Open access paper published in Atmosphere Remote Sensing
HT/Leif Svalgaard
Abstract
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.
1. Introduction
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) [1].
The first measurement of TSI from space was made in 1969 [2], and continuous monitoring of the TSI with space radiometers started in 1978 [3]. In general, TSI radiometers measure at different absolute levels [4], and are subject to ageing due to solar exposure [5]. 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 [10]. 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’ [11]. The TSI level observed during the 11 year cycle minima has long been a matter of speculation. Following [12], 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’ [13], where the 11 year cycle amplitude is supposed to be maximal. Centennial TSI reconstructions, such as the one of [14], 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. [18] 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 [9] 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 [18]. This new centennial TSI reconstruction is a paradigm shift [22] compared to the long-held belief based on [12] 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.
…….
4. Discussion
Since [12], 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 [13] 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) [48] from the 15th to the 19th century, where the temperatures in the Northern Hemisphere dropped by about 0.6 °C. For example, in [15], 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 [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.
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 [49] 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 [12], we do not find a significant increase in TSI and hence solar influence on climate change between the Maunder Minimum and the present.
5. Conclusions
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.
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
At last a small break in the clouds of confirmation bias.
Because of the 4th power relationship a constant TSI can yield an infinite number of different values for average T depending upon the variance of T.
Earth with a dark side 10C and a warm side 30C has an average temp of 20C but radiates greater energy than earth with a dark and warm side both 20C.
The same holds true equator to poles. So unkess you include variance the regression can yield nonsense.
We have a body of research that says LIA has a different variance than today.
That European temps were abnormal. So TSI is misleading because of the non linear relationship. .
That is referred to as the rectification effect in literature. For Earth it is about 6 w/m2 or 1 K.
Energy is proportional to frequency. A constant TSI with a variable frequency tells us that the number of photons released by the sun must vary with the frequency. But the number of photons produced by fusion/neutron decay is proportional to the energy which is constant. So we have a contradiction. Something in our assumptions must be false.
the photons are emitted by the surface of the sun not the fusion core
Yes, we assume that the solar system is a closed system, with all the photon energy being produced by nuclear fusion within our sun. This is clearly not the case, as we also get significant photon energy from our galaxy and the rest of the universe beyond. This is why they had to come up with the neutrino fudge to explain away the sun’s missing ~15% of energy…
“Today it is accepted that the neutrinos produced in the Sun are not massless particles as predicted by the Standard Model but rather mixed quantum states made up of defined mass-eigenstates in different (complex) proportions. That allows a neutrino produced as a pure electron neutrino to change during propagation into a mixture of electron, muon and tau neutrinos, with a reduced probability of being detected by a detector sensitive to only electron neutrinos.” …Wiki
BTW – Main-steam physics doesn’t understand that neutrinos are simply coherent packets of photons.
It strikes me a critical test for climate drivers is to explain the Little Ice Age and the recovery in temperatures we see now. What cooled us down and then heated us up again in the Northern Hemisphere?
indeed what happened then???
Perhaps a temporary reduction in total solar system energy brought on the LIA? This perhaps caused by it’s passage through a denser patch of galactic dust.
Ian:
Examination of the Central England Instrumental Temperatures Data Set (1659-present, which spanned about a third of the LIA)) shows that, although the LIA was a period where annual temperatures constantly ranged below 0 deg. C, the intensity of the cold constantly fluctuated over the years, with every decrease in temperatures being coincident with a known VEI4 or larger volcanic eruption, somewhere around the world.
The reflective SO2 aerosols injected into the stratosphere from the eruptions cooled the planet’s surface, and there were so many eruptions that it never had the opportunity to warm up (except for the 33 year period between 1721 and 1754 when there were only 5 eruptions).
Since the LIA was caused by volcanic activity, it was not just a northern hemisphere happening, but actually a world-wide event, as others have already concluded, but never explained why.
The 33 year interval with few eruptions would have melted a LOT of ice, changing Earth’s albedo, and beginning the end of the LIA. Between 1754 and 1850, there were 39 more eruptions, but with three 9-year intervals of no eruptions in between and thus, additional melting.
As noted above,the cause of the LIA was due to an extensive occurrence of volcanic eruptions, and, therefore, could happen again.
See “The Definitive Cause of Little Ice Age Temperatures”
https://doi.org/10.30574/wjarr.2022.13.2.0170
If you had a friend with an above ground pool, you’d remember when everyone would walk in a circle, adding energy, it’d create a smooth, controlled whirlpool. It was when everyone got out (or worse, stop & push against) that the water became choppy & chaotic with rogue waves.