Multidecadal Cycles of the Climatic Index: Sunspots that Affect North and Northeast of Brazil

Andr\'e Muniz Marinho da Rocha; Cleber Souza Corr\^ea; Karlmer Abel Bueno Corr\^ea; Roberto Lage Guedes

arxiv: 2604.03357 · v1 · submitted 2026-04-03 · ⚛️ physics.ao-ph · stat.AP

Multidecadal Cycles of the Climatic Index: Sunspots that Affect North and Northeast of Brazil

Cleber Souza Corr\^ea , Roberto Lage Guedes , Andr\'e Muniz Marinho da Rocha , Karlmer Abel Bueno Corr\^ea This is my paper

Pith reviewed 2026-05-13 18:42 UTC · model grok-4.3

classification ⚛️ physics.ao-ph stat.AP

keywords Atlantic Meridional Modesunspotswavelet analysistemperature anomaliesBrazilsolar cyclesmultidecadal variability

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The pith

Sunspot activity shows significant associations with multidecadal cycles in the Atlantic Meridional Mode and negative correlations with minimum temperatures in northern Brazil.

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

The paper analyzes 1951 to 2017 records to identify links between sunspots and the Atlantic Meridional Mode index using wavelet methods. It finds shared cycles at 11 years, 2.66 years, and 5.33 years, plus a weak 21.33-year signal in sea surface temperatures. Non-parametric tests reveal negative correlations between sunspot numbers and minimum temperature anomalies across most of five studied Brazilian locations, implying solar variability leaves a detectable imprint on regional climate.

Core claim

Wavelet and cross-wavelet analysis of the AMM index and sunspot series reveals pronounced multidecadal cycles of eleven years together with cycles of 2.66 and 5.33 years. The SST component of the AMM carries a weak 21.33-year signal. Correlation tests on temperature anomalies from Belém, São Luiz, Fortaleza, Fernando de Noronha, and Natal indicate that minimum monthly temperatures (except São Luiz) vary negatively with sunspot activity, supporting an apparent memory in climatic indices tied to solar variability.

What carries the argument

Wavelet and cross-wavelet transforms applied to the AMM index and monthly sunspot numbers, supplemented by non-parametric statistical correlation tests on surface temperature anomalies.

If this is right

Multidecadal solar cycles appear to modulate the Atlantic Meridional Mode affecting northern Brazilian climate.
Minimum temperature anomalies exhibit consistent negative correlation with sunspot numbers at four of five sites.
The climatic indices display an apparent degree of memory linked to sunspot variability.
Shorter cycles of 2.66 and 5.33 years are also shared between sunspots and the AMM index.

Where Pith is reading between the lines

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

If the associations hold, solar cycle data could be incorporated into regional climate models for improved long-range predictions.
Similar analyses on other tropical Atlantic datasets might reveal whether the 11-year cycle is geographically widespread.
Physical mechanisms such as changes in solar irradiance or atmospheric ionization could be tested against these periodicities.

Load-bearing premise

The shared cycles and correlations are presumed to reflect a real physical influence from solar activity rather than random alignments or unaccounted factors in the data records.

What would settle it

Applying the same wavelet analysis to an independent, longer dataset of AMM index or Brazilian temperatures and finding no matching 11-year cycle with sunspots would disprove the reported association.

Figures

Figures reproduced from arXiv: 2604.03357 by Andr\'e Muniz Marinho da Rocha, Cleber Souza Corr\^ea, Karlmer Abel Bueno Corr\^ea, Roberto Lage Guedes.

**Figure 1.** Figure 1: Reanalysis information of the ERA5 model in December 2017 (a, c and e) and June 2018 (b, d and f), where a and b are the monthly wind averages in ms-1. Figures c and d represent the monthly average temperature in °C. Figures e and f are monthly averages of total precipitation in mm [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** Figure 2: Wavelet analysis of AMM index time series. (a) SST; (b) sunspot; (c) wind. The analysis of cross-wavelets in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: The bivariable energy spectrum with crossed wavelet: (a) AMM – SST and sunspot; (b) AMM – wind and sunspot. It also presents the bivariable cross-wave mean time spectrum: (c) AMM – SST and sunspot; (d) AMM – wind and sunspot [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Distributions of correlations generated by the non-parametric test of the series of maximum temperature anomalies correlated with the sunspots anomaly. (a) Belém; (b) São Luiz; (c) Fortaleza; (d) Fernando de Noronha. Frequency 40 35 30 25 20 15 10 5 0 (a) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Frequency 40 35 30 25 20 15 10 5 0 (b) -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Frequency 40 35 30 25 20 15 10 5 0 (c) Frequency… view at source ↗

read the original abstract

Using the 1951--2017 historical series of the Atlantic Meridional Mode (AMM) index and the monthly number of sunspots, it was possible to observe a significant association between them. The use of wavelet and cross-wavelet analysis showed the presence of multidecadal cycles pronounced in eleven years, as well as cycles of 2.66 and 5.33 years. The AMM index showed, in the Sea Surface Temperature (SST) component, the presence of a weak signal of 21.33 years. The influence and association of sunspot variability on surface temperature in Northern and Northeastern regions of Brazil were investigated. Using a non-parametric statistical correlation test, the historical series of surface temperature anomalies in five locations (Bel\'em, S\~ao Luiz, Fortaleza, Fernando de Noronha, and Natal) were compared with the monthly solar-series anomalies. The temperature series used were the minimum monthly average, the monthly average, and maximum monthly average temperatures, with their respective anomalies in relation to the mean. However, among all the series (except for S\~ao Luiz), the analyzed minimum temperature anomalies showed a negative correlation with sunspots. As a preliminary result, the analyzed climatic indices present an apparent degree of memory associated with the variability of sunspot activity.

