Total Solar Irradiance (TSI) quantifies the solar energy received by the Earth and therefore is of direct relevance for a possible solar influence on climate change on Earth. We analyse the TSI space measurements from 1991 to 2021, and we derive a regression model that reproduces the measured daily TSI variations with a Root Mean Square Error (RMSE) of 0.17 W/m2. 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/m2. 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/m2 higher than the TSI level of the grand minimum in the beginning of the 18th century.
The climate on Earth is determined by the balance between the incoming solar radiation—quantified by the Total Solar Irradiance (TSI)—and the outgoing terrestrial radiation. A change in TSI is a solar force of climate change on Earth; therefore, the TSI needs to be monitored as an Essential Climate Variable (ECV) .
The first measurement of TSI from space was made in 1969 , and continuous monitoring of the TSI with space radiometers started in 1978 . In general, TSI radiometers measure at different absolute levels , and are subject to ageing due to solar exposure . Several authors have proposed so-called TSI composite time series quantifying the long-term TSI variation as measured by the space instruments [5,6,7,8,9].
From the available TSI composites, it is now well-established that the TSI varies in phase with the 11 year sunspot cycle . In particular, there is a short-term TSI decrease—referred to as sunspot darkening—when a sunspot characterised by a strong surface magnetic field occurs. There is also a longer-term TSI increase—referred to as facular brightening—caused by the facula, characterised by an intermediate-strength magnetic field, which form when a sunspot decays and which have a significantly longer lifetime than the original sunspot.
On top of the 11 year solar cycle TSI variation, there exists a longer-term variation of the ’quiet sun’ . The TSI level observed during the 11 year cycle minima has long been a matter of speculation. Following , it was believed that the sun evolved from the so-called ’Maunder Minimum’ from about 1645 until 1715 when the 11 year cycle amplitude was minimal, to a so-called ’Grand Modern Maximum’ , where the 11 year cycle amplitude is supposed to be maximal. Centennial TSI reconstructions, such as the one of , used for the characterisation of solar climate forcing by the Intergovernmental Panel on Climate Change (IPCC), include a slow increase in the ’quiet sun’ TSI level from the Maunder Minimum to the Grand Modern Maximum by 1.25 W/m2 over a period of about 300 years. Table 1 gives an overview of the TSI increase since the Maunder Minimum found by different studies.
Table 1. List of various studies on the TSI increase since the Maunder Minimum.
Recently, the Sunspot Index and Long-term Solar Observations (SILSO) Sunspot Number (SN) have been revised [20,21]. Following the latest insights, the Grand Modern Maximum does not exist, and so the 300 year increase in the TSI level from the Maunder Minimum to the Grand Modern Maximum should also be revisited. Independently from the SN revision, from an analysis of the extended 2008–2009 solar minimum, ref.  came to the conclusion that the TSI increase from the Maunder Minimum to the present needs to be revised. In addition, the careful intercomparison of all available space radiometer TSI time series in  indicates no variation of the quiet sun TSI level over a 32 year period from 1984 to 2016 within a 95% uncertainty of ±0.17 W/m2.
The goal of this paper is to reconstruct the centennial TSI variation back to 1700 based on the available TSI space measurements and the revised SN, in agreement with the insights from . This new centennial TSI reconstruction is a paradigm shift  compared to the long-held belief based on  that there was a significant increase in the TSI, and hence solar climate change forcing, from the Maunder Minimum to the present. In Section 2, we review the available TSI space measurements and TSI regression models reproducing the sunspot darkening and facular brightening from observations of the solar surface magnetic field. In Section 3, we reconstruct the TSI variation back to 1700 based on the revised SN.
Since , solar-climate research has been dominated by the idea that during the Maunder Minimum, the TSI was significantly lower than the current conditions, characterised by a Grand Modern Maximum  of solar activity, and that this lower TSI could be at least partially responsible for the lower temperatures during the so-called Little Ice Age (LIA)  from the 15th to the 19th century, where the temperatures in the Northern Hemisphere dropped by about 0.6 °C. For example, in , it is estimated that the TSI during the Maunder Minimum could be 3.3 W/m2 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  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.
A reconstruction of past TSI variations needs to be based on the analysis of existing TSI space measurements. We demonstrated in Section 2 that the daily composite TSI from 1991 to 2021 can be reconstructed with an RMSE as low as 0.17 W/m2 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.
We can then endeavour the extrapolation of the TSI variations prior to their reliable measurement from space. On annual mean timescales, facular brightening and sunspot darkening are strongly correlated since the faculae result from the decay of sunspots on timescales shorter then 1 year, so that a single proxy for both can be used. In Section 3, we have used two facular brightening proxies—the MgII core-to-wing ratio and the F10.7 radio flux—and one sunspot darkening estimate—the SN—to reconstruct the measured annual mean TSI variation from 1992 to 2020, with RMSEs of 0.071 W/m2, 0.081 W/m2 and 0.086 W/m2, 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/m2. A TSI reconstruction similar to ours was used in  for an adequate reconstruction of global temperature change from 1850 to 2019, increasing the confidence in the validity of our TSI reconstruction.
The occurrence of grand solar minima and maxima [50,51] can be studied from the 11 year running mean TSI reconstruction shown in Figure 5. An RMSD analysis as a function of timeshift confirms the existence of a 105 year Gleissberg cycle, similar to the one found in [45,46]. The TSI levels during the earlier grand minima in the beginning of the 18th and the 19th centuries are comparable, around 1363.05 W/m2, 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/m2, only 0.15 W/m2 higher than the earlier grand minima. Clearly, this small TSI level variation cannot explain the occurrence of the LIA.
The main contribution of our study is that, in opposition to earlier studies based on , we do not find a significant increase in TSI and hence solar influence on climate change between the Maunder Minimum and the present.
We have obtained a new TSI reconstruction from 1700 to 2020. It is based on a careful intercomparison and analysis of the TSI space measurements from 1991 to 2021 and an extrapolation back to 1700 based on the latest version of the annual mean SN. The daily mean TSI space measurements can be reconstructed with an RMSE of 0.71 W/m2 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/m2 and has an estimated stability of ±0.25 W/m2. 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/m2 higher than the TSI level of the earliest grand minimum.
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