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

Ian Edmonds; Peter Killen

arxiv: 2510.14355 · v3 · submitted 2025-10-16 · 🌌 astro-ph.SR

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

Ian Edmonds , Peter Killen This is my paper

Pith reviewed 2026-05-18 06:42 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords solar cyclesgrand minimumsunspot numberspectral analysisMaunder minimumsolar predictionFourier components

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The pith

Spectral analysis of sunspot records projects a Maunder-like grand minimum from 2030 to 2110.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies Fourier analysis to the annual sunspot number record from 1700 to 2023 to detect four strong components near the 10-11 year solar cycle period and four weaker components near the 8-9 year period. Narrow band pass filtering isolates the time variation of each component so that sinusoids can be fitted at the record's end for forward projection. Back projection of the same components reproduces the long-term structure of the historical Maunder Minimum, lending support to the forward projection of another extended low-activity interval. If the projection holds, solar cycles 26 through 35 would show markedly reduced peak amplitudes, with the weakest cycle near 2070 and average activity roughly half that of cycles 24 and 25.

Core claim

The central claim is that four decadal and four octal sinusoidal components extracted from the 1700-2023 sunspot number series persist long enough to be projected forward, producing a Maunder-like grand minimum from 2030 to 2110 that includes solar cycles 26 to 35, with cycle amplitudes for 26 and 28 near 50 and cycle 30 the lowest around 2070.

What carries the argument

Narrow band pass filtering after Fourier analysis to isolate and sinusoidally fit the four decadal and four octal components for forward and backward projection.

If this is right

Cycles 26 and 28 are projected to reach maximum sunspot numbers of about 50.
Cycle 30 is expected to be the weakest, occurring near 2070.
The grand minimum spans solar cycles 26 to 35 from 2030 to 2110.
Octal components can at times exceed the contribution of decadal components.
Component interference produces short-term features such as the Waldmeier Effect.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Lower solar output over eight decades could alter the balance of factors in long-term climate records if solar irradiance variations are a significant driver.
Solar dynamo models would need to sustain stable multi-decadal periodicities rather than purely stochastic or chaotic behavior.
Independent checks could compare the projection against cosmogenic isotope records or other solar proxies over the same interval.

Load-bearing premise

The amplitudes and phases of the identified sinusoidal components will continue unchanged for the next century without alteration by the solar dynamo or stochastic processes.

What would settle it

Sunspot number measurements for cycle 26 beginning around 2030 that reach peak amplitudes well above 50 would falsify the projection.

Figures

Figures reproduced from arXiv: 2510.14355 by Ian Edmonds, Peter Killen.

**Figure 4.** Figure 4: The decadal group sinusoids to be projected backwards were fitted to the sum of the INF decadal components, (red, diamond symbol), at the solar cycle indicated by the dotted reference line, ~1717. The sum of the projected sinusoids, (* symbol), forms a 100 year long grand minimum extending from about 1580 to about 1680. The projected grand minimum overlaps the time span of the Maunder Grand Minimum as indi… view at source ↗

**Figure 6.** Figure 6: (A) The decadal component sum, (red line), and the octal component sum, (blue *), and the overall sum, (black diamonds). The octal contribution exceeds the decadal contribution during 1750 to 1800. The amplitude of the overall sum during this interval is more than double the decadal amplitude. The SSN cycle amplitude largely depends on whether the octal and decadal components are in phase or out of phase. … view at source ↗

read the original abstract

We introduce a new method for predicting sunspot number (SSN) that, based on successful back projections, can predict features of the SSN several solar cycles in advance. The method applies Fourier analysis to the annual SILSO SSN record, from 1700.5 to 2023.5, to identify in the spectrum, four strong components in the decadal, 10 to 11 year period, range and four weaker components in the octal, 8 to 9 year period, range. The time variation of each component is isolated by a new method of narrow band pass filtering. The components are fitted with sinusoids at the beginning/end of the SSN record for back/forward projection. Back projection successfully replicated the long term features of the Maunder Minimum. Forward projection predicts a Maunder-like grand minimum from 2030 to 2110, encompassing solar cycles 26 to 35. Details of short term features of SSN within the grand minimum are less certain. The octal contribution to SSN is shown to occasionally exceed the decadal contribution both in the projection and also within the observational record. Predicted SSN amplitudes for cycles 26 and 28 are about 50, about half the amplitude of cycles 24 and 25. The amplitude of cycle 27 is difficult to forecast as it may emerge as a double peak of cycle 26 rather than as two separate cycles 26 and 27. Amplitudes forecast for cycles 29 to 33 are, on average, about half the amplitude of cycles 26 and 27 with the lowest cycle of the grand minimum, cycle 30, occurring around 2070. Interference between the octal and decadal components evident in the SSN spectrum are shown to result in micro changes in SSN such as the Waldmeier Effect. Inter group results in the occurrence of grand solar minima and maxima. Intra component group interference results in long term variation grand maxima/minima patterns that may relate to the occurrence of long term climate variability.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a standard spectral fit to the SSN record that reproduces the Maunder Minimum on back-projection but simply extends the same sinusoids forward with no test of whether the modes stay stable.

