# Centennial Total Solar Irradiance Variation

^{1}

^{2}

^{3}

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## Abstract

**:**

^{2}. The daily TSI regression model uses the MgII core to wing ratio as a facular brightening proxy and the Photometric Sunspot Index (PSI) as a measure of sunspot darkening. We reconstruct the annual mean TSI backwards to 1700 based on the Sunspot Number (SN), calibrated on the space measurements with an RMSE of 0.086 W/m

^{2}. The analysis of the 11 year running mean TSI reconstruction confirms the existence of a 105 year Gleissberg cycle. The TSI level of the current grand minimum is only about 0.15 W/m

^{2}higher than the TSI level of the grand minimum in the beginning of the 18th century.

## 1. Introduction

^{2}over a period of about 300 years. Table 1 gives an overview of the TSI increase since the Maunder Minimum found by different studies.

^{2}.

## 2. Materials and Methods

#### 2.1. TSI Composite

- The $TS{I}_{i}\left(t\right)$ are scaled with an instrument adjustment factor ${a}_{i}$, such that the adjusted time series ${a}_{i}TS{I}_{i}\left(t\right)$ have the same absolute level. The reference absolute level is the one from the Differential Absolute Radiometer (DIARAD) instrument, as part of the Solar Variability and Irradiance Monitor (SOVIM) experiment on the International Space Station (ISS) [24], with application of the new calibration procedure of [25]. The corresponding TSI level at solar minimum, also known as the quiet sun TSI level, is 1362.9 W/m
^{2}. - The adjusted time series ${a}_{i}TS{I}_{i}\left(t\right)$ are quality-controlled by intercomparison. Parts of individual time series which differ too much from the other time series—for details, see [9]—are removed, and the Total Irradiance Monitor (TIM) on the Solar Radiation and Climate Experiment (SORCE) satellite [26] is corrected for its apparent linear drift compared to the other TSI radiometers. This results in quality-controlled adjusted time series ${a}_{i}TS{I}_{i}^{qc}\left(t\right)$.
- For every day t, the composite $TSI\left(t\right)$ is calculated as the mean of the available time series ${a}_{i}TS{I}_{i}^{qc}\left(t\right)$:$$TSI\left(t\right)=\frac{{\sum}_{i}{a}_{i}TS{I}_{i}^{qc}\left(t\right)}{{\sum}_{i}}$$

#### 2.2. Daily TSI Regression Model

^{2}and a correlation coefficient of 0.89.

^{2}and a correlation coefficient of 0.94.

^{2}is shown as the yellow line in Figure 2.

## 3. Results

- The above-mentioned MgII index, extending from 1979 to 2020;
- The above-mentioned F10.7 radio flux, extending from 1948 to 2020;
- The SILSO SN, extending from 1700 to 2020.

^{2}.

^{2}.

^{2}.

- The purple curve shows the difference between the SN-based model and the F10.7-based model.
- The green curve shows the difference between the SN-based model and the MgII-based model.
- The light blue curve shows the difference between the SN-based model and the composite TSI observations.

^{2}, which we will adopt as an uncertainty estimate of the SN-based long-term TSI reconstruction.

^{2}. The corresponding variation of the solar forcing is 4 times smaller, so equal to 0.7/4 = 0.175 W/m

^{2}. Factor 4 is the ratio of the surface of a sphere to the surface of a circle with the same radius. The centennial solar variability is 5.6% of the estimated 3.1 W/m

^{2}greenhouse gas radiative forcing in 2015 [47]. Over the last 50 years, the TSI varied by approximately −0.5 W/m

^{2}(a drop from 1363.7 W/m

^{2}to 1363.2 W/m

^{2}, see Figure 5). Using the same factor 4 as earlier, the sun has caused a modest radiative cooling of −0.5/4 = −0.125 W/m

^{2}over the last 50 years, which was not sufficient to counteract the strong radiative warming from greenhouse gases.

^{2}, indicated by the green line in Figure 5.

## 4. Discussion

^{2}lower then its mean value from 1980 to 1986. The theory of the Grand Modern Maximum had to be abandoned after the revision of the sunspot number [20] and after the occurrence of the low solar cycle 24 occurring between 2008 and 2019—see Figure 3. Therefore, the long-term TSI reconstruction needs to be revised.

^{2}and a correlation coefficient as high as 0.94 from a regression model based only on a facular brightening proxy and a sunspot darkening estimate. There is no evidence that other physical effects other than facular brightening and sunspot darkening, both linked to the magnetic field on the solar surface, are needed to explain observed TSI variations.

^{2}, 0.081 W/m

^{2}and 0.086 W/m

^{2}, respectively. Prior to the used TSI space observations, the annual TSI extrapolations using any of these proxies agree well during their period of overlap, giving confidence in the soundness of the extrapolation. From the comparison of the sunspot-based TSI model with the other TSI estimates during their period of overlap, the stability of the annual mean sunspot-based TSI reconstruction is estimated to be ±0.25 W/m

^{2}. A TSI reconstruction similar to ours was used in [49] for an adequate reconstruction of global temperature change from 1850 to 2019, increasing the confidence in the validity of our TSI reconstruction.

^{2}, while the TSI levels during the later grand minima, in the beginning of the 20th and 21st centuries are also comparable, around 1363.2 W/m

^{2}, only 0.15 W/m

^{2}higher than the earlier grand minima. Clearly, this small TSI level variation cannot explain the occurrence of the LIA.

