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arxiv: 2605.22399 · v1 · pith:LVY4HEUInew · submitted 2026-05-21 · 🌌 astro-ph.SR

Reconstruction of annual solar irradiance over the last three millennia

D. Temaj , N.A. Krivova , S.K. Solanki , I.G. Usoskin , T. Chatzistergos This is my paper

Pith reviewed 2026-05-22 03:59 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords total solar irradianceTSI reconstructionsunspot numberscosmogenic isotopessolar variabilitySATIRE-T modelthree millennia
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The pith

A physics-based model produces the first annual total solar irradiance record over the last three millennia.

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

The paper extends the SATIRE-T model, calibrated on modern satellite and telescopic data, to reconstruct total solar irradiance at annual resolution back three thousand years. It does this by feeding the model with newly available sunspot number series derived from cosmogenic isotope records. The reconstruction yields a continuous TSI series from the satellite era through the pre-telescopic period, with the 50-year running mean showing a maximum difference of 1.04 W m^{-2} between its highest and lowest values. A sympathetic reader would care because direct irradiance measurements exist only for recent decades, so any long-term solar record helps separate solar contributions from other drivers of past climate change.

Core claim

The authors produce a continuous physics-based total solar irradiance record at annual resolution covering the last three millennia by extending the SATIRE-T model with annually resolved sunspot numbers from cosmogenic isotope records, resulting in a maximum difference of 1.04 with uncertainties of -0.2 to +0.14 W m^{-2} between the maximum and minimum of the 50-year running mean values over the full interval.

What carries the argument

The SATIRE-T model, which calculates irradiance changes from the evolution of solar surface magnetic features, applied to sunspot numbers reconstructed from cosmogenic isotopes.

If this is right

  • The record supplies a uniform annual TSI series that bridges the satellite era and earlier times for direct use in climate studies.
  • It quantifies the amplitude of long-term solar variability as no more than about one watt per square meter in smoothed values.
  • It demonstrates that a physics-based approach can be carried backward in time once suitable sunspot input series exist.

Where Pith is reading between the lines

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

  • Climate simulations could now ingest this TSI series to test how much of observed past temperature changes can be attributed to solar forcing alone.
  • If later work confirms the small amplitude, it would tighten upper limits on solar contributions to centennial-scale climate shifts.
  • The method opens a path for similar annual reconstructions of other solar parameters such as ultraviolet flux once suitable input data become available.

Load-bearing premise

The model relating sunspot numbers to irradiance changes, which was tuned on recent observations, continues to hold when applied to sunspot numbers from thousands of years ago.

What would settle it

An independent TSI proxy or reconstruction from a different method that shows a range in 50-year averages substantially larger than 1.04 W m^{-2} over the same three-millennia span.

Figures

Figures reproduced from arXiv: 2605.22399 by D. Temaj, I.G. Usoskin, N.A. Krivova, S.K. Solanki, T. Chatzistergos.

Figure 1
Figure 1. Figure 1: (a) Annual sunspot numbers (ISNv2 in red and 14C-based SN in different shades of blue, as indicated in the legend – U21, U25, and U26 stand for Usoskin et al. 2021, 2025, 2026). The different blue shades cor￾respond only to the origin of the input data and do not reflect sepa￾rate reconstructions. These SN val￾ues are used as input to reconstruct: (b) Total magnetic flux, (c) Open so￾lar magnetic flux, and… view at source ↗
Figure 2
Figure 2. Figure 2: Same as [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Solar irradiance measurements are limited to the last few decades, requiring reconstructions to assess solar variability on longer timescales and its impact on Earth's climate. We present the first physics-based reconstruction of total solar irradiance (TSI) at annual resolution over the last three millennia. The reconstruction is obtained by extending the SATIRE-T model beyond the telescopic era using recently published, annually resolved sunspot number series derived from cosmogenic isotope records. This yields a continuous, physics-based TSI record extending from the satellite era back over the last three millennia, with annual resolution throughout the pre-telescopic period. Over the full three-millennia interval, the reconstructed TSI exhibits a maximum difference of $1.04_{-0.2}^{+0.14}\,\mathrm{W\,m^{-2}}$, defined as the difference between the maximum and minimum of the 50-yr running mean values.

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

2 major / 2 minor

Summary. The paper extends the SATIRE-T semi-empirical model, previously calibrated on satellite-era TSI and telescopic sunspot data, to produce an annual-resolution reconstruction of total solar irradiance (TSI) over the last three millennia. Input sunspot numbers are taken from an inversion of cosmogenic 14C and 10Be production rates. The central quantitative result is a maximum difference of 1.04_{-0.2}^{+0.14} W m^{-2} between the maximum and minimum of the 50-year running-mean TSI values over the full interval.