read the letter

The main takeaway is that the authors decompose the 1700-2023 SSN series into four decadal and four octal sinusoidal components using Fourier analysis plus narrow bandpass filtering, then continue those fitted sinusoids to forecast a grand minimum from 2030 to 2110. The back-projection step recovers the broad shape of the Maunder Minimum, which is a basic consistency check on the fit. They also note that the octal terms can occasionally exceed the decadal ones and that interference between the two groups can generate short-term features such as the Waldmeier effect. Those observations line up with patterns already visible in the data and are presented clearly enough to be useful for anyone cataloging time-series behavior in the record. The filtering isolation itself is a modest technical step beyond plain Fourier decomposition, though it remains within the family of established spectral methods for solar cycles. The citation list covers the usual SSN sources and prior spectral studies without obvious omissions. The math is elementary sinusoid summation with no machine-checked proofs or external data validation. The central limitation is that the forward projection assumes the fitted amplitudes, phases, and frequencies remain fixed for the next century. Nothing in the paper supplies a physical reason why the underlying dynamo would preserve those exact modes, and past grand minima show that regime shifts do occur. There is also no sensitivity test on the parameter choices or propagated uncertainty on the predicted amplitudes and timings. Because the sinusoids were adjusted to the full historical interval, the back-test success is partly automatic, while the future segment has no independent anchor. This work is aimed at researchers who track long-term solar variability for space-weather or climate applications and who are open to purely empirical extrapolations. A reader seeking new constraints on dynamo physics will find little here. It could go to peer review if an editor wants an external check on whether the bandpass procedure is reproducible and adds anything measurable over standard Fourier fits, but the forecast itself rests on an untested stationarity assumption that would need substantial extra validation before it could be treated as reliable.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a spectral method that applies Fourier analysis to the annual SILSO sunspot-number record (1700.5–2023.5) to isolate four decadal (10–11 yr) and four octal (8–9 yr) components via narrow-band-pass filtering. Sinusoidal fits to the endpoint segments of these components are used for back-projection, which reproduces long-term features of the Maunder Minimum, and for forward projection that forecasts a Maunder-like grand minimum spanning 2030–2110 (cycles 26–35) with SSN amplitudes of order 50 for cycles 26 and 28 and a minimum near cycle 30 around 2070.

Significance. A data-driven technique capable of reproducing a known grand minimum and generating multi-cycle forecasts would be of interest to solar-cycle studies and space-weather applications. The work explicitly demonstrates that octal components can occasionally dominate the decadal contribution and links component interference to observed micro-features such as the Waldmeier effect, providing concrete observational anchors for the decomposition.

major comments (3)

[Forward projection description] The forward-projection procedure continues the identical eight sinusoids whose frequencies, amplitudes, and phases were determined by fitting to the filtered 1700–2023 record. Because the projection contains no additional dynamical constraint or stochastic term, the predicted grand-minimum amplitudes for cycles 26–35 are direct extrapolations of the fitted model and inherit the stationarity assumption without independent support.
[Back-projection results] The back-projection test replicates Maunder-Minimum features once the eight-component parameters have been adjusted to the entire historical interval. This success is expected by construction and therefore supplies no out-of-sample evidence that the same linear combination remains valid when integrated forward across a regime transition.
[Method and projection sections] No sensitivity analysis or uncertainty propagation is reported for small perturbations in the fitted frequencies and amplitudes of the decadal and octal sinusoids. Given that the 2030–2110 SSN forecast depends directly on these eight parameters remaining fixed, the absence of such quantification leaves the quantitative amplitude predictions (e.g., SSN ≈ 50 for cycle 26) without assessed error bars.

minor comments (2)

[Filtering procedure] The precise pass-band widths and roll-off characteristics of the narrow-band-pass filter should be stated explicitly (e.g., in a methods subsection or table) so that the isolation of the 10–11 yr and 8–9 yr groups can be reproduced.
[Results figures] Figure captions for the projected SSN time series should indicate whether the plotted curves represent a single realization or an envelope; inclusion of at least a simple sensitivity range would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us improve the clarity and robustness of our manuscript. We address each major comment in detail below, indicating where revisions have been made to the revised version.

read point-by-point responses

Referee: The forward-projection procedure continues the identical eight sinusoids whose frequencies, amplitudes, and phases were determined by fitting to the filtered 1700–2023 record. Because the projection contains no additional dynamical constraint or stochastic term, the predicted grand-minimum amplitudes for cycles 26–35 are direct extrapolations of the fitted model and inherit the stationarity assumption without independent support.

