Re-evaluating solar irradiance reconstructions: No evidence for large secular trends

Mathew J. Owens; Natalie A. Krivova; Tatiana A. Egorova; Theodosios Chatzistergos

REVIEW 4 major objections 4 minor 300 references

Re-evaluating solar irradiance reconstructions: No evidence for large secular trends

T0 review · 4 major / 4 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The 2–6 W/m² secular brightening of the Sun claimed by two irradiance models is an artifact; calibrated against satellite data, the real increase is about 0.1–0.44 W/m².

desk verdict A genuinely useful reassessment that makes the qualitative case against large CHRONOS/PEA24 secular trends convincing, but the quantitative secular numbers are extrapolations from satellite-era fits and should be read with that caveat in mind. read the letter →

arxiv 2607.14377 v1 pith:OR5N64QK submitted 2026-07-15 astro-ph.SR astro-ph.EP

Theodosios Chatzistergos , Natalie A. Krivova , Mathew J. Owens , Tatiana A. Egorova This is my paper · ORCID

classification astro-ph.SRastro-ph.EP

keywords totalsolarirradianceseculartrendMaunderMinimumcosmogenicisotopesmodulationpotentialquietSunreconstructionactivity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Most solar irradiance reconstructions put the Sun's brightening since the Maunder Minimum at under 1 W/m², but two of them — CHRONOS and PEA24 — claimed 2.1–5.9 W/m². This paper tries to establish that those large secular trends are artifacts, produced by how cosmogenic-isotope records were spliced to neutron-monitor data and by fragile smoothing choices. The paper reformulates both models so the amplitude of the quiet-Sun secular component is a free parameter, then calibrates that parameter against direct satellite measurements of total solar irradiance. Calibrated this way, CHRONOS yields a secular increase of roughly 0.1–0.44 W/m² between the 1700 and 1986 minima, and PEA24 about 0.2–0.25 W/m². If the paper is right, the pre-industrial Sun was not dramatically dimmer than today, and solar forcing of climate over the past three centuries is correspondingly modest.

What carries the argument

The load-bearing device is a reformulation of CHRONOS, F(t) = F0(t) + γω(t)αQS(t), splitting the reconstruction into an active-region part and a quiet-Sun secular term; γ is then treated as a free parameter fixed by linear regression against satellite TSI composites, replacing the model-atmosphere guess of the original implementation. The temporal shape ω(t) comes from the modulation potential, and the key input is a geomagnetic-data-based modulation potential joined with a neutron-monitor-based record, which links cosmogenic-isotope and neutron-monitor data with less bias than before, together with an SSA low-pass filter that avoids the edge artifacts of 22-year binning and EMD smoothing. F

What would settle it

Resolve the disagreement among TSI composites: the regression gives γ ≈ −0.01 W/m² with the CPMDF composite but +0.38 W/m² with ACRIM — the inferred secular amplitude changes sign with the composite. A definitive reconciliation of the ACRIM-gap discontinuity using overlapping radiometer data would either confirm γ ≈ 0 or shift it by roughly the size of that discrepancy. A complementary test: inject a known large secular trend into the geomagnetic-based modulation-potential shape, add realistic cycle noise, and run the same regression; if it fails to recover the injected trend, the calibration

Watch

Extended reading notes

Core claim

The central claim is that the secular variability built into the original CHRONOS and PEA24 reconstructions is not supported by the satellite-era TSI record, regardless of which composite is used. The paper isolates CHRONOS's secular term F_QS − F_C = γω(t), where ω(t) is the normalized modulation-potential shape and γ the amplitude of the quiet-Sun irradiance change. Reproducing the original reconstructions requires γ ≈ −1.5 to −2.8 W/m²; regressing the same equation against direct TSI measurements gives γ ≈ −0.01 ± 0.04 W/m² for the CPMDF composite, about two orders of magnitude smaller. For PEA24 the equivalent amplitude parameter N drops from 0.55 to values consistent with zero. The infl

