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Solar Irradiance Reconstruction over the Telescopic Era Using a Revised Photospheric Magnetic Field Model

D. Temaj, N. A. Krivova, T. Chatzistergos, S. K. Solanki, B. Hofer

Abstract

The Sun is the primary source of energy for Earth and one of the main external drivers of its climate. Solar irradiance -- the radiative power emitted by the Sun and received at 1-AU -- varies on all observable timescales. It is measured as total solar irradiance (TSI), the spectrally integrated flux, or as spectral solar irradiance (SSI), its wavelength-dependent distribution. However, direct space-based irradiance measurements span only about five decades and are too short to capture long-term trends, making reconstructions crucial for studying solar influence on climate. On climate-relevant timescales, irradiance variations are driven by changes in the solar surface magnetic field, which form the basis of reconstructions guided by physics. Here we present revised reconstructions of TSI and SSI over the past four centuries using the physics-based SATIRE-T (Spectral And Total Irradiance REconstruction, for the Telescopic era) model. SATIRE-T relates irradiance variability to the evolution of the solar surface magnetic field inferred from sunspot number records. In this work, we implement a recently revised description of magnetic field evolution that more realistically links the emergence of small-scale magnetic features to sunspot activity, constrained by modern observations. Using two independent sunspot number series as input, we obtain consistent reconstructions of magnetic flux and solar irradiance. The model reproduces the observed or independently reconstructed total and open magnetic flux, and agrees closely with satellite measurements of TSI and Lyman-$α$ irradiance, with correlation coefficients of 0.81-0.98 for 81-day-smoothed space-based TSI records, 0.69-0.85 for TSI at daily cadence, and 0.92 for daily Lyman-$α$ irradiance. On secular timescales, the reconstructed TSI increases by 0.67-0.75$\,\mathrm{W/m^2}$ between the 50-year means over 1650-1700 and 1967-2017.

Solar Irradiance Reconstruction over the Telescopic Era Using a Revised Photospheric Magnetic Field Model

Abstract

The Sun is the primary source of energy for Earth and one of the main external drivers of its climate. Solar irradiance -- the radiative power emitted by the Sun and received at 1-AU -- varies on all observable timescales. It is measured as total solar irradiance (TSI), the spectrally integrated flux, or as spectral solar irradiance (SSI), its wavelength-dependent distribution. However, direct space-based irradiance measurements span only about five decades and are too short to capture long-term trends, making reconstructions crucial for studying solar influence on climate. On climate-relevant timescales, irradiance variations are driven by changes in the solar surface magnetic field, which form the basis of reconstructions guided by physics. Here we present revised reconstructions of TSI and SSI over the past four centuries using the physics-based SATIRE-T (Spectral And Total Irradiance REconstruction, for the Telescopic era) model. SATIRE-T relates irradiance variability to the evolution of the solar surface magnetic field inferred from sunspot number records. In this work, we implement a recently revised description of magnetic field evolution that more realistically links the emergence of small-scale magnetic features to sunspot activity, constrained by modern observations. Using two independent sunspot number series as input, we obtain consistent reconstructions of magnetic flux and solar irradiance. The model reproduces the observed or independently reconstructed total and open magnetic flux, and agrees closely with satellite measurements of TSI and Lyman- irradiance, with correlation coefficients of 0.81-0.98 for 81-day-smoothed space-based TSI records, 0.69-0.85 for TSI at daily cadence, and 0.92 for daily Lyman- irradiance. On secular timescales, the reconstructed TSI increases by 0.67-0.75 between the 50-year means over 1650-1700 and 1967-2017.
Paper Structure (18 sections, 8 equations, 9 figures, 4 tables)

This paper contains 18 sections, 8 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Data
  3. Input data
  4. Data used for the optimisation process
  5. Data used for validation and comparisons
  6. Open magnetic flux.
  7. Total solar irradiance TSI.
  8. Spectral solar irradiance SSI.
  9. Model
  10. Magnetic field evolution
  11. Modeling irradiance variability
  12. Optimisation of model parameters
  13. Results
  14. Magnetic flux
  15. Solar irradiance reconstruction
  16. ...and 3 more sections

Figures (9)

  • Figure 1: Evolution of the open magnetic flux over time. Our reconstruction is shown in red for the ISNv2 input (top panel) and the CEA17 GSN (bottom panel), both at one-CR cadence. In dark and light green, we show the OSF from lockwood_reconstruction_2024, reconstructed from the geomagnetic aa-index for 13-CR and 1-CR cadence, respectively. The blue dashed line shows the in-situ OSF measurements from owens_sunward_2017 and the black dashed line shows the OSF estimates from lockwood_excess_2009.
  • Figure 2: OSF reconstruction from this study (red) and by krivova_modelling_2021 using ISNv2 (top) and GSN (bottom; CEA17 here and HoSc98 in krivova_modelling_2021) as input. The pink shaded area shows our upper limit estimate for the Maunder Minimum, where the SN from carrasco_numerical_2025 was used as input. Black: OSF reconstructed from the cosmogenic isotope data by wu_solar_2018.
  • Figure 3: a) Reconstructed TSI using ISNv2 as input (pink: daily values; red: 81-day smoothing). Blue dots and blue line: the TSI composite of montillet_data_2022. b) Difference between our reconstruction and the montillet_data_2022 composite (blue dots: daily; blue line: 81-day smoothing). The horizontal black dashed line marks zero, and the orange line is the linear fit to the daily residuals. c) and d) same as a) and b), but using the CEA17 GSN as an input to the model. e) Our TSI reconstructions based on ISNv2 and CEA17 (red and black). For comparison, the montillet_data_2022 composite, the TSI reconstruction of wu_solar_2018, and that of chatzistergos_revisiting_2025 are shown. All datasets in panel e) are shown as 81-day (faint lines) and annual moving means (solid lines).
  • Figure 4: Reconstructed TSI (annual means) since 1700 using ISNv2 (red) and CEA17 GSN (black) as input. The pink shaded area shows our upper limit estimate in TSI, where the carrasco_numerical_2025 SN were used. The TSI composite of montillet_data_2022 is shown in blue; the TSI reconstruction of wu_solar_2018 in green.
  • Figure 5: Total solar irradiance (TSI) reconstruction based on ISNv2 as an input (red). The green and black curves show the contribution of different components of magnetic flux to TSI. Green shows the contribution of AR magnetic flux to TSI, and black shows the contribution of small-scale emergences. Thin and thick lines show the annual means or 11-year running means, respectively.
  • ...and 4 more figures