Significance. A validated annual TSI reconstruction spanning three millennia would be a useful input for climate-sensitivity studies and for testing solar-dynamo models on centennial timescales. The physics-based character of SATIRE-T and the use of annually resolved proxy sunspot numbers are strengths relative to purely empirical long-term reconstructions. However, the significance is limited by the absence of explicit validation that the modern-calibrated flux-to-irradiance mapping remains unchanged when applied to the statistical properties of the pre-telescopic SSN series.

major comments (2)
  1. [Abstract and §2] Abstract and §2 (model description): the central claim that the 1.04 W m^{-2} range is robust rests on the assumption that SATIRE-T parameters (spot/facular contrasts and area-filling factors) calibrated on post-1978 data remain valid for the amplitude, cycle length, and grand-minimum depth statistics of the isotope-derived SSN series. No sensitivity tests that vary these parameters within their modern uncertainties or that compare the resulting TSI against independent proxies (e.g., 10Be-based reconstructions or tree-ring 14C) are reported.
  2. [§3] §3 (reconstruction results): the reported asymmetric uncertainties on the 1.04 W m^{-2} difference appear to reflect only the uncertainty in the 50-yr running-mean extrema; they do not propagate the uncertainty arising from possible secular changes in the SSN-to-magnetic-flux conversion or in the contrast ratios. A quantitative assessment of this additional systematic uncertainty is required for the quoted range to be interpreted as a total error budget.
minor comments (2)
  1. [Abstract] The definition of the reported maximum difference (difference between max and min of the 50-yr running mean) should be stated explicitly in the abstract and again in the results section for clarity.
  2. [Figures] Figure captions should indicate the time intervals covered by the satellite calibration data versus the proxy-driven reconstruction to avoid visual conflation of the two regimes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the robustness of our reconstruction. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2 (model description): the central claim that the 1.04 W m^{-2} range is robust rests on the assumption that SATIRE-T parameters (spot/facular contrasts and area-filling factors) calibrated on post-1978 data remain valid for the amplitude, cycle length, and grand-minimum depth statistics of the isotope-derived SSN series. No sensitivity tests that vary these parameters within their modern uncertainties or that compare the resulting TSI against independent proxies (e.g., 10Be-based reconstructions or tree-ring 14C) are reported.

    Authors: SATIRE-T is a physics-based model in which spot and facular contrasts are determined from the wavelength-dependent radiative properties of magnetic features, quantities that are intrinsic to the Sun and independent of the statistical properties of the input sunspot series. The area-filling factors are likewise tied to the observed magnetic flux. Because the underlying physics does not change on millennial timescales, the same parameter set calibrated on the satellite era is applied to the isotope-derived SSN series. Nevertheless, we agree that an explicit demonstration of robustness is valuable. In the revised manuscript we will add sensitivity tests that vary the contrast ratios and filling-factor scaling within the uncertainties reported in the original SATIRE-T calibration papers and will include a brief comparison of the resulting TSI envelope with independent 10Be-based reconstructions. revision: yes

  2. Referee: [§3] §3 (reconstruction results): the reported asymmetric uncertainties on the 1.04 W m^{-2} difference appear to reflect only the uncertainty in the 50-yr running-mean extrema; they do not propagate the uncertainty arising from possible secular changes in the SSN-to-magnetic-flux conversion or in the contrast ratios. A quantitative assessment of this additional systematic uncertainty is required for the quoted range to be interpreted as a total error budget.

    Authors: The asymmetric uncertainties quoted for the 1.04 W m^{-2} range are obtained solely from the extrema of the 50-year running mean of the central reconstruction. We acknowledge that this does not yet incorporate systematic contributions from possible secular changes in the SSN-to-flux conversion or in the adopted contrasts. In the revised version we will add a quantitative assessment of these systematics, for example by recomputing the TSI range for the upper and lower bounds of the conversion factor and contrast uncertainties, and will present the resulting total error budget alongside the existing statistical range. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the reconstruction chain

full rationale

The paper computes TSI by applying the pre-existing SATIRE-T model (with parameters fixed from modern satellite and telescopic data) to an externally derived, annually resolved sunspot-number time series obtained by inverting cosmogenic isotope production rates. The reported 1.04 W m^{-2} maximum difference is obtained by taking the max-minus-min of the 50-year running mean of this forward-modelled TSI series. This is a standard forward application of a calibrated model to independent proxy input; the output series is not redefined as or fitted to the same quantities that entered the model. No load-bearing step reduces by construction to the paper's own fitted values or to a self-citation chain whose validity is assumed inside the present work. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The reconstruction rests on the transferability of the SATIRE-T sunspot-to-irradiance relationship outside the calibration period and on the accuracy of the cosmogenic sunspot series; no explicit free parameters or new entities are named in the abstract.

free parameters (1)
  • SATIRE-T model parameters
    Parameters calibrated on modern observations are required to extend the model; their specific values are not stated in the abstract.
axioms (1)
  • domain assumption The physical relationship between sunspot number and total solar irradiance encoded in SATIRE-T holds for pre-telescopic solar conditions.
    Invoked when the model is extended beyond the telescopic era using the cosmogenic sunspot series.

pith-pipeline@v0.9.0 · 5695 in / 1285 out tokens · 59375 ms · 2026-05-22T03:59:40.725679+00:00 · methodology

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