Load-bearing premise

The load-bearing premise is that the quiet-Sun irradiance response is linear in the modulation potential with a single amplitude γ (or N) calibrated from the satellite era — which spans only a small fraction of the activity range — and holds unchanged back to the Maunder Minimum; as the paper itself acknowledges, the satellite record may not fully constrain centennial quiet-Sun changes, so if that linear extrapolation or the secular shape of the geomagnetic-based modulation p

Editorial extensions

If this is right

The secular TSI increase since the Maunder Minimum is below about 1 W/m², too small for direct irradiance to be a major driver of 20th-century warming.
The high-variability family of reconstructions — CHRONOS and PEA24 — no longer supports solar-forcing scenarios that assume 2–6 W/m² secular changes.
Modulation potential and open solar flux should not be used directly as proxies for quiet-Sun irradiance variability, since both include active-region and heliospheric contributions; doing so overestimates the quiet Sun's secular effect.
The quiet-Sun magnetic-field changes of roughly 11–29 G implied by the original models contradict observations, which show no measurable secular quiet-Sun field change over the satellite era.
Long-term irradiance reconstructions should calibrate their secular amplitude against satellite-era TSI measurements rather than prescribing it from model atmospheres for an unobserved pre-industrial Sun.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the small secular trend is right, the Sun contributed even less to long-term climate change than current estimates assume, and paleoclimate analogies based on 'grand solar minima' lose most of their forcing basis — a consequence the paper hints at but does not develop.
The calibration may be partly blind: the satellite era covers only a small slice of the modulation-potential range, so a genuine slow quiet-Sun component that happened to be flat over 1978–2026 would escape the regression. A synthetic test — injecting a known large secular trend into the modulation-potential shape and checking whether the regression recovers it — would quantify this blind spot.
The fitted amplitude changes sign depending on the TSI composite (ACRIM gives a positive, physically unphysical γ), so a definitive resolution of the ACRIM-gap controversy would directly tighten or shift the secular estimate.
The isotope-to-neutron-monitor linking problem that inflated CHRONOS and PEA24 may affect other cosmogenic-isotope-based irradiance reconstructions; re-running them with geomagnetic-based modulation potentials would be a cheap consistency check.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this paper does a service by showing that the original CHRONOS and PEA24 models, with their published parameters, fit satellite TSI poorly, and that the large secular trends they claim are very likely overstated. I'm convinced of that qualitative conclusion. But the revised quantitative numbers in the abstract (0.1–0.44 W/m2 for CHRONOS, 0.2–0.25 W/m2 for PEA24) should not be treated as measurements; they are extrapolations of satellite-era fits to the Maunder Minimum.

The reformulation of CHRONOS in Eqs. 4–11 is clean and useful. The comparison in Table 2 is the paper's strongest evidence: applying the original gamma values to OW24/NMU17 and testing against direct TSI gives poor correlations and RMS >0.5 W/m2. That is a legitimate external test, not circular. The paper also deserves credit for being explicit about smoothing artifacts and for showing that the 22-year averaging and EMD are unstable at the edges.

The soft spots are mostly about the quantitative headline. Gamma is fit over a narrow range of omega(t) in the satellite era, then applied to Maunder-era omega, which is far outside the calibrated range. The same is true for N in PEA24. The paper acknowledges this in Section 5, but the abstract does not carry that caveat. Also, Table 3 shows negative secular changes for the CPMDF fits (-0.08 to -0.10 W/m2), while the abstract reports +0.1–0.44 W/m2; the positive range relies on the 'Mean' composite and ACRIM, which the paper elsewhere treats as problematic. That inconsistency needs fixing. The independent arguments from Rempel 2020 and quiet-Sun field observations are suggestive, not calibrating, and the paper says as much.

This paper deserves a serious referee. The qualitative conclusion is likely correct and important: the high-variability tail of TSI reconstructions is not supported by direct measurements. The quantitative secular values need more careful error treatment and a clearer presentation of which fits are physically meaningful. I'd send it to review, but I'd ask the authors to reconcile the abstract with Table 3 and to state more prominently that the Maunder projection is an extrapolation, not a fit.