Authors: We agree that the forward projection is an extrapolation based on the fitted sinusoids without additional dynamical constraints or stochastic elements. This approach is central to our spectral method, which posits that the identified components continue to govern the SSN variability. The justification for this assumption comes from the method's ability to back-project and reproduce key features of the Maunder Minimum, suggesting that the components capture the underlying dynamics over extended periods. We have revised the manuscript to explicitly state this assumption and discuss its limitations in the context of regime transitions. revision: yes
Referee: The back-projection test replicates Maunder-Minimum features once the eight-component parameters have been adjusted to the entire historical interval. This success is expected by construction and therefore supplies no out-of-sample evidence that the same linear combination remains valid when integrated forward across a regime transition.

Authors: The referee is correct that the parameters are derived from the full historical record. However, the back-projection procedure fits sinusoids specifically to the endpoint segments of the components and projects backward, allowing the emergence of Maunder-like features through component interference without direct fitting to that period. While this does not constitute fully independent out-of-sample validation, it demonstrates the method's capacity to capture historical transitions. We have updated the text to clarify that the back-projection serves primarily as a test of the decomposition's consistency rather than definitive proof of forward validity. revision: partial
Referee: No sensitivity analysis or uncertainty propagation is reported for small perturbations in the fitted frequencies and amplitudes of the decadal and octal sinusoids. Given that the 2030–2110 SSN forecast depends directly on these eight parameters remaining fixed, the absence of such quantification leaves the quantitative amplitude predictions (e.g., SSN ≈ 50 for cycle 26) without assessed error bars.

Authors: We acknowledge the lack of sensitivity analysis in the original submission. To address this, we have performed additional analyses in the revised manuscript, including perturbing the frequencies and amplitudes within reasonable ranges based on the fitting uncertainties and propagating these to the projections. This results in estimated uncertainty ranges for the forecasted SSN amplitudes, which are now reported in the updated projection section. revision: yes

Circularity Check

1 steps flagged

Forward projection is direct extrapolation of sinusoids fitted to the 1700-2023 record

specific steps

fitted input called prediction [Abstract]
"The components are fitted with sinusoids at the beginning/end of the SSN record for back/forward projection. ... Forward projection predicts a Maunder-like grand minimum from 2030 to 2110, encompassing solar cycles 26 to 35. ... Predicted SSN amplitudes for cycles 26 and 28 are about 50"

The forward SSN time series is produced by continuing the same sinusoids whose amplitudes and phases were obtained by fitting to the narrow-band-filtered historical components; therefore the projected values are the direct extension of the input fit rather than an independent forecast.

full rationale

The paper extracts four decadal and four octal components via Fourier analysis and narrow-band filtering on the full 1700.5-2023.5 SILSO SSN series, fits sinusoids to those isolated components, and then extends the identical fitted sinusoids forward to generate the 2030-2110 grand-minimum forecast. This matches the 'fitted input called prediction' pattern: the claimed prediction is the mathematical continuation of the model whose parameters were determined from the target data itself. The back-projection test only confirms that the same linear combination can reconstruct a known historical interval when integrated backward; it supplies no independent dynamical justification for stationarity. The component-identification step retains independent empirical content, preventing a score of 8-10, but the central forward-projection claim reduces by construction to the fitted extrapolation.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central forecast rests on fitting eight sinusoidal components to the historical record and assuming those components persist unchanged; this introduces multiple free parameters and a domain assumption about the stationarity of the solar signal.

free parameters (3)

frequencies and amplitudes of the four decadal components
Extracted from the Fourier spectrum and fitted to match the SSN record for projection.
frequencies and amplitudes of the four octal components
Weaker components also fitted to the same record.
phase offsets for all eight sinusoids
Determined at the beginning and end of the record to enable back and forward extension.

axioms (1)

domain assumption The annual SSN time series is adequately described as a linear sum of a small number of stable sinusoidal components with fixed periods.
Invoked when the Fourier spectrum is decomposed and the components are isolated by narrow bandpass filtering.

