  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.