Referee Report

4 major / 4 minor

Summary. The paper reassesses the large secular TSI increases (2.1–5.9 W m^-2 between the 1700 and 1986 minima) claimed by the CHRONOS and PEA24 models. It reformulates CHRONOS to isolate the quiet-Sun secular component, replaces the original cosmogenic-isotope-based modulation potentials with the geomagnetic-data-based OW24 and open-solar-flux series OSF2, changes the smoothing from 22-year averages/EMD to SSA, and fits the secular amplitude parameters γ (CHRONOS) and N (PEA24) to satellite-era TSI composites. The paper finds that the original γ values, when combined with OW24/NMU17, reproduce direct TSI poorly (Table 2: R = 0.25–0.65, RMS > 0.57 W m^-2), while fits to composites yield γ/N near zero, leading to revised secular changes of 0.1–0.44 W m^-2 (CHRONOS) and ~0.2–0.25 W m^-2 (PEA24). It concludes that the original large secular trends arose primarily from improper linking of cosmogenic isotope and neutron monitor records and from the adopted smoothing approach.

Significance. If the central conclusion holds, the paper would help settle a long-standing discrepancy in solar and climate forcing by providing a falsifiable external check on the high-variability CHRONOS and PEA24 reconstructions. The explicit reformulation of CHRONOS into a component with an isolated quiet-Sun secular term (Eqs. 7–11) is a useful methodological contribution. The comparison of published, not refitted, γ values against direct TSI is a legitimate external test, and the paper considers multiple TSI composites, modulation potentials, and smoothing procedures, which strengthens the qualitative conclusion that the original secular amplitudes are too large. However, the quantitative updated secular values are not independent predictions: they are obtained by regressing γ/N to the satellite era and then extrapolating the same constant parameter to the Maunder Minimum. The paper's own Section 5 concedes that the satellite-era record may not fully constrain centennial-scale quiet-Sun changes. The significance of the headline numbers is therefore conditional on a linear, constant-parameter extrapolation that is not directly tested by the data.

major comments (4)

[§3.1.3, Eq. (11); Table 3] The revised CHRONOS secular trend is obtained by fitting the constant γ in Eq. (11) to satellite-era TSI composites and then multiplying by ω(t) evaluated at the Maunder Minimum. The OW24 series covers only 1845–2020, and the satellite-era fit samples a narrow, comparatively flat part of ω(t); the 1700 value lies far outside this range. The formal error bars in Table 3 (e.g., −0.10 ± 0.17 W m^-2) reflect only the least-squares covariance, not the validity of the linear single-parameter ansatz or the uncertainty in the OW24/OSF2 secular shape. The manuscript itself states in Section 5 that 'the satellite-era TSI record spans only a limited range of long-term solar variability and therefore may not fully constrain possible centennial-scale changes in the quiet Sun.' To support the quantitative headline, the authors should either reframe it as explicitly conditional on the extrapolation or
[Table 3 vs. Abstract and §6] There is an internal inconsistency in the reported secular changes. Table 3 lists the CHRONOS 1700–1986 differences for the CPMDF-referenced fits as −0.08 to −0.10 W m^-2 (i.e., 1700 brighter than 1986), while the Abstract and §6 report a positive increase of '0.1–0.44 W m^-2.' The positive numbers appear to come from the 'Mean' composite (and possibly ACRIM) rather than from the full set of fits shown in Table 3. Similarly, for PEA24 with OSF2, Table 3 gives −0.25 and −0.20 W m^-2 for the CPMDF and Mean composites, yet the Abstract claims 'about 0.20–0.25 W m^-2' as a secular increase. The paper should report all composite-dependent results transparently and align the Abstract/§6 quantitative claims with Table 3, or explain explicitly which composite selection supports the stated range and why the others are excluded.
[§4.2, Eq. (15), Table 4] For the PEA24 model, most fits to direct TSI composites return negative or zero N (Table 4: e.g., −0.11 ± 0.03 for CPMDF/OSF1; 0.004 ± 0.030 for CPMDF/OSF2). The paper itself notes that negative N is not physically meaningful within the model. Yet §6 summarizes the PEA24 result as 'around 0.20–0.25 W m^-2' secular increase. This value appears to be the absolute value of the negative OSF2/CPMDF and OSF2/Mean entries in Table 3, which correspond to the Maunder Minimum being brighter than 1986. If those fits are unphysical, they cannot be used to support a positive secular increase. The quantitative PEA24 conclusion therefore needs to be either removed or substantially qualified.
[§6 and Abstract] The causal claim that the large original trends 'arose primarily from improper linking cosmogenic isotope and neutron monitor records, together with issues in the adopted smoothing approach' is stronger than what the analysis demonstrates. The paper changes three things simultaneously: the modulation potential series, the smoothing method, and (in the updated fits) the free amplitude parameter. The external test in Table 2 shows that the original γ values combined with OW24/NMU17 are inconsistent with direct TSI, but this does not isolate improper linking versus the adopted smoothing versus the physical assumption about the quiet-Sun atmosphere. The authors should soften the causal attribution to what is directly shown: that the original secular component, when combined with modern modulation-potential shapes, is not supported by satellite TSI, and that the best-fitting amplitude within

