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REVIEW 4 major objections 4 minor 49 references

No single solar latitude follows the sunspot cycle exactly.

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2026-08-04 18:21 UTC pith:UD6FZZSN

load-bearing objection A useful 100-year latitude–lag map, but the headline intensity lag of 1.25–1.5 yr is likely an interpolation artifact from yearly sampled data. the 4 major comments →

arxiv 2509.09974 v1 pith:UD6FZZSN submitted 2025-09-12 astro-ph.SR

Which Solar Latitude Follows the Sunspot Cycle Exactly?

K P Raju This is my paper
classification astro-ph.SR
keywords supergranulationsolar cycleCa II K spectroheliogramsnetwork lane widthchromospheric networklatitudinal dependencecross-correlationquiet Sun irradiance
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper asks whether any latitude on the Sun tracks the sunspot cycle in lockstep, and answers no. Using a century of Ca II K spectroheliograms, it measures two properties of the supergranular network—the width of the bright network lanes and their intensity—at every latitude from 60°N to 60°S, and cross-correlates each with the sunspot number. Lane width correlates most strongly near 18–20° latitude with zero phase lag, while intensity peaks near 13–14° but runs 1.25 to 1.5 years behind the cycle. Both correlations reach about 0.8 and are roughly north–south symmetric. If correct, this result pinpoints which latitudes actually encode the cycle and separates the timing of magnetic-flux buildup from brightness response, with direct consequences for flux transport and quiet-Sun UV irradiance.

Core claim

The central discovery is that the supergranular network responds to the solar cycle differently in its geometry and its brightness. Lane widths—a proxy for magnetic flux concentrated at cell boundaries—follow the sunspot cycle almost perfectly near ±20° latitude, with no measurable phase delay. Mean network intensity, however, correlates most strongly near ±13–14° and peaks 1.25–1.5 years after sunspot maximum. Thus no unique latitude can be said to follow the sunspot cycle exactly; the correlation surface has broad, symmetric peaks whose latitude and lag depend on the quantity measured. The paper also finds significant, cycle-correlated lane-width variations across 55°S to 55°N, whereas int

What carries the argument

The key quantities are the supergranular network lane width and its mean Ca II K intensity, extracted from small image windows of century-long Ca II K spectroheliograms after equal-contrast calibration, limb-darkening correction, and rejection of the top and bottom 5% of window intensities. Lane width is measured as the width of the autocorrelation function of each window. The argument is carried by latitude-by-latitude cross-correlation functions between these yearly averaged time series and the sunspot number, with the lags refined by interpolating the correlation curves to 0.01-year resolution. This machinery isolates which latitudes lock onto the cycle and at what delay.

Load-bearing premise

The load-bearing premise is that the equal-contrast calibration of the century-long Ca II K series—especially the trial-and-error rejection of the top and bottom 5% of window intensities—preserves true latitude-dependent changes in lane width and intensity; if seeing degradation or the threshold choice biases some latitudes, the correlation peaks and lags could shift.

What would settle it

Compute the same latitude-resolved cross-correlation on raw, uncalibrated Ca II K contrast data and on a modern space-based network-brightness dataset. If the lane-width peak moves away from 18–20° by more than the stated ±2°, or if the intensity peak no longer lags by 1.25–1.5 years, the central claim would be falsified. A simpler check: split the 1907–1990 record into early and late halves; if the latitude and lag of maximum correlation are not stable across halves, the result is likely an artifact of calibration drift.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Lane width at roughly ±20° can serve as a phase-zero tracer of the sunspot cycle, useful for cycle timing and amplitude prediction.
  • Intensity lags the cycle by 1.25–1.5 years at ±13–14°, meaning brightness-based quiet-Sun indices will peak after sunspot maximum.
  • The different latitude and lag structure implies flux transport redistributes network magnetic field before it is seen in brightness, affecting surface flux-transport models.
  • Quiet-Sun UV irradiance reconstructions should use latitude-dependent network intensity with a post-maximum lag rather than sunspot number directly.
  • The contrast between the broad 55°N–S significant correlation range for lane width and the narrow 5–35° bands for intensity cautions against using a single latitude to represent the quiet Sun.

