During the last few years a number of works have proposed that planetary harmonics regulate solar oscillations. Also the Earth's climate seems to present a signature of multiple astronomical harmonics. Herein I address some critiques claiming that planetary harmonics would not appear in the data. I will show that careful and improved analysis of the available data do support the planetary theory of solar and climate variation also in the critiqued cases. In particular, I show that: (1) high-resolution cosmogenic 10Be and 14C solar activity proxy records both during the Holocene and during the Marine Interglacial Stage 9.3 (MIS 9.3), 325-336 kyear ago, present four common spectral peaks (confidence level 95 %) at about 103, 115, 130 and 150 years (this is the frequency band that generates Maunder and Dalton like grand solar minima) that can be deduced from a simple solar model based on a generic non-linear coupling between planetary and solar harmonics; (2) time-frequency analysis and advanced minimum variance distortion-less response (MVDR) magnitude squared coherence analysis confirm the existence of persistent astronomical harmonics in the climate records at the decadal and multidecadal scales when used with an appropriate window lenght (L=110 years) to guarantee a sufficient spectral resolution to solve at least the major astronomical harmonics. The optimum theoretical window length deducible from astronomical considerations alone is, however, L=178.4 years because the planetary frequencies are harmonics of such a period. However, this length is larger than the available 164-year temperature signal. Thus, the best coherence test can be currently made only using a single window as long as the temperature instrumental record and comparing directly the temperature and astronomical spectra as done in Scafetta (J. Atmos. Sol. Terr. Phys. 72(13):951-970, 2010) and reconfirmed here. The existence of a spectral coherence between planetary, solar and climatic oscillations is confirmed at the following periods: 5.2 year, 5.93 year, 6.62 year, 7.42 year, 9.1 year (main lunar tidal cycle), 10.4 year (related to the 9.93-10.87-11.86 year solar cycle harmonics), 13.8-15.0 year, 20 year, 30 year and 61 year, 103 year, 115 year, 130 year, 150 year and about 1000 year. This work responds to the critiques of Cauquoin et al. (Astron. Astrophys. 561:A132, 2014), who ignored alternative planetary theories of solar variations, and of Holm (J. Atmos. Sol. Terr. Phys. 110-111:23-27, 2014a), who used inadequate physical and time frequency analyses of the data.
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