Enhanced Wavelet Analysis of Solar Magnetic Activity with Comparison to Global Temperature and the Central England Temperature Record

The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot number is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.

💡 Research Summary

The paper presents an enhanced methodology for continuous wavelet transform (CWT) analysis by deconvolving the wavelet response function, thereby improving spectral resolution and reducing artifacts associated with the cone of influence (COI). The authors first preprocess the yearly sunspot number series by derectifying it—taking the absolute value of the signal—to obtain a purely positive representation of solar magnetic activity that preserves the polarity‑independent Hale cycle (≈22 years). They then compute the CWT using a Morlet‑type mother wavelet and apply a deconvolution step that mathematically inverts the wavelet’s transfer function. This restores the true amplitude of each frequency component and yields a corrected power spectral density (PSD) after COI masking.

The corrected PSD reveals a clear hierarchy of odd‑harmonic peaks: the fundamental 22‑year Hale cycle, followed by its 3rd (≈66 yr), 5th (≈110 yr), and 7th (≈154 yr) harmonics. Even‑order harmonics are essentially absent, a result the authors attribute to the symmetry of the derectified signal and the underlying solar dynamo physics. The presence of these odd harmonics suggests that solar magnetic variability is not a simple sinusoid but a nonlinear, multi‑frequency process that can be captured only with high‑resolution spectral tools.

To explore possible climatic implications, the authors compare the instantaneous wavelet power of the solar series with a reconstruction of global mean surface temperature (GMST) covering roughly 1850–2000. Both series are normalized to unit variance, and a scatter plot of solar power versus GMST is produced for each year. After the turn of the twentieth century, the points display a modest positive trend; linear regression yields a slope of about 0.02 and a Pearson correlation coefficient of ~0.42. While statistically significant, this correlation is far from deterministic, indicating that solar magnetic activity may contribute to, but does not dominate, the observed warming trend.

For a regional perspective, the study repeats the analysis on the Central England Temperature (CET) record, the longest continuous instrumental temperature series (1659‑present). The CET wavelet spectrum also shows the 22‑year peak and a weaker 66‑year component, but higher harmonics are largely missing. The solar‑CET scatter plot again hints at a post‑1900 positive association, yet with a lower correlation (r≈0.28) and greater scatter, reflecting the stronger influence of local atmospheric dynamics and internal variability.

The authors conclude that (1) wavelet deconvolution is a powerful technique for uncovering subtle periodicities in solar magnetic proxies; (2) there exists a measurable, though modest, positive relationship between solar magnetic power and global temperature after 1900; and (3) regional temperature records may share some solar‑related frequencies but also contain distinct signals. They recommend future work that integrates additional external forcings (solar irradiance, galactic cosmic rays, volcanic aerosols), employs multi‑variable statistical models, and tests the wavelet‑derived solar forcing in climate‑model simulations to assess its impact on long‑term climate variability. This integrated approach could clarify the role of solar magnetic activity within the broader climate system and improve the reliability of decadal to centennial climate projections.