A Wavelet Analysis of Solar Climate Forcing: I) Solar Cycle Timescales
  We use the technique of wavelet analysis to quantitatively investigate the role of solar variability in forcing terrestrial climate change on solar cycle timescales (roughly 11 years). We examine the connection between mean annual solar irradiance, as reconstructed from sunspot and isotope records, and the climate, as proxied by two Northern Hemisphere surface air temperature reconstructions. By applying wavelet transforms to these signals, we are able to analyze both the frequency content of each signal, and also the time dependence of that content. After computing wavelet transforms of the data, we perform correlation analyses on the wavelet transforms of irradiance and temperature via two techniques: the Pearson's method and the conditional probability method. We thus track the correlation between individual frequency components of both signals as a function of time. A nonzero correlation between the irradiance and temperature wavelet spectra requires a phase lag between the two data sets (i.e., terrestrial response to solar output is not instantaneous). We search for the optimal phase lag that maximizes the correlation. By choosing an appropriate phase for each year, we find a significant, positive sun-climate correlation for most of the period AD 1720-1950. We find that this phase-optimized correlation varies in time, oscillating between 0.12 and 0.71 throughout the past 400 years. We find that the phase lag varies from 0-10 years. We also present a test to determine whether terrestrial response to solar output is enhanced via stochastic resonance, wherein the weak periodic solar signal is amplified by terrestrial noise. 
Matthew J. Lewis and Katherine Freese