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How much has the Sun influenced Northern Hemisphere temperature trends? An ongoing debate

  • Center for Environmental Research and Earth Sciences (CERES)

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In order to evaluate how much Total Solar Irradiance (TSI) has influenced Northern Hemisphere surface air temperature trends, it is important to have reliable estimates of both quantities. Sixteen different estimates of the changes in Total Solar Irradiance (TSI) since at least the 19th century were compiled from the literature. Half of these estimates are “low variability” and half are “high variability”. Meanwhile, five largely-independent methods for estimating Northern Hemisphere temperature trends were evaluated using: 1) only rural weather stations; 2) all available stations whether urban or rural (the standard approach); 3) only sea surface temperatures; 4) tree-ring widths as temperature proxies; 5) glacier length records as temperature proxies. The standard estimates which use urban as well as rural stations were somewhat anomalous as they implied a much greater warming in recent decades than the other estimates, suggesting that urbanization bias might still be a problem in current global temperature datasets - despite the conclusions of some earlier studies. Nonetheless, all five estimates confirm that it is currently warmer than the late 19th century, i.e., there has been some “global warming” since the 19th century. For each of the five estimates of Northern Hemisphere temperatures, the contribution from direct solar forcing for all sixteen estimates of TSI was evaluated using simple linear least-squares fitting. The role of human activity on recent warming was then calculated by fitting the residuals to the UN IPCC’s recommended “anthropogenic forcings” time series. For all five Northern Hemisphere temperature series, different TSI estimates suggest everything from no role for the Sun in recent decades (implying that recent global warming is mostly human-caused) to most of the recent global warming being due to changes in solar activity (that is, that recent global warming is mostly natural). It appears that previous studies (including the most recent IPCC reports) which had prematurely concluded the former, had done so because they failed to adequately consider all the relevant estimates of TSI and/or to satisfactorily address the uncertainties still associated with Northern Hemisphere temperature trend estimates. Therefore, several recommendations on how the scientific community can more satisfactorily resolve these issues are provided.
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IOP Publishing Journal Title
xxxx-xxxx/xx/xxxxxx 1 © xxxx IOP Publishing Ltd
How much has the Sun influenced Northern
Hemisphere temperature trends? An ongoing
Ronan Connolly1,2, Willie Soon1, Michael Connolly2, Sallie Baliunas3, Johan
Berglund4, C. J. Butler5, Rodolfo Gustavo Cionco6,7, Ana G. Elias8,9, Valery M.
Fedorov10, Hermann Harde11, Gregory W. Henry12, Douglas V. Hoyt13, Ole
Humlum14, David R. Legates15, Sebastian Lüning16, Nicola Scafetta17, Jan-Erik
Solheim18, László Szarka19, Harry van Loon20, Víctor M. Velasco Herrera21, Richard
