🔭 astrophysics

Reconstruction of annual solar irradiance over the last three millennia

This paper presents the first physics-based, annually resolved reconstruction of total solar irradiance over the last three millennia by extending the SATIRE-T model using cosmogenic isotope-derived sunspot records, revealing a maximum variation of approximately 1.04 W/m² in 50-year running means.

Original authors: D. Temaj, N. A. Krivova, S. K. Solanki, I. G. Usoskin, T. Chatzistergos

Published 2026-05-22

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CC BY 4.0

Original authors: D. Temaj, N. A. Krivova, S. K. Solanki, I. G. Usoskin, T. Chatzistergos

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun as a giant, glowing campfire that keeps our planet warm. For most of human history, we've only been able to measure how bright this fire is for the last 40 years (since we put satellites in space). But to understand how the Earth's climate changes over centuries or millennia, we need to know how bright that fire was thousands of years ago.

This paper is like building a time machine for sunlight. The authors have created the first detailed, year-by-year record of how much energy the Sun has been sending to Earth over the last 3,000 years.

Here is how they did it, using simple analogies:

1. The Problem: We Only Have a Short Video

We have a high-definition video of the Sun's brightness from 1978 to today. But before that? We only have blurry, old sketches (sunspot counts) from the last 400 years, and before that, we had nothing direct.

2. The Clues: Cosmic "Fingerprints"

To figure out what happened before we had telescopes, the scientists used a clever trick. They looked at tree rings.

The Analogy: Think of the Sun's magnetic activity as a shield. When the shield is strong, it blocks cosmic rays (particles from deep space) from hitting Earth. When the shield is weak, more cosmic rays hit our atmosphere and get trapped in tree rings as a special type of carbon (Carbon-14).
The Detective Work: Scientists have recently figured out how to read these tree rings to estimate how many sunspots the Sun had, year by year, for the last 3,000 years. It's like reading the "footprints" left behind by the Sun's activity.

3. The Engine: A Physics Simulator

Knowing the number of sunspots isn't enough to know the total brightness, because the Sun isn't just dark spots; it also has bright patches (faculae) that make it shine brighter.

The Tool: The authors used a sophisticated computer model called SATIRE-T. Think of this model as a recipe book that tells you exactly how much the Sun's brightness changes based on its magnetic "ingredients."
The Innovation: In the past, this recipe book only worked well when you had daily observations. The authors updated the recipe so it works even when you only have a yearly summary (like a yearly weather report instead of a daily log). They fed the "tree ring" sunspot data into this model to simulate the Sun's brightness for every single year of the last three millennia.

4. The Results: A Gentle Wobble

What did they find?

The Big Picture: Over 3,000 years, the Sun's brightness hasn't changed wildly. It's more like a gentle wave than a rollercoaster.
The Numbers: The difference between the Sun's brightest 50-year period and its dimmest 50-year period is about 1 Watt per square meter.
- Analogy: Imagine the Sun is a 1,360-watt lightbulb. The difference between its "max" and "min" over 3,000 years is like flicking a tiny switch that adds or removes just one single watt. It's a very small change, but over centuries, it matters for Earth's climate.
The "Grand Minima": The model successfully captured famous "dark ages" of the Sun (like the Maunder Minimum), where the Sun was very quiet. The model shows that even when sunspots disappear, the Sun doesn't go completely dark; it just settles into a low, steady background glow.

5. Why This Matters

This paper provides the first year-by-year physics-based record of solar energy for the pre-telescope era.

Before this, we only had rough, 10-year averages for that time.
Now, scientists have a precise "fuel gauge" for the Sun that stretches back 2,500 years before we ever looked through a telescope.

In summary: The authors took ancient tree-ring data, fed it into a physics engine, and generated a continuous, year-by-year movie of the Sun's brightness for the last 3,000 years, showing us that our star has been remarkably stable, with only tiny, slow ripples in its energy output.

Technical Summary: Reconstruction of Annual Solar Irradiance over the Last Three Millennia

Problem Statement
Direct measurements of Total Solar Irradiance (TSI) are limited to the satellite era (since 1978), leaving a significant gap in understanding solar variability on timescales longer than a few decades. While sunspot numbers (SN) provide a direct observational record extending back four centuries, they represent only the dark component of solar surface magnetism. They offer no direct information on bright magnetic features (faculae and network) which dominate irradiance variability on solar-cycle and longer timescales. Consequently, irradiance reconstructions based solely on SN must indirectly infer the total magnetic field evolution, a limitation that becomes critical during prolonged periods of very low activity (grand minima) when SN approaches zero. Previous physics-based reconstructions over the Holocene were restricted to decadal resolution due to the low signal-to-noise ratio in cosmogenic isotope data.