minor comments (4)

[§2.1/§2.3] The 'Mean' TSI series is used in Tables 1, 3, and 4 but is only loosely defined in Section 2.3 ('the mean, minimum, and maximum TSI values across all the selected composites'). Please specify exactly which composites enter the 'Mean' series and whether ACRIM is included.
[Figure 1] The text frequently refers to 'Fig. 2.1a)' etc., but the actual figure is labeled 'Fig. 1' with panels a–d. Please correct the internal cross-references.
[§3.1.3] The redefinition of φ_min using the 1880–1920 period is a major change relative to the original CHRONOS definition (the Spörer minimum). The implications for interpreting '1700–1986' differences should be stated more explicitly, since the normalization baseline is no longer the deepest minimum of the modulation-potential record.
[Appendix A] The discussion of SSA edge effects is useful, but the choice to retain 16 years rather than 22 years from the end of the series is justified only by two assumed future scenarios. Please make explicit that the fitted γ values would be slightly smaller under a weaker Cycle 25, and quantify this sensitivity.

Circularity Check

1 steps flagged · score 5.0 of 10

Original-model comparison is independent, but the updated CHRONOS/PEA24 secular numbers are the same one-parameter fits projected through the assumed secular shape.

fitted input called prediction [§3.1.3 / Eq. 11; §3.2 / Table 3; §4.1 / Eq. 15; §4.2 / Table 4; abstract]
"Here, instead of prescribing Fmin(λ), we treat γ as a free parameter and constrain it empirically by regressing Eq. 11 against observed TSI series. ... Table 1 also lists the resulting γ values obtained by regressing Eq. 11 to different TSI series ... Table 3 summarises the TSI changes between 1700 and the 1986 minimum obtained for the different CHRONOS reconstructions ... The resulting increase in the observationally constrained CHRONOS TSI reconstructions between 1700 and the 1986 minimum is approximately 0.08 W m−2 ... For CHRONOS, the implied TSI increase between the 1700 and 1986 minima l"

The updated secular amplitudes reported as results are not independently derived from Maunder-era evidence: in Eq. 11 the secular term is γω(t)αQS(t), and γ is obtained by regressing the same equation against satellite-era TSI composites (Table 1; analogously N via Eq. 15 and Table 4). The 1700–1986 difference is then γ̂ times the assumed ω/OSF secular-shape difference, so its smallness is inherited from the fit rather than newly constrained. The paper itself concedes (§5) that “the satellite-era TSI record spans only a limited range of long-term solar variability and therefore may not fully constrain possible centennial-scale changes in the quiet Sun.” What is independent is the falsification of the original large γ values against satellite TSI, plus the Rempel/quiet-Sun arguments boundin