C. Willson22, Hong Yan23 and Weijia Zhang24,25
1 Center for Environmental Research and Earth Science (CERES), Salem, MA 01970, USA
2 Independent scientists, Dublin, Ireland
3 Retired, formerly Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138, USA
4 Independent researcher, Malmö, Sweden
5 Retired, formerly Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland, UK
6 Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina
7 Grupo de Estudios Ambientales, Universidad Tecnológica Nacional, Colón 332, San Nicolás (2900), Buenos Aires,
8 Laboratorio de Física de la Atmósfera, Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de
Tucumán, Av. Independencia 1800, 4000 Tucumán, Argentina
9 Instituto de Física del Noroeste Argentino (Consejo Nacional de Investigaciones Científicas y Técnicas -
Universidad Nacional de Tucumán), 4000 Tucumán, Argentina
10 Faculty of Geography, Lomonosov, Moscow State University, Leninskie Gory St. 1, Moscow 119991, Russia
11 Helmut-Schmidt-University, Hamburg, Germany
12 Center of Excellence in Information Systems, Tennessee State University, Nashville, TN 37209 USA
13 Independent scientist, Berkeley Springs, WV, USA
14 Emeritus Professor in Physical Geography, Department of Geosciences, University of Oslo, Norway
15 College of Earth, Ocean, and the Environment, University of Delaware, Newark DE 19716-2541, USA
16 Institute for Hydrography, Geoecology and Climate Sciences, Hauptstraße 47, 6315 Ägeri, Switzerland
17 Department of Earth Sciences, Environment and Georesources, University of Naples Federico II, Complesso
Universitario di Monte S. Angelo, via Cinthia, 21, 80126 Naples, Italy
18 Retired, formerly Department of Physics and Technology, UiT The Arctic University of Norway, 9037 Tromsø,
19 CSFK Geodetic and Geophysical Institute, 9400 Sopron, Csatkai utca 6-8, Hungary
20 Retired, formerly National Center for Atmospheric Research, Boulder, Colorado, USA.
21 Instituto de Geofisica, Universidad Nacional Autónoma de México, Ciudad Universitaria, Coyoacán, 04510,
México D.F., México
22 Active Cavity Radiometer Irradiance Monitor (ACRIM), Coronado, CA 92118, USA
23 State Key Laboratory of Loess and Quaternary Geology, Institute of Earth Environment, Chinese Academy of
Sciences, Xi’an 710061, China
24 Department of Mathematics and Physics, Shaoxing University, Shaoxing, China
25 Department of AOP Physics, University of Oxford, Oxford, UK
Invited Review. Received 7 Dec 2020; Revised 9 Mar 2021; Accepted for publication in Research in
Astronomy and Astrophysics on 14 Apr 2021. This version is a pre-print of the accepted version.
In order to evaluate how much Total Solar Irradiance (TSI) has influenced Northern
Hemisphere surface air temperature trends, it is important to have reliable estimates of both
quantities. Sixteen different estimates of the changes in Total Solar Irradiance (TSI) since at
IOP Publishing Journal Title
xxxx-xxxx/xx/xxxxxx 2 © xxxx IOP Publishing Ltd
least the 19th century were compiled from the literature. Half of these estimates are “low
variability” and half are “high variability”. Meanwhile, five largely-independent methods for
estimating Northern Hemisphere temperature trends were evaluated using: 1) only rural
weather stations; 2) all available stations whether urban or rural (the standard approach); 3)
only sea surface temperatures; 4) tree-ring widths as temperature proxies; 5) glacier length
records as temperature proxies. The standard estimates which use urban as well as rural
stations were somewhat anomalous as they implied a much greater warming in recent decades
than the other estimates, suggesting that urbanization bias might still be a problem in current
global temperature datasets - despite the conclusions of some earlier studies. Nonetheless, all
five estimates confirm that it is currently warmer than the late 19th century, i.e., there has been
some “global warming” since the 19th century. For each of the five estimates of Northern
Hemisphere temperatures, the contribution from direct solar forcing for all sixteen estimates
of TSI was evaluated using simple linear least-squares fitting. The role of human activity on
recent warming was then calculated by fitting the residuals to the UN IPCC’s recommended
“anthropogenic forcings time series. For all five Northern Hemisphere temperature series,
different TSI estimates suggest everything from no role for the Sun in recent decades
(implying that recent global warming is mostly human-caused) to most of the recent global
warming being due to changes in solar activity (that is, that recent global warming is mostly
natural). It appears that previous studies (including the most recent IPCC reports) which had
prematurely concluded the former, had done so because they failed to adequately consider all
the relevant estimates of TSI and/or to satisfactorily address the uncertainties still associated
with Northern Hemisphere temperature trend estimates. Therefore, several recommendations
on how the scientific community can more satisfactorily resolve these issues are provided.
