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Register a new userGlobal temperatures and sunspot numbers. Are they related? Yes, but non linearly. A reply to Gil-Alana et al. (2014)
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Nicola Scafetta
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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.
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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.
We demonstrate that the concerns expressed by Garcia et al. are misplaced, due to (1) a misreading of our findings in [1]; (2) a widespread failure to examine and present words in support of asserted summary quantities based on word usage frequencies; and (3) a range of misconceptions about word usage frequency, word rank, and expert-constructed word lists. In particular, we show that the English component of our study compares well statistically with two related surveys, that no survey design influence is apparent, and that estimates of measurement error do not explain the positivity biases reported in our work and that of others. We further demonstrate that for the frequency dependence of positivity---of which we explored the nuances in great detail in [1]---Garcia et al. did not perform a reanalysis of our data---they instead carried out an analysis of a different, statistically improper data set and introduced a nonlinearity before performing linear regression.
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