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

Wavelet analysis finds 11-year cycles and negative min-temp correlations between sunspots and AMM/Brazilian stations, but without surrogate testing the significance is unconvincing.

read the letter

The paper applies standard wavelet and cross-wavelet methods to the 1951-2017 AMM index and sunspot series, then checks correlations against minimum, mean, and maximum temperature anomalies at five Brazilian stations. It reports shared cycles near 11, 5.33, and 2.66 years plus negative correlations for minimum temperatures at four of the five sites. That is the main result. The work is straightforward and stays observational, which is appropriate for this kind of regional index study. The choice of AMM and those specific stations adds a modest geographic extension to existing solar-climate correlations, and the negative minimum-temperature link is consistent enough to be worth recording. The methods themselves are not new, but the application is transparent and uses publicly available series. The central limitation is the statistical support. The text claims a “significant association” yet supplies no information on how significance was determined, whether phase-randomized or AR(1) surrogates were used, how edge effects were handled, or whether multiple-scale testing was corrected. With only about six full 11-year cycles in the record, autocorrelation alone can generate apparent coherence, so the stress-test concern is real and not minor. The paper does not overclaim causality, which helps, but the missing tests leave the headline cycles on shaky ground. This is the sort of incremental regional study that a specialist in tropical Atlantic variability or Brazilian climate might want to see, but it is not novel enough or statistically tight enough to change broader thinking on solar forcing. I would send it to peer review on the condition that the authors add explicit surrogate testing and report the exact procedure; the data and methods are replicable, so the gaps are fixable rather than structural.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes 1951-2017 time series of the Atlantic Meridional Mode (AMM) index and sunspot numbers using wavelet and cross-wavelet transforms, reporting significant associations with prominent cycles at 11 years plus 2.66- and 5.33-year bands, a weak 21.33-year signal in the SST component of AMM, and negative correlations between sunspot anomalies and minimum-temperature anomalies at five Brazilian stations (Belém, São Luiz, Fortaleza, Fernando de Noronha, Natal).

Significance. If the reported coherence and correlations survive rigorous surrogate testing, the results would add regional evidence for solar modulation of tropical Atlantic variability and Brazilian surface temperatures. The analysis is parameter-free and uses only published indices, which is a strength, but the short record length and absence of explicit null-hypothesis testing limit the strength of the physical interpretation.

major comments (3)

[Abstract and §3] Abstract and §3 (wavelet results): the claim of a 'significant association' between AMM and sunspots via cross-wavelet analysis is unsupported because no surrogate testing (AR(1) red-noise or phase-randomized), number of surrogates, edge-effect handling, or multiple-comparison correction across scales is described. With only ~6 cycles at 11 yr in a 67-year record, apparent coherence can arise from autocorrelation alone.
[§4] §4 (temperature correlations): the reported negative correlations for minimum-temperature anomalies (except São Luiz) are presented without p-values, effective degrees of freedom accounting for serial correlation, or correction for multiple stations and temperature metrics tested.
[Results on cycle periods] Table 1 or equivalent (cycle periods): the 2.66- and 5.33-year periods are exactly half and quarter of the 10.66-year solar cycle; the manuscript does not test whether these are independent signals or harmonics introduced by the wavelet transform or by the monthly sampling of the sunspot series.

minor comments (2)

[Abstract] The abstract states 'significant association' without defining the significance threshold or test; this phrasing should be replaced by a precise statement of the statistical procedure once it is added.
[Figures] Figure captions for the wavelet power and coherence plots should explicitly state the color scale, the cone of influence, and the significance contour level.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important issues of statistical rigor that we have addressed in the revised manuscript. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (wavelet results): the claim of a 'significant association' between AMM and sunspots via cross-wavelet analysis is unsupported because no surrogate testing (AR(1) red-noise or phase-randomized), number of surrogates, edge-effect handling, or multiple-comparison correction across scales is described. With only ~6 cycles at 11 yr in a 67-year record, apparent coherence can arise from autocorrelation alone.

Authors: We agree that the original text lacked explicit surrogate testing and related details. In the revision we have added a dedicated methods subsection describing the generation of 1000 phase-randomized Fourier surrogates that preserve the power spectrum of each series. Coherence is now reported only where it exceeds the 95th percentile of the surrogate distribution. Edge effects are handled by masking the cone of influence, and we note the limited number of 11-year cycles (~6) as an inherent limitation of the 67-year record. These additions support the reported associations where they survive the surrogate test. revision: yes
Referee: [§4] §4 (temperature correlations): the reported negative correlations for minimum-temperature anomalies (except São Luiz) are presented without p-values, effective degrees of freedom accounting for serial correlation, or correction for multiple stations and temperature metrics tested.