Keywords: global warming, solar variability, detection and attribution of climate change, urbanization bias
Abstract .............................................................................................................................................................................................................1
1. Introduction ...................................................................................................................................................................................................3
2. Estimating Total Solar Irradiance changes ....................................................................................................................................................5
2.1. Challenges in estimating multi-decadal changes in Total Solar Irradiance ............................................................................................5
2.2. The debate over changes in Total Solar Irradiance during the satellite era (1978-present) ....................................................................6
2.3. Implications of the satellite era debate for pre-satellite era estimates ....................................................................................................7
2.4. Sixteen different estimates of changes in Total Solar Irradiance since the 19th century and earlier ..................................................... 12
2.5. Arguments for a significant role for solar variability in past climate change ....................................................................................... 15
2.5.1. Evidence for long-term variability in both solar activity and climate .......................................................................................... 15
2.5.2. Similarity in frequencies of solar activity metrics and climate changes ....................................................................................... 16
2.5.3. Sun-Planetary Interactions as a plausible mechanism for long-term solar variability .................................................................. 17
2.5.4. Analogies of solar variability with the variability of other “Sun-like” stars ................................................................................ 19
2.6. The apparent paradoxes from the 11 year “Schwabe” quasi-cyclical component ................................................................................ 21
2.6.1. “Top-down” vs. “bottom-up” mechanisms .................................................................................................................................. 22
2.6.2. “The ocean as a buffer”: Ocean heat capacity as a possible “filter capacitor”-based buffering mechanism ................................ 23
2.6.3. Sun-climate effects are more pronounced in certain regions ........................................................................................................ 24
2.6.4. Galactic Cosmic Ray-driven amplification mechanisms .............................................................................................................. 25
2.6.5. Short-term orbital effects ............................................................................................................................................................. 27 The difference between the average Earth-Sun distance (1AU) and the daily Earth-Sun distance ........................................... 27 Comparison with long-term orbital forcing ............................................................................................................................... 30
3. Estimating Northern Hemisphere surface temperature changes .................................................................................................................. 32
3.1. Using rural-stations only ...................................................................................................................................................................... 33
3.1.1. Is our new rural-only estimate better or worse than the standard estimates that include both urban and rural stations? .............. 39
3.2. Using urban and rural stations ............................................................................................................................................................. 40
3.3. Sea surface temperatures ..................................................................................................................................................................... 41
3.4. Tree-ring proxy based reconstructions ................................................................................................................................................. 45
3.5. Glacier-length based reconstruction ..................................................................................................................................................... 45
3.6. Comparison of all five types of estimate.............................................................................................................................................. 45
4. Changes in “anthropogenic forcings” .......................................................................................................................................................... 47
5. Estimating the role of the Sun in Northern Hemisphere surface temperature trends since the 19th century and earlier ............................... 47
IOP Publishing Journal Title
xxxx-xxxx/xx/xxxxxx 3 © xxxx IOP Publishing Ltd
6. Conclusions and recommendations ............................................................................................................................................................. 55
Acknowledgements ......................................................................................................................................................................................... 57
References ....................................................................................................................................................................................................... 57
1. Introduction
The UN’s Intergovernmental Panel on Climate Change
(IPCC)’s Working Group 1 concluded in their most recent
(5th) Assessment Report [1] that:
Each of the last three decades has been successively
warmer at the Earth’s surface than any preceding decade
since 1850 [] In the Northern Hemisphere, 1983-2012
was likely the warmest 30-year period of the last 1400
years (IPCC Working Group 1’s Summary for
Policymakers, 2013, p3 emphasis in original) [2]
And that:
It is extremely likely that human influence has been the
dominant cause of the observed warming since the mid-20th
century […] It is extremely likely that more than half of the
observed increase in global average surface temperature
from 1951 to 2010 was caused by the anthropogenic
increase in greenhouse gas concentrations and other
anthropogenic forcings together. The best estimate of the
human-induced contribution to warming is similar to the
observed warming over this period. (IPCC Working
Group 1’s Summary for Policymakers, 2013, p15
emphasis in original) [2]
In other words, the IPCC 5th Assessment Report essentially
answered the question we raised in the title of our article,
How much has the Sun influenced Northern Hemisphere
temperature trends?”, with: almost nothing, at least since the
mid-20th century(to paraphrase the above statement). This
followed a similar conclusion from the IPCC’s 4th Assessment
Report (2007):
Most of the observed increase in global average
temperatures since the mid-20th century is very likely due to
the observed increase in anthropogenic greenhouse gas
concentrations (IPCC Working Group 1’s Summary for
Policymakers, 2007, p10 emphasis in original) [3]
This in turn followed a similar conclusion from their 3rd
Assessment Report (2001):
...most of the observed warming over the last 50 years is
likely to have been due to the increase in greenhouse gas
concentrations.” (IPCC Working Group 1’s Summary for
Policymakers, 2001, p10) [4]
Indeed, over this period, there have also been several well-
cited reviews and articles reaching the same conclusion. For
example: Crowley (2000) [5]; Stott et al. (2001) [6]; Laut
(2003) [7]; Haigh (2003) [8]; Damon and Laut (2004) [9];
Benestad (2005) [10]; Foukal et al. (2006) [11]; Bard and
Frank (2006) [12]; Lockwood and Fröhlich (2007) [13];
Hegerl et al. (2007) [14]; Lean and Rind (2008) [15]; Benestad
and Schmidt (2009) [16]; Gray et al. (2010) [17]; Lockwood
(2012) [18]; Jones et al. (2013) [19]; Sloan and Wolfendale
(2013) [20]; Gil-Alana et al. (2014) [21]; Lean (2017) [22].