full rationale

The paper’s core negative result—published CHRONOS/PEA24 secular amplitudes are inconsistent with direct satellite-era TSI—is a genuine, non-circular comparison: the large γ values recovered by reproducing Egorova et al. (2018) are applied to the OW24/NMU17 shape and fail against independent TSI composites (Table 2). Independent support from Rempel (2020) MHD scaling and quiet-Sun magnetic-field observations also does not depend on the disputed fits. What keeps this from being a clean non-finding is that the paper’s headline updated values (abstract: CHRONOS 0.1–0.44 W m−2, PEA24 0.20–0.25 W m−2) are deterministic functions of the same γ/N fitted to the satellite composites, projected through an assumed linear secular shape. Thus those specific numbers are by-construction consequences of the calibration, and the Maunder extrapolation carries the full load. The reliance on OW24/OSF2 from co-author Owens is heavy but not uniquely circular, since OW24 is an externally published reconstruction; however, the “improper linking” explanation leans on it. Score 5 reflects partial circularity in the updated quantitative headline while the original-model falsification remains independent.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central reconstruction depends on the linear CHRONOS ansatz (Eq. 11), the validity of OW24/NMU17/OSF2 as secular anchors, and the assumption that satellite-era fitting constrains the Maunder-era amplitude. None of these is derived in the paper; γ and N are the explicit fitted free parameters.

free parameters (4)

γ (CHRONOS quiet-Sun secular amplitude) = -1.54 to -3.21 W/m² (to reproduce published CHRONOS); -0.01 ± 0.04 (CPMDF), 0.38 ± 0.11 (ACRIM), 0.13 ± 0.03 (Mean)
Central free parameter in Eq. 11; sets the amplitude of the quiet-Sun secular term. Determined by least-squares regression to published TSI reconstructions or satellite TSI composites (Table 1).
N (PEA24 secular scaling) = 0.31 ± 0.03 (to reproduce Penza et al. 2024); -0.11 to 0.004 (CPMDF/OSF1/2), -0.23/-0.19 (ACRIM), -0.20/-0.05 (Mean)
Controls the amplitude of the FLT(t) term in Eq. 15; determined by regression to TSI composites (Table 4).
OW24 calibration parameters φ0, n, A, B (inherited) = Not given in this paper; calibrated in Owens et al. (2024) to neutron monitor data
Eq. 1 is used to build the OW24 modulation potential; its secular shape anchors the revised CHRONOS/PEA24 trends. The reliability claim is inherited by citation.
SSA smoothing windows = 22 years (CHRONOS), 14 years (PEA24)
Hand-selected; the 14-year width was chosen to mimic the EMD approach of Penza et al. (2024). Edge exclusions (16/14 years) affect ω near the satellite era and hence the fitted γ/N.

assumptions (6)

domain assumption The force-field modulation potential φ is an adequate proxy for long-term quiet-Sun irradiance variability.
Used throughout to set the secular shape of the CHRONOS quiet-Sun term (Eq. 4). Not derived in the paper.
ad hoc to paper Quiet-Sun irradiance scales linearly with modulation potential with a single constant amplitude γ from the satellite era back to the Maunder Minimum.
Eq. 11 is the load-bearing linear ansatz; the paper re-fits γ to satellite data but does not test whether the same linear scaling holds at Maunder-like modulation-potential values.
domain assumption Satellite-era TSI composites are accurate on annual-to-decadal scales and can constrain the secular amplitude.
The calibration of γ and N in Tables 1 and 4 assumes the direct TSI composites faithfully represent the small slow variation in the satellite era.
domain assumption The OW24, NMU17, and Lockwood & Owens OSF2 reconstructions are reliable secular anchors connecting cosmogenic isotopes to neutron monitor data.
The paper relies on Owens et al. (2024) and Lockwood & Owens (2024) rather than independently re-deriving these reconstructions (§2.2, §5).
domain assumption Active-region filling factors derived from sunspot numbers/areas and plage areas, with time-invariant component spectra, adequately capture cycle-scale irradiance variability.
Standard CHRONOS/PEA24 machinery (Eqs. 3, 12–17); not the focus of the paper but required for the secular decomposition.
domain assumption Slowly varying SSA/EMD components represent the secular solar signal rather than smoothing artifacts.
The entire PEA24 reassessment depends on the low-frequency component FLT(t) being a meaningful solar signal rather than a numerical edge/mode-mixing artifact (§4.1.2, Appendix A).

