We investigate whether or not the decadal and multi-decadal climate oscillations have an astronomical origin. Several global surface temperature records since 1850 and records deduced from the orbits of the planets present very similar power spectra. Eleven frequencies with period between 5 and 100 years closely correspond in the two records. Among them, large climate oscillations with peak-to-trough amplitude of about 0.1 and 0.25°C, and periods of about 20 and 60 years, respectively, are synchronized to the orbital periods of Jupiter and Saturn. Schwabe and Hale solar cycles are also visible in the temperature records. A 9.1-year cycle is synchronized to the Moon's orbital cycles. A phenomenological model based on these astronomical cycles can be used to well reconstruct the temperature oscillations since 1850 and to make partial forecasts for the 21st century. It is found that at least 60% of the global warming observed since 1970 has been induced by the combined effect of the above natural climate oscillations. The partial forecast indicates that climate may stabilize or cool until 2030-2040. Possible physical mechanisms are qualitatively discussed with an emphasis on the phenomenon of collective synchronization of coupled oscillators

The Schwabe frequency band of the Zurich sunspot record since 1749 is found to be made of three major cycles with periods of about 9.98, 10.9 and 11.86 years. The side frequencies appear to be closely related to the spring tidal period of Jupiter and Saturn (range between 9.5-10.5 years, and median 9.93 years) and to the tidal sidereal period of Jupiter (about 11.86 years). The central cycle may be associated to a quasi 11-year solar dynamo cycle that appears to be approximately synchronized to the average of the two planetary frequencies. A simplified harmonic constituent model based on the above two planetary tidal frequencies and on the exact dates of Jupiter and Saturn planetary tidal phases, plus a theoretically deduced 10.87-year central cycle reveals complex quasi-periodic interference/beat patterns. The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years. We show that equivalent synchronized cycles are found in cosmogenic records used to reconstruct solar activity and in proxy climate records throughout the Holocene(last12,000years) up to now. The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium known as Oort, Wolf, Spörer, Maunder and Dalton minima, as well as the seventeen 115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years. The millennial three-frequency beat cycle hindcasts equivalent solar and climate cycles for 12,000 years. Finally, the harmonic model herein proposed reconstructs the prolonged solar minima that occurred during 1900-1920 and 1960-1980, the secular solar maxima around 1870-1890, 1940-1950 and 1995-2005, and a secular upward trending during the 20th century: this modulated trending agrees well with some solar proxy model, with the ACRIM TSI satellite composite and with the global surface temperature modulation since 1850. The model forecasts a new prolonged solar grand minimum during 2020-2045, which would be produced by the minima of both the 61 and 115-year reconstructed cycles. Finally, the model predicts that during low solar activity periods, the solar cycle length tends to be longer, as some researchers have claimed. These results clearly indicate that solar and climate oscillations are linked to planetary motion and, furthermore, their timing can be reasonably hindcast and forecast for decades, centuries and millennia. The demonstrated geometrical synchronicity between solar and climate data patterns with the proposed solar/planetary harmonic model rebuts a major critique (by Smythe and Eddy, 1977) of the theory of planetary tidal influence on the Sun. Other qualitative discussions are added about the plausibility of a planetary influence on solar activity.Keywords: Planetary theory of solar variation; Coupling between planetary tidal forcing and solar dynamo cycle; Reconstruction and forecast of solar and climate dynamics during the Holocene; Harmonic mo...

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called diffusion entropy analysis ͑DEA͒. We adopt artificial Gauss and Lévy time series, as prototypes of ordinary and anomalous statistics, respectively, and we analyze them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of Lévy statistics.

Power spectra of global surface temperature (GST) records (available since 1850) reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. Equivalent oscillations are found in numerous multisecular paleoclimatic records. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC Fifth Assessment Report (AR5, 2013), are analyzed and found not able to reconstruct this variability. In particular, from 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 o C/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. For example, a quasi 60-year natural oscillation simultaneously explains the 1850-1880, 1910-1940 and 1970-2000 warming periods, the 1880-1910 and 1940-1970 cooling periods and the post 2000 GST plateau. This hypothesis implies that about 50% of the ∼ 0.5 o C global surface warming observed from 1970 to 2000 was due to natural oscillations of the climate system, not to anthropogenic forcing as modeled by the CMIP3 and CMIP5 GCMs. Consequently, the climate sensitivity to CO 2 doubling should be reduced by half, for example from the 2.0-4.5 o C range (as claimed by the IPCC, 2007) to 1.0-2.3 o C with a likely median of ∼ 1.5 o C instead of ∼ 3.0 o C. Also modern paleoclimatic temperature reconstructions showing a larger preindustrial variability than the hockey-stick shaped temperature reconstructions developed in early 2000 imply a weaker anthropogenic effect and a stronger solar contribution to climatic changes. The observed natural oscillations could be driven by astronomical forcings. The ∼ 9.1 year oscillation appears to be a combination of long soli-lunar tidal oscillations, while quasi 10-11, 20 and 60 year oscillations are typically found among major solar and heliospheric oscillations driven mostly by Jupiter and Saturn movements. Solar models based on heliospheric oscillations also predict quasi secular (e.g. ∼ 115 years) and millennial (e.g. ∼ 983 years) solar oscillations, which hindcast observed climate oscillations during the Holocene. Herein I propose a semi-empirical climate model made of six specific astronomical oscillations as constructors of the natural climate variability spanning from the decadal to the millennial scales plus a 50% attenuated radiative warming component deduced from the GCM mean simulation as a measure of the anthropogenic plus volcano contribution to climatic changes. The semi-empirical model reconstructs the 1850-2013 GST patterns significantly better than any CMIP5 GCM simulation. Under the same CMIP5 anthropogenic emission scenarios, the model projects a possible 2000-2100 average warming ranging from about 0.3 o C to 1.8 o C. This range is significantly below the original CMIP5 GCM ensemble mean projections spanning from about 1 o C to 4 o C. Future research should investigate spaceclimate coupling mechanisms in order to develop more advanced analytic...