| Summary: | We use the benefits of the full-resolution methodology for time-series decomposition singular spectrum analysis to assess the quantitative impact of orbital and, for the first time, millennial-scale Sun-related climate responses from EPICA records. The quantitative impact of the three Sun-related cycles (unnamed ~9.7-kyr; proposed ‘Heinrich-Bond’ ~6.0-kyr; Hallstatt ~2.5-kyr), cumulatively explain ~4.0% (δD), 2.9% (CO2), and 6.6% (CH4) in variance, demonstrating for the first time the minor role of solar activity in the regional budget of Earth's climate forcing. A cycle of ~3.6 kyr, which is little known in literature, results in a mean variance of 0.6% only, does not seem to be Sun-related, although a gravitational origin cannot be ruled out. According to the recurrence analysis of Heinrich events (6.03 ± 1.4 kyr) and their correlation with EPICA stack ~6.0-kyr cycle, it is proposed that this band of solar activity be named the ‘Heinrich-Bond cycle’. On these basis, it is deemed that the ‘Heinrich-Bond’ solar cycle may act on the ice-sheet as an external instability factor both related to excess ice leading to calving process and IRD-layers (‘cold-related’ Heinrich events), and surface heating with meltwater streams (‘warm-related’ Heinrich events). The Hallstatt cycle is found in a number of solar proxies, geomagnetic secular variations, paleoclimatic oscillations, combination tones of Milankovitch forcings and resonant planetary beats, indicating an apparent ‘multi-forcing’ origin possibly related to planetary beat hypothesis. The orbital components consistently reflects the post-Mid-Pleistocene transition nature of the EPICA records in which the short eccentricity results in most of the variance (51.6%), followed by obliquity (19.0%) and precession (8.4%). Beyond the Milankovitch theory, evidence is emerging of a multiple-forcing cosmoclimatic system with stochastic interactions between external (gravitational resonances, orbitals, solar activity) and Earth's internal (geodynamics, atmosphere composition, feedback mechanisms) climate components, each having a strong difference in terms of the relative quantitative impact on Earth's climate.
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