Where Pith is reading between the lines

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

  • A natural extension would be to track the same lane-width/intensity lag pattern in modern space-based magnetograms; if the lag reversal near ±25° and ±40° persists, it would strengthen the flux-transport interpretation and yield a direct transport-speed estimate.
  • The paper's lane-width/cycle relationship may help resolve contradictory reports on supergranular size versus cycle: if size correlates with lane width only at certain latitudes, comparisons at mismatched latitudes would explain the disagreement.
  • The reported difference between zero lag for lane width and 1.25–1.5-year lag for intensity could be tested with other chromospheric or EUV network brightness proxies, where the lag should shift systematically with formation temperature.
  • Because the analysis stops before 1990 due to seeing degradation, applying the same method to modern uninterrupted space-based images would show whether the correlation surface is stable across solar cycles 23–25.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper analyzes ~34,000 Kodaikanal Ca II K spectroheliograms (1907–1990) to measure yearly averaged supergranular lane widths and intensities as functions of latitude (60°N–60°S). It cross-correlates these quantities with the international sunspot number at each latitude and reports that the maximum correlation for lane widths occurs near 18–20° latitude with zero lag, while intensities peak near 13–14° latitude with a lag of 1.25–1.5 yr after solar maximum. The paper concludes that no single latitude follows the sunspot cycle exactly for all quantities and discusses implications for flux transport and quiet-Sun UV irradiance. The main result—that correlation with the solar cycle is strongest in low-to-mid latitudes—is visible in the figures and is broadly plausible, but the paper's most specific quantitative claims (the sub-annual intensity lag and the quoted latitude uncertainties) are not supported by the statistical analysis as presented.

Significance. If the central claims can be established, the paper would provide a valuable long-baseline, latitude-resolved characterization of how the supergranular network responds to the solar cycle. Its strengths include the use of a nearly century-long homogeneous archive, an external sunspot-number series rather than a self-referential proxy, and a clear presentation of the latitude-lag structure. The finding that lane width and intensity peak at different latitudes and lags, if robust, would be relevant to flux-transport models and to understanding the quiet-Sun UV irradiance cycle. However, the paper currently overstates the precision of its headline phase lag: the CCF is computed from yearly averages and then interpolated to 0.01-yr intervals, which cannot create the missing sub-annual information. In addition, the significance threshold does not account for autocorrelation or multiple testing across 120 latitudes. These issues do not invalidate the broad correlation pattern, but they do affect the quantitative conclusions and need to be addressed before the paper can be accepted.

major comments (4)
  1. [Section 3, Figure 2 and interpolation paragraph] The headline intensity lag of 1.25–1.5 yr is not established by the analysis described. The cross-correlation is computed from yearly averaged quantities, so it is defined only at integer-year lags. Interpolating the ±5-yr window with 0.01-yr spacing cannot create genuine sub-annual phase information; the reported lag lies between lags 1 and 2, precisely where interpolation of a broad, noisy CCF is most uncertain. The authors should either (a) compute the CCF using sub-annually binned sunspot and network data, (b) fit a parametric model to the CCF with an uncertainty estimate, or (c) provide a bootstrap/permutation distribution of the peak lag. Without such a test, the contrast between the zero-lag lane-width result and the 1.25–1.5-yr intensity lag remains an interpolation artifact.
  2. [Section 3, Figure 3 top and bottom panels] The significance threshold of 0.29 (claimed 99% confidence) does not account for the strong autocorrelation in the annual sunspot number and in the yearly averaged lane-width/intensity series. The effective number of independent samples is far below the number of years, and scanning 120 latitudes introduces a multiple-testing problem that can easily produce spurious peaks above 0.29. The claim that correlations are 'highly significant' over a broad latitude range therefore needs support from a test that preserves temporal autocorrelation (e.g., block bootstrap, phase scrambling, or ARMA-based effective degrees of freedom) and controls the false-discovery rate across latitudes.
  3. [Section 2, intensity rejection threshold] The 5% top/bottom intensity rejection threshold is chosen by trial and error, and the manuscript asserts that 'varying the threshold by a few percentage does not significantly affect the correlation' without showing any quantitative test. Because this threshold directly determines which windows contribute to the latitude-dependent lane-width and intensity time series, a few-percent change could shift the correlation peaks and lags that are central to the conclusions. Please provide a sensitivity analysis (e.g., thresholds of 3%, 5%, 7%, 10%) and report the resulting peak latitudes and lags, or at least show that the headline values are stable.
  4. [Section 3, Figures 2 and 3] Correlation coefficients are reported without uncertainties, and the quoted latitude uncertainties of ±2° have no stated derivation. The text does not explain how the peak latitude or its uncertainty was obtained from the smoothed curves, nor does it give confidence intervals on the correlation values. Since the paper compares the latitude peaks of lane width and intensity (18°N/20°S vs. 13°N/14°S) and interprets their difference, a bootstrap or Monte Carlo procedure that yields uncertainties on the peak locations and lags is necessary to support those comparisons.
minor comments (4)
  1. [Title and abstract] There are typographical errors: 'F ollows' in the title, 'intensitiy' in the abstract, and 'coefficients' in several places. Please correct these.
  2. [Section 2, Data & Analysis] The description of the 'equal-contrast technique' is brief; a reader unfamiliar with Raju (2020) and Singh et al. (2021) will not know how the FWHM contrast target (0.10–0.11) is converted into an intensity scale or whether this calibration is stable across the different photographic emulsions over 100 years. A sentence summarizing the main calibration steps would improve reproducibility.
  3. [Section 3, lag sign convention] The paper reports lags for lane width and intensity but never explicitly defines the sign convention (e.g., positive lag means quantity follows the sunspot cycle). Adding a sentence explaining the convention would prevent misinterpretation of the values in the bottom panel of Figure 3.
  4. [References] The reference list contains an incomplete author name for Roudier et al. (2014): 'Roudier, T., Švanda, M., Rieutord, ., et al.' The missing author initial/name should be corrected.

