlation coefficients between the original and reconstructed driving force are larger than 0.96 for three commonly used maps for single-species discrete chaotic ecosystems. By using the above method, we reconstructed the driving force for an observed time series of the northern hemisphere monthly mean surface air temperature anomalies. Wavelet transformation method is applied to analyze the calculated driving forces. The results illustrated that the driving forces are characterized by the Hale's solar cycle and the Atlantic Multi-decadal Oscillation, which are the two main separate degrees of freedom on the climate.