Introduction Climate scientists in general attribute global warming to the increase in CO2 in the atmosphere[IPCC]. Since the variation of the sun’s irradiance amounts to only about 0.1 percent[IPCC], this seems to be a reasonable conclusion.

However, Nicola Scafetta of Duke University, Bruce West of the Army Research Office and several colleagues have identified a stochastic resonance phenomenon between the sun and the earth that indicates a substantial part of global warming may be due to solar influence.

In part this result is not new. C. Nicolis studied the nearly periodic recurrence of ice ages using stochastic resonance theory [Anishschenko 2002,

Scholarpedia Stochastic Resonance article] and concluded there is substantial solar influence on climate over the approximately 100,000 year period of the ice ages [Nicolis 1981]. What is new is that Scafetta et. al. find evidence that the 11 year Schwabe (sunspot) cycle and other short term cycles in solar output influence earth’s climate. This review provides a roadmap of several of Scafetta et. al.’s papers that lead to their results.

Their result doesn’t contradict the overall conclusion that global warming has been occurring since the early part of the twentieth century. However, if correct, their result indicates that limiting CO2 emissions may not have the desired effect. Indeed, their results indicate that we may be on the verge of a global cooling cycle, in which case limiting CO2 emissions is exactly the wrong thing to do.

Outline of Scafetta et. al.’s approach Scafetta and colleagues demonstrate three points:

1. Solar flares can be characterized by a time series in which the probability density of the waiting time between solar flares is an inverse power law. The solar flare time series exhibits Levy scaling with an inverse power law scaling exponent between 2 and 3

2. Temperature changes in earth’s atmosphere exhibit a slight Levy component with inverse power law scaling exponent between 2 and 3

3. When two coupled processes, one, the source, delivering energy to the other, the sink, are characterized by Levy scaling with similar inverse power law exponents, the sink becomes synchronized to the source and energy transfer is maximized.

Frequency of solar flares Scafetta et. al. present the results of a statistical analysis of several records of sunspot activity dating back to 1600, [Scafetta 2007] postulating that periods of high sunspot activity correspond to periods of high solar irradiance. They verify this assumption with 20th century data records, which include both sunspot activity and solar irradiance.

They analyze the solar irradiance data using wavelets, [Grigolini 2002] Diffusion Entropy Analysis (DEA) and Standard Deviation Analysis (SDA) to show that the solar irradiance exhibits Levy statistics.

Frequency of atmospheric temperature fluctuations In [Scafetta 2004, Scafetta 2008] atmospheric temperature fluctuations are studied and a Levy component is identified. They show that the temperature time series is a nonpoisson renewal process with an inverse power law exponent close to that of the solar irradiance time series.

The Complexity Matching EffectIn [Allegrini] 2006] the Complexity Matching Effect (CME) is studied. Briefly the CME is a phenomenon in which two coupled systems whose time evolution is described by inverse power laws with similar exponents can become synchronized, achieving maximum energy transfer between the two. They demonstrate that when the inverse power law exponent of the perturbing system (the sun, which they denote by P) approaches the value of that of the driven system (the earth, designated by S), that energy transfer is maximized. I am less certain that they demonstrate that the earth’s temperature fluctuations can inherit the sun’s solar flare power law exponent. However, if the two power laws have similar exponents, energy transfer is maximized. They display a figure (their Figure 1, reproduced below)that looks very much like the resonance experienced when a second order system is driven near its resonant frequency.

FIG. 1: Inset: fitting of Eq. (9) (solid lines) to Monte Carlo

data (open circles) using TS = TP = 1, μS = 1.6 with μP =

1.35 (upper) and μP = 1.85 (lower). Dashed lines are the

asymptotic dominant term in Eq. (9). Our Monte Carlo used

107 system-perturbation pairs. Main figure: Amplitudes AP

(squares), AS (triangles), Eqs. (8) (solid line) and (7) (dashed

line) as a function of μP , with μS = 1.6.

ReferencesNote that the papers for which Scafetta is author/coauthor are available from Scafetta's web site:

Scafetta web site[Allegrini] 2006] Paolo Allegrini, Mauro Bologna, Paolo Grigolini, and Bruce J. West, Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect, Draft kindly furnished by Bruce J. West

[Anishschenko 2002] V. S. Anishschenko, V. V. Astakhov, A. B. Neiman, T. E. Vadivasova, and L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems, Berlin, Springer 2002

[Grigolini 2002] Paolo Grigolini, Deborah Leddon, and Nicola Scafetta, Diffusion entropy and waiting time statistics of hard-x-ray solar flares, PHYSICAL REVIEW E, VOLUME 65, 046203

[IPCC] Various Reports of the Intergovernmental Panel on Climate Change:

IPCC[Nicolis 1981] Solar Variability and Stochastic Effects on Climate, Solar Physics 74 (1981) pp 473-478

[Scafetta 2007] N. Scafetta1 and B. J. West, Phenomenological reconstructions of the solar signature in the Northern Hemisphere surface temperature records since 1600, Journal of Geophysical Research 112 (2007) D24S03

[Scafetta 2004] Nicola Scafetta, Paolo Grigolini, Timothy Imholt, J.A. Roberts and Bruce J. West, Solar turbulence in earth's global and regional temperature anomalies, Phys. Rev. E 69, 026303 (2004)

[Scafetta 2008] N. Scafetta, T. Imholt, P. Grigolini, J. Roberts, Statistical analysis of air and sea temperature anomalies, (Preprint retrieved from Scafetta’s archives)