Combining spectral analysis and narrow band pass filtering to predict solar cycle parameters in the next solar grand minimum

Technical Summary: Combining Spectral Analysis and Narrow Band Pass Filtering of Sunspot Number Records to Forecast the Next Solar Grand Minimum

Problem Statement
The forecasting of solar activity, specifically the Schwabe cycle (approx. 11-year sunspot cycle) and the occurrence of "grand minima" (extended periods of weak solar activity), remains a significant challenge in space science. Existing prediction methods, often relying on precursors from the most recent cycle, yield disparate results with high uncertainty, particularly for forecasts extending beyond a single cycle. While low-resolution forecasts exist for centuries ahead, high-resolution forecasting of cycle-to-cycle variations and the timing of grand minima is poorly understood, with some experts suggesting reliable prediction beyond one cycle is impossible. The paper addresses the need for a deterministic method to forecast future solar activity and explain the formation of grand minima and phenomena such as the Waldmeier Effect.

Methodology
The authors propose a new prediction method based on Fourier analysis (FFT) and very narrow band pass filtering. The methodology involves:

1. Data Sources: Analysis of two datasets: the SILSO annual sunspot number (SSN) record (1700.5–2024.5) and a reconstructed annual SSN record (971–1899).
2. Spectral Analysis: Identification of periodicities via FFT. The SILSO record reveals eleven near-decadal periodicities (8–15 years), while the reconstructed record reveals four centennial-scale periodicities (60–800 years).
3. Inverse Notch Filtering (INF): A novel application of narrow band pass filtering (using a Press notch filter) to isolate specific frequency components. For the SILSO record, a 2% bandwidth is used; for the reconstructed record, a 5% bandwidth is applied.
4. Sinusoidal Fitting and Projection: The isolated components are fitted with sinusoids based on amplitude and phase measured at Solar Cycle 24 (~2012). These sinusoids are then projected forward and backward in time. The method assumes that the identified periodicities are persistent and that future grand minima/maxima arise from the constructive and destructive interference of these sinusoidal components.
5. Planetary Modeling: To investigate the origin of these periodicities, the authors construct a model summing the orbital periods of the four outer planets (Jupiter, Saturn, Uranus, Neptune). This sum is rectified to simulate a non-linear response, and its spectrum is compared against the observed SSN periodicities.

Key Contributions and Results

• Spectral Decomposition of SSN: The study identifies that 80% of SSN variability is contributed by three groups of periodicities: an "octal" group (approx. 8–9 years), a "decadal" group (approx. 10–12 years), and a "decadal-plus" group (approx. 13–15 years). The decadal group generally has the highest amplitude, but the summed amplitude of the octal and decadal-plus groups occasionally exceeds it.
• Forecast of the Next Grand Minimum:
  • High-Resolution Forecast: Projecting the eleven near-decadal components forward from 2024 forecasts a solar grand minimum extending from approximately 2030 to 2150. The model predicts Solar Cycles 26 through 30 will be significantly weaker than recent cycles, with cycle lengths potentially shortening to ~8 years due to the dominance of octal components.
  • Low-Resolution Forecast: Projecting the four centennial components from the reconstructed record (971–1899) validates the method by correctly reproducing the Gleissberg Minimum and the Modern Grand Maximum. This projection also forecasts a broad minimum from ~2030 to ~2200, consistent with the high-resolution forecast.
  • Validation: Back-projection of the SILSO components successfully reproduces the timing and duration of historical grand minima (Dalton, Maunder, Sporer, Wolf, Oort), lending credibility to the forward forecast.
• Explanation of the Waldmeier Effect: The paper demonstrates that the Waldmeier Effect (the inverse correlation between solar cycle amplitude and rise time) can be explained by the interference between the summed octal and decadal components. When these components are in anti-phase, they produce long rise times and low amplitudes; when in phase, they produce short rise times and high amplitudes.
• Model of Grand Minima Formation: The authors introduce a "shah" model, illustrating that a series of equally spaced frequency components (approximating the observed decadal group) transforms into a time-domain signal characterized by alternating grand maxima and minima. The specific type of minimum (e.g., Dalton-like vs. Sporer-like) depends on the relative amplitudes and phases of the interfering components.
• Planetary Connection: The study establishes a close correspondence between the periodicities observed in the SILSO SSN record and those generated by a non-linear model of the orbital periods of the four outer planets. Specifically, the beat frequencies and harmonics of planetary orbits (e.g., Jupiter-Saturn-Uranus-Neptune interactions) generate periodicities in the 7–15 year range that align with the observed SSN peaks. The authors suggest that the solar dynamo may act as a damped oscillator triggered by impulsive planetary influences every ~179 years.

Significance and Claims
The paper claims to offer a deterministic framework for understanding solar variability, contrasting with views that grand minima are purely stochastic or chaotic events triggered by internal solar fluctuations. By demonstrating that interference between a small number of persistent spectral components can reproduce complex historical patterns (including the Waldmeier Effect and the timing of grand minima), the authors argue that solar activity is largely governed by these interference patterns.

The primary significance lies in the forecast of a prolonged grand minimum beginning around 2030, which has implications for space weather and radiation exposure. The authors assert that their method, validated by successful back-projections and alignment with planetary periodicities, provides a reliable basis for long-term solar forecasting, extending up to 100 years for cycle-to-cycle details and potentially 500 years for broad activity trends. The work suggests that the "trigger" for grand minima is not a random internal failure of the dynamo but a predictable result of the phasing of persistent spectral components, potentially driven by planetary orbital mechanics.