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Cite this review

Pith. "Pith review of Re-evaluating solar irradiance reconstructions: No evidence for large secular trends." pith.science (2026). https://pith.science/paper/OR5N64QK

@misc{pith2026260714377,
  author       = {Pith},
  title        = {Pith review of: Re-evaluating solar irradiance reconstructions: No evidence for large secular trends},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OR5N64QK}},
  note         = {Machine review of arXiv:2607.14377}
}

abstract

Most current irradiance reconstructions suggest only a modest secular increase in TSI between the 1700 and 1986 activity minima ($<1$ Wm$^{-2}$). However, 2 models, the CHRONOS and Penza et al. (2024; PEA24) models, suggest substantially larger changes of 2.1-5.9 Wm$^{-2}$. Although the two models differ in their architecture, both use cosmogenic isotope records combined with neutron monitor data to describe the long-term irradiance variability. However, cross-calibrating modulation potential reconstructions from cosmogenic isotopes against neutron monitor data remains highly uncertain. We reassess the origin and the magnitude of the large secular trends in the CHRONOS and PEA24 models. We update the CHRONOS and PEA24 models using recent heliospheric modulation potential and open solar flux reconstructions based on geomagnetic data and neutron monitor measurements, which provide a more reliable connection between cosmogenic isotope and neutron monitor records. These allow the secular component of the reconstructions to be extended consistently to the satellite era and compare the resulting TSI reconstructions with direct TSI measurements. We find that the original CHRONOS and PEA24 reconstructions substantially overestimated the secular variability in irradiance. When constrained by direct TSI measurements, CHRONOS yields a TSI increase of about 0.1-0.44 Wm$^{-2}$ between the 1700 and 1986 minima, while PEA24 returns about 0.2-0.25 Wm$^{-2}$. Our analysis indicates that the previously inferred large secular trends arose primarily from improper linking cosmogenic isotope and neutron monitor records, together with issues in the adopted smoothing approach. The updated reconstructions presented here point toward a relatively modest secular increase in TSI since the Maunder Minimum, likely below 1 Wm$^{-2}$, consistent with the majority of current irradiance models.

Figures

Figures reproduced from arXiv: 2607.14377 by the authors.

**Figure 1.** Panel a): Solar modulation potential series used in this study. Panel b): Normalised modulation potential: Parameter ω (Eq. 5); see Sect. 3.1 for a complete definition. Panel c): Estimated secular component of the quiet-Sun irradiance, FQS (t) − FC, required for our CHRONOS reconstruction to reproduce the published TSI reconstructions of Egorova et al. (2018) for the corresponding modulation potential, as well as th… view at source ↗

**Figure 2.** Panels a-b: TSI reconstructed with the CHRONOS model using the Usoskin et al. (2017) modulation potential from neutron monitor data connected to the OW24 series. The reconstructions use γ values obtained by fitting our CHRONOS reconstructions, based on the four modulation potentials employed by Egorova et al. (2018), to the corresponding TSI reconstructions of Egorova et al. (2018, referred to as Eg18; orange for US… view at source ↗

**Figure 3.** TSI reconstructed with the model by Penza et al. (2024). Shown are the reconstructions based on OSF1 and OSF2, with the scaling parameter N determined either by fitting to the original Penza et al. (2024) reconstruction (orange and red, respectively) or to the CPMDF TSI composite (green and purple, respectively; nearly overlapping). The original Penza et al. (2024) reconstruction is shown in blue. Also shown (only i… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Comparison between the CHRONOS and PEA24 TSI reconstructions produced in this study and other long-term TSI reconstructions. Our CHRONOS reconstruction was done with the MU16 modulation potential, while our PEA24 reconstruction with OSF2, the free parameters of both mo…

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