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arxiv: 2604.03359 · v1 · submitted 2026-04-03 · ⚛️ physics.ao-ph · stat.AP

Multidecadal Cycles Study in the Climate Indexes Series Using Wavelet Analysis in North/Northeast Brazil

Cleber Souza Corr\^ea , Roberto Lage Guedes , Karlmer Abel Bueno Corr\^ea , Felipe Gustavo Pilau This is my paper

Pith reviewed 2026-05-13 18:38 UTC · model grok-4.3

classification ⚛️ physics.ao-ph stat.AP
keywords wavelet analysismultidecadal cyclesclimate indicessolar activityrainfall variabilityPDOSOIBrazil
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The pith

Wavelet analysis detects 2.7-, 5.3-, 10.7-, and 21.3-year cycles in Brazilian rainfall that match solar and ocean indices.

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

This paper applies Morlet wavelet transforms to 80 years of monthly Pacific Decadal Oscillation, Southern Oscillation Index, and sunspot number records, then compares the resulting power spectra with rainfall series from five stations along a north-to-northeast Brazil transect. It identifies repeated periodicities at 32, 64, 128, and 256 months that appear across both the global indices and the local rainfall data. The authors interpret the longer cycles as evidence of possible links between solar variability and ocean-atmosphere processes that shape regional precipitation. A reader would care because these periods, if real, could help anticipate multi-year wet and dry episodes in drought-sensitive areas.

Core claim

The central claim is that the Morlet wavelet power spectra of the PDO, SOI, and sunspot series display predominant cycles at scales of 32, 64, 128, and 256 months from January 1933 to September 2016, and that the same scales appear in rainfall records from Belém, São Luiz, Fortaleza, Natal, and Fernando de Noronha between 1951 and 2017. The longer cycles are presented as suggestive of an association with solar activity variability and ocean-atmosphere climate variability.

What carries the argument

Morlet wavelet power spectra generated via the WaveletComp R package, supplemented by bivariate cross-wavelet transforms from the biwavelet package, to localize periodic signals and compare coherence between the climate indices and rainfall series.

If this is right

  • The cycles imply that decadal and multidecadal variability is the dominant feature in the examined climate indices over the 80-year window.
  • Rainfall at the five Brazilian stations shares the same periodicities, pointing to a common large-scale driver.
  • The 10.7- and 21.3-year cycles may reflect solar forcing transmitted through the ocean-atmosphere system.
  • Wavelet methods can be used to characterize multidecadal oscillations in regional climate data.

Where Pith is reading between the lines

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

  • If the cycles hold, extending the same wavelet approach to other tropical rainfall stations or longer proxy records could test whether the pattern is geographically widespread.
  • The observed similarity leaves open whether solar activity directly forces the cycles or whether ocean-atmosphere modes simply share the same periods by chance.
  • Quantifying phase lags between the sunspot and rainfall cycles in the 128- and 256-month bands could reveal whether one leads the other enough for practical forecasting.

Load-bearing premise

That matching patterns in the wavelet power spectra of the climate indices and rainfall series indicate a physical association rather than coincidental overlap or shared external forcing.

What would settle it

An independent rainfall record from the same region, extended beyond the study period and tested against red-noise significance levels, that shows no statistically significant power in the 128- or 256-month bands would falsify the reported association.

read the original abstract

This study investigates the climatic index time series over the most recent 80 years, using monthly mean values from the Pacific Decadal Oscillation Index (PDO), Southern Oscillation Index (SOI), and monthly solar activity represented by sunspot numbers (MS), obtained from the National Weather Service Climate Prediction Center and the World Data Center SILSO, Royal Observatory of Belgium, Brussels. The statistical software R was used with the \texttt{WaveletComp} package to generate Morlet wavelet power spectra, and bivariate cross-wavelet analysis using the \texttt{biwavelet} package. The results show predominant cycles with variability scales of 32, 64, 128, and 256 months, corresponding approximately to 2.66, 5.33, 10.66, and 21.33 years. These frequencies are observed in the period from January 1933 to September 2016, totaling 993 months (82.75 years), characterizing decadal and multidecadal variability. These multidecadal cycles (of the order of 10.66 and 21.33 years) suggest a possible association with solar activity variability and climate variability in the ocean-atmosphere system. Rainfall data from January 1951 to September 2017 were analyzed for Bel\'em, S\~ao Luiz, Fortaleza, Natal, and Fernando de Noronha, forming a north to northeast Brazilian transect. These series show similarity with the decadal and multidecadal cycles observed in the SOI, PDO, and sunspot series.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript applies Morlet continuous wavelet transforms (via WaveletComp) and bivariate cross-wavelet analysis (via biwavelet) to monthly PDO, SOI, sunspot-number, and rainfall series from five North/Northeast Brazil stations spanning ~80 years. It reports dominant power at scales of 32, 64, 128 and 256 months and interprets the longer two bands as evidence of multidecadal cycles possibly linked to solar activity and ocean-atmosphere variability.