Circularity Check

0 steps flagged

No significant circularity: lane widths/intensities are cross-correlated with the external SILSO sunspot series, so the central result is anchored outside the paper's own fitted values. Self-citations supply only the measurement pipeline and do not force the found peak latitudes or lags. The 1.25-1.5 yr intensity lag rests on interpolating a yearly-sampled CCF, a resolution limitation, not a circu

full rationale

The derivation chain is: (1) lane widths (autocorrelation FWHM) and mean intensities are measured from Kodaikanal Ca II K windows; (2) yearly averages are cross-correlated with external World Data Center SILSO sunspot numbers; (3) latitudes and lags of the CCF maxima are read off. None of these steps defines the target result in terms of the inputs. No parameter is fitted and then renamed a prediction: the equal-contrast normalization, the 5% window rejection, and the autocorrelation width are fixed preprocessing choices from published work (Singh et al. 2021; Raju 2020; Raju et al. 2023). The paper asserts threshold robustness without a quantitative sensitivity test, which is missing support, not a circular step. Self-citations (Raju 2016/2018/2020/2023) supply the measurement methodology and prior evidence of cycle dependence; they are published, parameter-free methods whose assumptions do not include the present peak latitudes or lags, so they constitute independent support and do not force the result. Two flagged limitations are correctness risks, not circularity: (a) Section 3 obtains the 1.25-1.5 yr intensity lag by interpolating a cross-correlation whose x-axis interval is 1 year to 0.01 yr; the CCF is defined only at integer-year lags, so the sub-annual peak location is not resolved by the data; (b) Section 2's trial-and-error top/bottom 5% window-intensity threshold is asserted to be insensitive to a few percent changes but no quantitative test is shown. Both could shift the claimed peaks/lags but do not make the analysis equivalent to its inputs. Because the central claim is a direct correlation of independent measurements with an external benchmark, the honest finding is no significant circularity (score 2 for minor, non-load-bearing self-citation).

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claim rests on the calibration of the Kodaikanal data and the interpretation of lane width and intensity as magnetic proxies. The main free parameters are the contrast target and rejection threshold; neither is fitted to the correlation result, but both influence the measured quantities. No new entities are introduced.