Methodology
The authors present a physics-based reconstruction of annual TSI over the last three millennia by extending the SATIRE-T (Spectral And Total Irradiance REconstructions) model beyond the telescopic era. The methodology relies on the following components:

Model Framework: The study utilizes the SATIRE-T model as revised and optimized in Temaj et al. (2026, "Paper 1"). This model computes irradiance variability from the fractional disc coverage of sunspots, faculae, and network regions, derived from the temporal evolution of the solar surface magnetic field. The magnetic flux evolution is governed by coupled ordinary differential equations accounting for flux emergence, transport, and decay. Crucially, the model incorporates a revised emergence model (Krivova et al. 2021) where magnetic regions of all sizes emerge according to a single power-law distribution. This ensures a continuous emergence of small-scale magnetic flux even during periods of zero or near-zero sunspot numbers, maintaining a realistic background magnetic field.
Input Data: The model is driven by annually resolved sunspot number reconstructions derived from cosmogenic isotope records (specifically $^{14}$ C in tree rings) by Usoskin et al. (2021, 2025, 2026). These datasets cover the periods 971–1899 CE, 997–1 BCE, and 1–969 CE.
Temporal Resolution Handling: Since the magnetic flux evolution model operates at a daily cadence, the annual SN inputs are converted to daily time series using a "box-car" representation, where the annual SN value is assigned uniformly to all days of the corresponding year. This preserves the annual mean exactly.
Handling Negative Values: The $^{14}$ C-based SN reconstructions occasionally yield slightly negative values during grand minima due to statistical noise. The authors retain these values as they reflect the underlying modulation of cosmic rays. For SN < 0, the activity-dependent slope of the flux-emergence distribution is linearly extrapolated from the lowest positive values, a choice deemed to have a negligible impact on the reconstructed irradiance given the vanishingly weak flux emergence in this regime.
Validation: The reconstruction is validated against the telescopic-era record (using ISNv2, GSN, and other datasets) and independent geomagnetic index reconstructions (Lockwood & Owens 2024).

Key Contributions

First Annual Physics-Based Reconstruction: This work provides the first physics-based, annually resolved reconstruction of TSI for the pre-telescopic era, extending the record by more than 2.5 millennia.
Consistency Across Eras: By applying the same physical model and parameters used for the telescopic era to the cosmogenic isotope-derived SN inputs, the study ensures a physically consistent extension of the irradiance record.
Resolution of Grand Minima: The approach addresses the limitation of previous SN-only models during grand minima by utilizing a flux emergence model that does not rely solely on the presence of sunspots to generate a background magnetic field.

Results

TSI Variability: Over the full three-millennia interval, the reconstructed TSI exhibits a maximum difference of $1.04^{+0.14}_{-0.2}$ W m $^{-2}$ between the maximum and minimum of the 50-year running mean values. The uncertainty range (0.84–1.18 W m $^{-2}$ ) reflects the spread obtained by driving the model with the upper and lower bounds of the $^{14}$ C-based SN reconstruction.
Comparison with Previous Work: The inferred amplitude of secular variability lies at the lower end of previously published multi-millennial reconstructions. The authors note that such comparisons are inherently limited by differences in temporal resolution and that long-term variability magnitudes are effectively constrained by the model's calibration to modern observations rather than the millennial extension itself.
Consistency Checks: The $^{14}$ C-based TSI reconstruction falls well within the range of uncertainties derived from alternative telescopic sunspot datasets (e.g., ISNv2 vs. CEA17 GSN) during the overlap period (1600–1900). The reconstructed Open Solar Flux (OSF) is also consistent with independent geomagnetic reconstructions.
Behavior at Low Activity: During extended minima, the reconstruction primarily constrains the mean activity level rather than resolving specific solar cycles. The authors note a slight asymmetry where positive excursions around zero SN increase TSI more effectively than negative excursions reduce it, potentially leading to a slight upward bias in time-averaged TSI during grand minima.

Significance
The paper claims to provide an important record for studies requiring long-term, annually resolved solar forcing. By demonstrating that annually resolved irradiance variability can be reconstructed in a physically consistent manner beyond the period of direct solar observations, this work bridges the gap between satellite-era measurements and the Holocene climate record. The authors emphasize that while the reconstruction is an extension of the validated SATIRE-T model, the magnitude of long-term variability remains constrained by the model's formulation and calibration to modern data. The resulting dataset is made available to the community for use in solar-terrestrial relation studies.

1. The Problem: We Only Have a Short Video

2. The Clues: Cosmic "Fingerprints"

3. The Engine: A Physics Simulator

4. The Results: A Gentle Wobble

5. Why This Matters

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