## 5. Conclusions

^{2}and a correlation coefficient of 0.94 by a regression model using the MgII core-to-wing ratio facular brightening proxy and the PSI sunspot darkening estimate. The annual mean TSI model agrees with the TSI space measurements with an RMSE of 0.086 W/m

^{2}and has an estimated stability of ±0.25 W/m

^{2}. The analysis of the 11 year running mean TSI reconstruction confirms the existence of a 105 year Gleissberg cycle with grand minima occurring in the beginning of each century. The TSI level of the latest grand minimum is only 0.15 W/m

^{2}higher than the TSI level of the earliest grand minimum.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ACRIM | Active Cavity Radiometer Irradiance Monitor |

DIARAD | Differential Absolute Radiometer |

ECV | Essential Climate Variable |

ERB | Earth Radiation Budget |

ERBS | Earth Radiation Budget Satellite |

ISS | International Space Station |

LIA | Little Ice Age |

PMO | Physikalishes und Meteorologisches Observatorium |

PREMOS | Precision Monitoring of Solar variability |

PSI | Photometric Sunspot Index |

RMSE | Root Mean Square Error |

SILSO | Sunspot Index and Long-term Solar Observations |

SN | Sunspot Number |

SORCE | Solar Radiation and Climate Explorer |

SOVA | Solar Variability |

SOVIM | Solar Variability and Irradiance Monitor |

TCTE | Total Solar Irradiance Calibration Transfer Experiment |

TIM | Total Irradiance Monitor |

TSI | Total Solar Irradiance |

TSIS | Total and spectral Solar Irradiance Sensor |

VIRGO | Variability of Irradiance and Gravity Oscillations |

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**Figure 1.**The 121 day running means of individual TSI instrument measurements and resulting composite after adjustment/homogenisation of the absolute level and quality control by intercomparison.

**Figure 2.**Purple curve: daily mean composite TSI values. Green curve: 121 day running mean composite TSI values. Light blue curve: 121 day running mean of TSI regression model based on F10.7 radio flux and Photometric Sunspot Index (PSI). Orange curve: 121 day running mean of TSI regression model based on MgII core to wing ratio and PSI.

**Figure 3.**Orange curve: annual mean TSI observations from 1992 to 2020. Light blue curve: annual mean MgII-based TSI model from 1979 to 2020. Green curve: annual mean F10.7-based model from 1948 to 2020. Purple curve: annual mean SN-based model from 1700 to 2020.

**Figure 4.**Difference between Sunspot-based annual mean TSI and other TSI estimates. Purple curve: difference with F10.7-based TSI Model. Green curve: difference with MgII-based TSI Model. Light blue curve: difference with Composite TSI Observations.

**Figure 5.**Purple curve: 11 year running mean of annual TSI between 1700 and 2020. Green line: long-term average of the TSI from 1700 to 2020: 1363.4 W/m

^{2}.

**Figure 6.**Root Mean Square Difference (RMSD) as a function of the time shift ${T}^{\prime}$ between the last 100 years of the 11 year running mean TSI variation and the 2 earlier periods, see Equation (7).

**Figure 7.**Purple curve, right scale: global temperature change. Green curve, left scale: greenhouse gas radiative forcing. Blue curve, left scale: solar radiative forcing. Ochre curve, left scale: combined greenhouse gas and solar radiative forcing.

Reference | TSI Increase Since Maunder Minimum |
---|---|

[15] | 3.3 W/m^{2} |

[16] | 1.3 W/m^{2} |

[14] | 1.25 W/m^{2} |

[17] | 6 W/m^{2} |

[18] | 0.34 W/m^{2} |

[19] | 0.93 W/m^{2} |

**Table 2.**Characteristics of individual TSI instrument time series. The instrument acronyms are listed at the end of the paper.

Instrument | Reference | Start | End | a_{i} |
---|---|---|---|---|

ACRIM 2 | [30] | 1991 | 2001 | 0.999220 |

SOVA 1 | [32] | 1992 | 1993 | 0.998723 |

SOVA 2 | [32] | 1992 | 1993 | 0.99744 |

DIARAD/VIRGO | [33] | 1997 | 2017 | 0.997873 |

PMO-6/VIRGO | [33] | 1997 | 2017 | 0.998241 |

ACRIM 3 | [6] | 2002 | 2013 | 1.001572 |

TIM/SORCE | [26,34] | 2003 | 2017 | 1.0039663 |

SOVA-Picard | [25,35] | 2010 | 2013 | 1.001152 |

PREMOS | [36] | 2010 | 2013 | 1.001719 |

TIM/TCTE | [27] | 2013 | 2019 | 1.001267 |

TIM/TSIS 1 | [28] | 2018 | 2021 | 1.001014 |

Instrument | RMSD (W/m^{2}) |
---|---|

ACRIM 2 | 0.16 |

DIARAD/VIRGO | 0.10 |

PMO-6/VIRGO | 0.12 |

TIM/SORCE | 0.15 |

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**MDPI and ACS Style**

Dewitte, S.; Cornelis, J.; Meftah, M. Centennial Total Solar Irradiance Variation. *Remote Sens.* **2022**, *14*, 1072.
https://doi.org/10.3390/rs14051072

**AMA Style**

Dewitte S, Cornelis J, Meftah M. Centennial Total Solar Irradiance Variation. *Remote Sensing*. 2022; 14(5):1072.
https://doi.org/10.3390/rs14051072

**Chicago/Turabian Style**

Dewitte, Steven, Jan Cornelis, and Mustapha Meftah. 2022. "Centennial Total Solar Irradiance Variation" *Remote Sensing* 14, no. 5: 1072.
https://doi.org/10.3390/rs14051072