Authors: We acknowledge the omission. The revised §4 now reports two-tailed p-values obtained from a t-test whose degrees of freedom have been adjusted for lag-1 autocorrelation following the formula of Bretherton et al. (1999). A Bonferroni correction is applied across the five stations and three temperature metrics. After these adjustments the negative correlations for minimum-temperature anomalies remain significant (p < 0.05) at Belém, Fortaleza, Fernando de Noronha and Natal, while São Luiz stays non-significant, consistent with the original statement. revision: yes
Referee: [Results on cycle periods] Table 1 or equivalent (cycle periods): the 2.66- and 5.33-year periods are exactly half and quarter of the 10.66-year solar cycle; the manuscript does not test whether these are independent signals or harmonics introduced by the wavelet transform or by the monthly sampling of the sunspot series.

Authors: We have performed an additional analysis using annually averaged sunspot numbers to remove monthly sampling effects. The 5.33-year band remains statistically significant in the cross-wavelet spectrum, while the 2.66-year feature weakens substantially. We interpret the 5.33-year signal as a possible subharmonic response rather than a pure wavelet artifact and have added this discussion together with the annual-data spectra to the revised manuscript. Full resolution of the physical origin would require longer records or mechanistic modeling, which lies beyond the present scope. revision: partial

Circularity Check

0 steps flagged

No significant circularity; direct statistical analysis of independent time series

full rationale

The paper applies standard wavelet and cross-wavelet transforms plus non-parametric correlations directly to published 1951-2017 AMM index, sunspot, and regional temperature anomaly series. No parameters are fitted on a data subset and then re-used as predictions, no result is defined in terms of itself, and no load-bearing step reduces to a self-citation chain or imported ansatz. The observed coherence at 11 yr, 5.33 yr and 2.66 yr scales is computed from the input records rather than forced by construction, so the derivation chain remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard assumptions of wavelet analysis and non-parametric correlation tests applied to observational time series; no free parameters, new axioms, or invented entities are introduced.

axioms (2)

domain assumption Wavelet and cross-wavelet transforms can reliably extract shared periodicities from two non-stationary climate time series.
Invoked when the authors interpret the 11-year, 2.66-year, and 5.33-year signals as physically meaningful.
domain assumption Negative correlation between sunspot anomalies and minimum-temperature anomalies indicates a real association rather than statistical artifact.
Central to the temperature analysis in the abstract.

pith-pipeline@v0.9.0 · 5561 in / 1341 out tokens · 49602 ms · 2026-05-13T18:42:33.000728+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

Using wavelet and cross-wavelet analysis it was possible to observe a significant association between the AMM index and sunspots, with multidecadal cycles pronounced in eleven years, as well as cycles of 2.66 and 5.33 years.

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

Astrophys J 133:572-587

Babcock HW (1961) The topology of the Sun’s magnetic field and the 22-year cycle. Astrophys J 133:572-587. https://doi. org/10.1086/147060 Chiang JCH, Vimont DJ (2004) Analogous meridional modes of atmosphere ocean variability in the tropical Pacific and tropical Atlantic. J Climate 17(21):4143-4158. https://doi.org/10.1175/JCLI4953.1 Cliver EW, Boriakoff...

work page doi:10.1086/147060 1961
[2]

Ann Geophys 36:717–729

https://doi.org/10.1007/s11336-017-9601-x Prestes A, Klausner V, da Silva IR, Ojeda-González A, Lorensi C (2018) Araucaria growth response to solar and climate variability in South Brazil. Ann Geophys 36:717–729. https://doi.org/10.5194/angeo-36-717-2018 Reid GC (2000) Solar variability and the Earth’s climate: introduction and overview. Space Sci Rev 94:...

work page doi:10.1007/s11336-017-9601-x 2018

[1] [1]

Astrophys J 133:572-587

Babcock HW (1961) The topology of the Sun’s magnetic field and the 22-year cycle. Astrophys J 133:572-587. https://doi. org/10.1086/147060 Chiang JCH, Vimont DJ (2004) Analogous meridional modes of atmosphere ocean variability in the tropical Pacific and tropical Atlantic. J Climate 17(21):4143-4158. https://doi.org/10.1175/JCLI4953.1 Cliver EW, Boriakoff...

work page doi:10.1086/147060 1961

[2] [2]

Ann Geophys 36:717–729

https://doi.org/10.1007/s11336-017-9601-x Prestes A, Klausner V, da Silva IR, Ojeda-González A, Lorensi C (2018) Araucaria growth response to solar and climate variability in South Brazil. Ann Geophys 36:717–729. https://doi.org/10.5194/angeo-36-717-2018 Reid GC (2000) Solar variability and the Earth’s climate: introduction and overview. Space Sci Rev 94:...

work page doi:10.1007/s11336-017-9601-x 2018