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Register a new userDiscussion on the spectral coherence between planetary, solar and climate oscillations: a reply to some critiques
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Nicola Scafetta
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During the last few years a number of works have proposed that planetary harmonics regulate solar oscillations and the Earth climate. Herein I address some critiques. Detailed analysis of the data do support the planetary theory of solar and climate variation. 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 kyr ago, present four common spectral peaks at about 103, 115, 130 and 150 yrs (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 length (110 years) to guarantee a sufficient spectral resolution. However, the best coherence test can be currently made only by comparing directly the temperature and astronomical spectra as done in Scafetta (J. Atmos. Sol. Terr. Phys. 72(13), 951-970, 2010). The spectral coherence between planetary, solar and climatic oscillations is confirmed at the following periods: 5.2 yr, 5.93 yr, 6.62 yr, 7.42 yr, 9.1 yr (main lunar tidal cycle), 10.4 yr (related to the 9.93-10.87-11.86 yr solar cycle harmonics), 13.8-15.0 yr, 20 yr, 30 yr and 61 yr, 103 yr, 115 yr, 130 yr, 150 yr 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, 2014) who used inadequate physical and time frequency analysis of the data.
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Holm (ASR, 2018) claims that Scafetta (ASR 57, 2121-2135, 2016) is irreproducible because I would have left undocumented the values of two parameters (a reduced-rank index p and a regularization term) that he claimed to be requested in the Magnitude Squared Coherence Canonical Correlation Analysis (MSC-CCA). Yet, my analysis did not require such two parameters. In fact: 1) using the MSC-CCA reduced-rank option neither changes the result nor was needed since Scafetta (2016) statistically evaluated the significance of the coherence spectral peaks; 2) the analysis algorithm neither contains nor needed the regularization term. Herein, I show that Holm could not replicate Scafetta (2016) because he used different analysis algorithms. In fact, although Holm claimed to be using MSC-CCA, for his figures 2-4 he used a MatLab code labeled gcs_cca_1D.m (see paragraph 2 of his Section 3), which Holm also modified, that implements a different methodology known as the Generalized Coherence Spectrum using the Canonical Correlation Analysis (GCS-CCA). This code is herein demonstrated to be unreliable under specific statistical circumstances such as those required to replicate Scafetta (2016). On the contrary, the MSC-CCA method is stable and reliable. Moreover, Holm could not replicate my result also in his figure 5 because there he used the basic Welch MSC algorithm by erroneously equating it to MSC-CCA. Herein I clarify step-by-step how to proceed with the correct analysis, and I fully confirm the 95% significance of my results. I add data and codes to easily replicate my results.
An oscillation with a period of about 2100-2500 years, the Hallstatt cycle, is found in cosmogenic radioisotopes (C-14 and Be-10) and in paleoclimate records throughout the Holocene. Herein we demonstrate the astronomical origin of this cycle. Namely, this oscillation is coherent to the major stable resonance involving the four Jovian planets - Jupiter, Saturn, Uranus and Neptune - whose period is p=2318 yr. The Hallstatt cycle could derive from the rhythmic variation of the circularity of the solar system disk assuming that this dynamics could eventually modulate the solar wind and, consequently, the incoming cosmic ray flux and/or the interplanetary/cosmic dust concentration around the Earth-Moon system. The orbit of the planetary mass center (PMC) relative to the Sun is used as a proxy. We analyzed how the instantaneous eccentricity vector of this virtual orbit varies from 13,000 B. C. to 17,000 A. D.. We found that it undergoes kind of pulsations as it clearly presents rhythmic contraction and expansion patterns with a 2318 yr period together with a number of already known faster oscillations associated to the planetary orbital stable resonances. We found that a fast expansion of the Sun-PMC orbit followed by a slow contraction appears to prevent cosmic rays to enter within the system inner region while a slow expansion followed by a fast contraction favors it. Similarly, the same dynamics could modulate the amount of interplanetary/cosmic dust falling on Earth. These would then cause both the radionucleotide production and climate change by means of a cloud/albedo modulation. Other stable orbital resonance frequencies (e.g. at periods of 20 yr, 45 yr, 60 yr, 85 yr, 159-171-185 yr, etc.) are found in radionucleotide, solar, aurora and climate records, as determined in the scientific literature. Thus, the result supports a planetary theory of solar and/or climate variation.
Power spectra of global surface temperature (GST) records reveal major periodicities at about 9.1, 10-11, 19-22 and 59-62 years. The Coupled Model Intercomparison Project 5 (CMIP5) general circulation models (GCMs), to be used in the IPCC (2013), are analyzed and found not able to reconstruct this variability. From 2000 to 2013.5 a GST plateau is observed while the GCMs predicted a warming rate of about 2 K/century. In contrast, the hypothesis that the climate is regulated by specific natural oscillations more accurately fits the GST records at multiple time scales. The climate sensitivity to CO2 doubling should be reduced by half, e.g. from the IPCC-2007 2.0-4.5 K range to 1.0-2.3 K with 1.5 C median. Also modern paleoclimatic temperature reconstructions yield the same conclusion. The observed natural oscillations could be driven by astronomical forcings. 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 and volcano contributions to climatic changes. The semi empirical model reconstructs the 1850-2013 GST patterns significantly better than any CMIP5 GCM simulation. The model projects a possible 2000-2100 average warming ranging from about 0.3 C to 1.8 C that is significantly below the original CMIP5 GCM ensemble mean range (1 K to 4 K).
Gil-Alana et al. (Physica A: 396, 42-50, 2014) compared the sunspot number record and the temperature record and found that they differ: the sunspot number record is characterized by a dominant 11-year cycle while the temperature record appears to be characterized by a singularity or pole in the spectral density function at the zero frequency. Consequently, they claimed that the two records are characterized by substantially different statistical fractional models and rejected the hypothesis that sun influences significantly global temperatures. I show that: (1) the singularity or pole in the spectral density function of the global surface temperature at the zero frequency does not exist - it is a typical misinterpretation that discrete power spectra of non-stationary signals can suggest; (2) appropriate continuous periodograms clarify the issue and also show a signature of the 11-year solar cycle (amplitude <0.1 K), which since 1850 has an average period of about 10.4 year, and of many other natural oscillations; (3) the solar signature in the surface temperature record can be recognized only using specific techniques of analysis that take into account non-linearity and filtering of the multiple climate change contributions; (4) the post 1880-year temperature warming trend cannot be compared or studied against the sunspot record and its 11-year cycle, but requires solar proxy models showing short and long scale oscillations plus the contribution of anthropogenic forcings, as done in the literature. Multiple evidences suggest that global temperatures and sunspot numbers are quite related to each other at multiple time scales through complex and non-linear processes. Finally, I show that the prediction of a semi-empirical model for the global temperature based on astronomical oscillations and anthropogenic forcing proposed by Scafetta since 2009 has up to date been successful.
Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha-effect. Finally, in the framework of a reduced, zero-dimensional alpha--Omega dynamo model we recover a 22.14-year cycle of the solar dynamo.
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