pith-pipeline@v0.9.0 · 5906 in / 1512 out tokens · 38736 ms · 2026-05-18T06:42:26.481060+00:00 · methodology

discussion (0)

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?

unclear
Relation between the paper passage and the cited Recognition theorem.

four strong components in the decadal, 10 to 11 year period, range and four weaker components in the octal, 8 to 9 year period, range... narrow band pass filtering... sinusoids... forward projection predicts a Maunder-like grand minimum from 2030 to 2110

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 1 internal anchor

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A., Beer, J., Steinhilber, F., Tobia, S

Abreu, J. A., Beer, J., Steinhilber, F., Tobia, S. M. & Weiss, N. O. (2008) For how long will the current grand maximum of solar activity persist? https://doi.org/10.1029/2008GL035442 Abreu, J. A., Beer, J. Ferris-Mas, A., McCracken, K. G. and Steinhilber, F. (2012) Is there a planetary influence on solar activity? A&A, 548, A88 DOI: m10.1051/0004-6361/20...

work page doi:10.1029/2008gl035442 2008

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grand solar minimum

Ahluwalia, H. S. & Jackiewicz, J. (2012) Sunspot cycle 23 descent to an unusual minimum and forecasts for cycle 24 activity, Adv. Space Res., 50 (6), 662-668, https://doi.org/10.1016/j.asr.2011.04.023 Anet, J. G., et al. (2013), Impact of a potential 21st century “grand solar minimum” on surface temperatures and stratospheric ozone, Geophys. Res. Lett., 4...

work page doi:10.1016/j.asr.2011.04.023 2012

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Biswas, A., Karak, B.B., Usoskin, I

Journal of Geophysical Research:SpacePhysics, 125, e2019JA027508. Biswas, A., Karak, B.B., Usoskin, I. et al. (2023) Long-Term Modulation of Solar Cycles. Space Sci Rev 219, 19 https://doi.org/10.1007/s11214-023-00968-w Cao, J., Xu, T., Deng, L., , Zhou, X., Li, S., Liu, Y. , Wang, W. & Zhou, W. (2024) An improved prediction of solar cycles 25 and 26 usin...

work page doi:10.1007/s11214-023-00968-w 2023

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Prediction of future fifteen solar cycles

V.A.Dergachev, V. A. , S.S.Vasiliev, S. S. , O.M.Raspopov, O. M., & Jungner, H. (2010) Long-term changes of formation rate of cosmogenic isotope 10Be for last 10 thousand years and variations of virtual dipole moment of the Earth. https://geo.phys.spbu.ru/materials_of_a_conference_2010/STP2010/Dergachev_Vasilyev_et_a l_2010.pdf 44 Echer, E., N. R. Rigozo,...

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F., Karoff, C., Olsen, J., Turek-Chieze, S

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work page doi:10.1038/ncomms8535 2015

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Grand Solar Minimum

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work page doi:10.1029/2011jd017013 2012

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, keywords =

287-367. 10.1007/s00159-003-0019-3. Peristykh, A. N., & Damon, P. E. (2003). Persistence of the Gleissberg 88-year solar cycle over the last ∼12,000 years: Evidence from cosmogenic isotopes. Journal of Geophysical Research: Space Physics, 108(A1), SSH 1-1-SSH 1-15. https://doi.org/10.1029/2002JA009390 Pesnell, W. D. (2016), Predictions of Solar Cycle 24: ...

work page doi:10.1007/s00159-003-0019-3 2003

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https://doi.org/10.1029/2018SW002080 Petrovay, K. (2020). Solar cycle prediction. Living Rev Sol Phys 17, 2 https://doi.org/10.1007/s41116-020-0022-z Pipin, V. V., Kosovichev, A. G.: (2011), The asymmetry of sunspot cycles and Waldmeier Relations as a result of nonlinear surface-shear shaped dynamo, Astrophys. J. 741(1), Id 1, doi:10.1088/0004-637X/741/1/...

work page doi:10.1029/2018sw002080 2020

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https://doi.org/10.1130/G20553.1 Press, W

- Geology, 32, 7, 581-584. https://doi.org/10.1130/G20553.1 Press, W. H., Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. Cambridge University Press 978-0-521-88068-8 - Numerical Recipes: the Art of Scientific Computing, Third Edition. (2007) Rahmanifard, F., Jordan, A. P., de Wet, W. C., Schwadron, N. A., Wilson, J. K., Owens, M. J., et a...

work page doi:10.1130/g20553.1 2007

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(2012,b), Does the Sun work as a nuclear fusion amplifier of planetary tidal forcing? A proposal for a physical mechanism based on the mass-luminosity relation

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