Significance. If the reported cycles survive proper significance testing and the claimed physical association is placed on a quantitative footing, the study would add a regional tropical-Atlantic perspective to the literature on decadal-to-multidecadal climate variability. The use of publicly available indices and standard open-source wavelet packages is a methodological strength.

major comments (3)
  1. [Methods] Methods section: the description of the Morlet wavelet and cross-wavelet procedures does not state whether significance testing against a red-noise (AR1) null model was performed, nor whether the 95 % significance contours were computed and displayed. Without these, the identification of “predominant cycles” at 32–256 months cannot be distinguished from spurious power arising from serial correlation or edge effects in an 82-year record that contains only ~4 cycles of the 21-year band.
  2. [Results] Results section: the claim of association between the climate-index spectra and the rainfall spectra rests on visual similarity of power at the 10.7- and 21.3-year bands. No quantitative cross-wavelet coherence, phase-difference statistics, or Monte-Carlo test of the null hypothesis that the observed overlap occurs by chance is reported.
  3. [Results] Results section: the 256-month (~21 yr) band is near the upper limit of the cone of influence for an 82-year series; the manuscript does not discuss how edge-effect tapering or padding affects the reported power at this scale.
minor comments (2)
  1. [Abstract] The abstract and text use inconsistent station names (Belém vs. Belém) and date ranges; a single consistent table of series lengths and sources would improve clarity.
  2. [Figures] Figure captions should explicitly state whether the displayed power is normalized, whether significance contours are shown, and what color scale is used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have identified important clarifications needed in our manuscript. We address each major comment below and will revise the paper accordingly to strengthen the methodological description and quantitative support for our findings.

read point-by-point responses

  1. Referee: [Methods] Methods section: the description of the Morlet wavelet and cross-wavelet procedures does not state whether significance testing against a red-noise (AR1) null model was performed, nor whether the 95 % significance contours were computed and displayed. Without these, the identification of “predominant cycles” at 32–256 months cannot be distinguished from spurious power arising from serial correlation or edge effects in an 82-year record that contains only ~4 cycles of the 21-year band.

    Authors: We agree that explicit mention of the significance testing is required. The WaveletComp package performs significance testing against an AR(1) red-noise null model by default, and the 95% significance contours are displayed in all wavelet power spectra shown in the manuscript. In the revised Methods section we will add a dedicated paragraph describing this procedure, the number of Monte Carlo realizations used, and confirmation that the contours appear in the figures. revision: yes

  2. Referee: [Results] Results section: the claim of association between the climate-index spectra and the rainfall spectra rests on visual similarity of power at the 10.7- and 21.3-year bands. No quantitative cross-wavelet coherence, phase-difference statistics, or Monte-Carlo test of the null hypothesis that the observed overlap occurs by chance is reported.

    Authors: We acknowledge that the current association is primarily visual. The biwavelet package supports computation of cross-wavelet coherence and phase differences, which we will now include for the key index–rainfall pairs. We will also add Monte Carlo significance testing of the coherence at the 10.7- and 21.3-year bands and report the resulting statistics and phase angles in the revised Results section. revision: yes

  3. Referee: [Results] Results section: the 256-month (~21 yr) band is near the upper limit of the cone of influence for an 82-year series; the manuscript does not discuss how edge-effect tapering or padding affects the reported power at this scale.

    Authors: We will add an explicit discussion of the cone of influence. The WaveletComp implementation applies zero-padding and the cone is already indicated on the plots; power at 256 months remains interpretable in the central portion of the record (roughly 1950–2000). In the revision we will quantify the fraction of the time series affected by edge effects at this scale and note the reduced reliability near the boundaries. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard wavelet spectra on raw series

full rationale

The paper applies off-the-shelf Morlet wavelet routines from the external WaveletComp and biwavelet R packages directly to the input PDO, SOI, sunspot, and rainfall time series. The reported 32/64/128/256-month scales are read off the resulting power spectra without any parameter fitting, self-referential definitions, or load-bearing self-citations. The interpretive suggestion of solar/ocean-atmosphere association is post-hoc commentary, not a derivation that reduces to the inputs by construction. The analysis remains self-contained against the supplied observational records.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper performs standard time-series decomposition on publicly available indices. No new physical constants, free parameters, or postulated entities are introduced; the only background assumptions are the validity of the Morlet wavelet transform and the stationarity properties implicit in the chosen analysis window.

axioms (1)
  • standard math Morlet wavelet transform correctly isolates periodic components in non-stationary climate series
    Invoked by the choice of WaveletComp and biwavelet packages without further justification.

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