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Multi-scale harmonic model for solar and climate cyclical variation throughout the Holocene based on Jupiter-Saturn tidal frequencies plus the 11-year solar dynamo cycle

The sunspot record since 1749 is made of three major cycles (9.98, 10.9 and 11.86 yr). The side frequencies are related to the spring tidal period of Jupiter and Saturn (9.93 yr) and to the tidal sidereal period of Jupiter (11.86 yr). 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 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. The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium known as Oort, Wolf, Sporer, Maunder and Dalton minima, as well as 17 115-year long oscillations found in temperature reconstructions during the last 2000 years. The millennial three-frequency beat cycle hindcasts equivalent solar and climate cycles for 12,000 years. Prolonged solar minima in 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 is recovered: 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. 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 critique by Smythe and Eddy (1977) is rebutted.