free parameters (3)
  • intensity rejection threshold = 5% (top and bottom)
    Windows with mean intensity in the top and bottom 5% of the distribution are rejected; the threshold is chosen by trial and error and is stated to be robust to a few percent changes (Section 2).
  • contrast FWHM target = 0.10 to 0.11
    Equal-contrast calibration adjusts images until the FWHM of the intensity distribution reaches this range; a hand-chosen calibration target that affects contrast and thus measured intensities (Section 2).
  • smoothing window = 5-point
    A 5-point smoothing average is applied to the maximum correlation versus latitude curves to emphasize peaks; the choice affects the reported peak widths and uncertainties (Section 3).
axioms (4)
  • standard math Cross-correlation is an appropriate measure of phase and amplitude relationship between annual time series
    Used throughout Section 3 without formal justification; assumes stationarity and linearity.
  • domain assumption Supergranular network lane width is a proxy for magnetic flux at cell boundaries
    Inherited from Simon and Leighton 1964 and used to interpret the correlations; not independently validated here.
  • domain assumption Ca II K intensity at quiet Sun scales with network magnetic flux and temperature
    Used to connect intensity correlations to solar cycle and irradiance; the paper notes intensity also depends on temperature and abundance.
  • domain assumption The Kodaikanal 100-year data, after calibration, represent the true solar cycle variation without significant seasonal or instrumental drifts
    Required for the cross-correlation to be meaningful; the paper truncates data after 1990 due to seeing degradation.

pith-pipeline@v1.3.0-alltime-deepseek · 7764 in / 11402 out tokens · 113026 ms · 2026-08-04T18:21:52.647205+00:00 · methodology

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Cite this review

Pith. "Pith review of Which Solar Latitude Follows the Sunspot Cycle Exactly?." pith.science (2026). https://pith.science/paper/UD6FZZSN

@misc{pith2026250909974,
  author       = {Pith},
  title        = {Pith review of: Which Solar Latitude Follows the Sunspot Cycle Exactly?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UD6FZZSN}},
  note         = {Machine review of arXiv:2509.09974}
}
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read the original abstract

The large-scale convection in the Sun known as supergranulation is manifested as a network structure on the solar surface. The network cells have an average lifetime of 24 hr, a size of about 30 Mm, and a lane width of about 6 Mm. We have obtained the lane widths and intensities at different latitudes from the Ca {\sc ii} K spectroheliograms from the 100 yr Kodaikanal archival data. We have then calculated the cross correlation function of lane widths and intensities with sunspot number at every latitude from 60$^{\circ}$ N to 60$^{\circ}$ S. The correlation coefficients of the quantities show an approximate North-South symmetry with broad peaks around $\pm$(11--22)$^{\circ}$ latitude with values of about 0.8. The results imply that these latitudes follow the sunspot cycle strongly. The maximum correlation for the lane widths occurs (18$\pm$2)$^{\circ}$ N and (20$\pm$2)$^{\circ}$ S with no phase difference. For intensities, this happens at (13$\pm$2)$^{\circ}$ N and (14$\pm$2)$^{\circ}$ S with a phase difference of 1.25 to 1.5 yr. It is interesting to note that the lane width correlations peak during the solar maximum whereas the intensitiy correlations peak 1.25--1.5 yr after the solar maximum. The results, generally show that no unique latitude exactly follows the solar cycle for all quantities. The results are important in flux transport on the solar surface and have implications for the quiet Sun UV irradiance variations.

Figures

Figures reproduced from arXiv: 2509.09974 by K P Raju.

Figure 1
Figure 1. Figure 1: Yearly averaged supergranular lane widths (pink) and Ca K intensity (black) as a function of time for different latitudes from 60◦ N to 60◦ S with an interval of 10◦ . The y-axis on the right gives the normalized intensity. The bottom panel shows the variation of the yearly averaged sunspot number with time. Sunspot data from the World Data Center SILSO, Royal Observatory of Belgium, Brussels [PITH_FULL_I… view at source ↗
Figure 2
Figure 2. Figure 2: Cross-correlation of lane widths (pink) and intensities (black) with sunspot cycle as a function of lag (yr) at different latitudes. The panels on the right give a magnified view of the central region (-5 < lag < 5) at selected latitudes.] for lane width. For intensity, the lag varies from -0.3 yr to about 2.5 yr. Also, note that there is a broad reversal in the lag values for both quantities; at about± (2… view at source ↗
Figure 3
Figure 3. Figure 3: Maximum correlation coefficient of lane width (pink) and intensity (black) with sunspot cycle at different latitudes (top). The continuous line represents a 5-point smoothing average. The horizontal dashed line represents the 99 % confidence level. Lag (yr) of lane width (pink) and intensity (black) with solar cycle at different latitudes (bottom). Only those points with a correlation coefficient above 0.2… view at source ↗

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