A wavelet transform cross -spectral analysis of 11-year (Schwabe) solar climate forcing.

Abstract

Recent measurements of Earth's temperature have indicated a warming trend, and understanding the role of the sun in climate change is crucial to determining causes of global-warming. Using a continuous Morlet wavelet transform we investigate the presence and persistence of Schwabe (approximately 11-year) solar climate forcing. We compare mean annual solar irradiance, as reconstructed by sunspot, isotope and satellite records, and two Northern Hemisphere climate time series, one reconstructed by multiple surface temperature proxies and the other by tree-ring growth measurements. Upon application of significance testing to the wavelet power spectrum using a Markov (AR-1) background noise model we find a 95% statistically significant mean solar cycle length of 10.4+/-0.6 years. Both climate wavelet power spectra show virtually no evidence of the Schwabe cycle even at 70% significance levels. Calculation of the wavelet cross-spectra between solar and climate data yields 90% significance regions which are too small to verify the existence of any prominent periodicities. We perform a noise-reduction of the data using WaveLab freeware, which applies wavelet shrinkage denoising techniques, producing climate time series containing fewer noise-induced fluctuations while retaining their original variances. The new wavelet power spectra and cross-spectra reveal different features than the original ones. We observe 90% significant solar-climate connections at the Schwabe period over certain time intervals spanning the mid-1700s to the late 1900s. Corresponding values of wavelet squared coherency, which is analogous to correlation, and wavelet phase show complicated time-varying relationships between the sun and Earth's climate.