Chaotic climate response to long-term solar forcing variability

It is shown that global climate exhibits chaotic response to solar forcing variability in a vast range of time scales: from annual to multi-millennial. Unlike linear systems, where periodic forcing leads to periodic response, nonlinear chaotic response to periodic forcing can result in exponentially decaying broad-band power spectrum with decay rate Te equal to the period of the forcing. It is shown that power spectrum of a reconstructed time series of Northern Hemisphere temperature anomaly for the past 2000 years has an exponentially decaying broad-band part with Te $\simeq$ 11 y, i.e. the observed decay rate Te equals the mean period of the solar activity. It is also shown that, power spectrum of a reconstruction of atmospheric-CO2 time fluctuations for the past 650000 years, has an exponentially decaying broad-band part with Te $\simeq$ 41000 years, i.e. the observed decay rate Te equals the period of the obliquity periodic forcing. A possibility of a chaotic solar forcing of the climate has been also discussed. These results clarify the role of solar forcing variability in long-term global-climate dynamics (in particular in the unsolved problem of the glaciation cycles) and help in construction of adequate dynamic models of the global climate