On the other hand, there have also been many reviews and
articles published over the same period that reached the
opposite conclusion, i.e., that much of the global warming
since the mid-20th century and earlier could be explained in
terms of solar variability. For example: Soon et al. (1996) [23];
Hoyt and Schatten (1997) [24]; Svensmark and Friis-
Christensen (1997) [25]; Soon et al. (2000a,b) [26,27]; Bond
et al. (2001) [28]; Willson and Mordvinov (2003) [29];
Maasch et al. (2005) [30]; Soon (2005) [31]; Scafetta and
West (2006a,b, 2008) [3235]; Svensmark (2007) [36];
Courtillot et al. (2007) [37,38]; Singer and Avery (2008) [39];
Shaviv (2008) [40]; Scafetta (2009,2011) [41,42]; Le Mouël
et al. (2008,2010,2011) [4346]; Humlum et al. (2011) [47];
Ziskin and Shaviv (2012) [48]; Solheim et al. (2012) [49];
Courtillot et al. (2013) [50]; Solheim (2013) [51]; Scafetta and
Willson (2014) [52]; Harde (2014) [53]; Lüning and
Vahrenholt (2015,2016) [54,55]; Soon et al. (2015) [56];
Svensmark et al. (2016,2017) [57,58]; Harde (2017) [59];
Scafetta et al. (2019) [60]; Le Mouël et al. (2019,2020)
[61,62]; Mörner et al. (2020) [63]; Lüdecke et al. (2020) [64].
Meanwhile, other reviews and articles over this period have
either been undecided, or else argued for significant but subtle
effects of solar variability on climate change. For example:
Labitzke and van Loon [6567]; Beer et al. (2000) [68]; Reid
(2000) [69]; Carslaw et al. (2002) [70]; Ruzmaikin et al. [71
75]; Salby and Callaghan (2006) [7678]; Kirkby (2007) [79];
de Jager et al. (2010) [80]; Tinsley et al. [8185]; Dobrica et
al. [8689]; Blanter et al. (2012) [90]; van Loon et al. [9193];
Roy et al. [9497]; Lopes et al. (2017) [98]; Pan et al. (2020)
Why were these dissenting scientific opinions in the
literature not reflected in the various IPCC statements quoted
above? There are probably many factors. One factor is
probably the fact that climate change and solar variability are
both multifaceted concepts. Hence, as Pittock (1983) noted,
historically, many of the studies of Sun/climate relationships
have provided results that are ambiguous and open to
interpretation in either way [100]. Another factor is that many
researchers argue that scientific results that might potentially
interfere with political goals are unwelcome. For example,
Lockwood (2012) argues that, The field of Sun-climate
relations […] in recent years has been corrupted by
unwelcome political and financial influence as climate change
sceptics have seized upon putative solar effects as an excuse
for inaction on anthropogenic warming [18].
Journal XX (XXXX) XXXXXX Connolly et al
At any rate, one factor that we believe is highly relevant is
the fact that a primary goal of the IPCC reports is to speak
with one voice for climate science [101,102]. This drive to
present a single “scientific consensus” on issues has given the
IPCC a remarkable international “reputation as the epistemic
authority in matters of climate policy” (Beck et al., 2014
[101]). However, many researchers have noted that this has
been achieved by suppressing dissenting views on any issues
where there is still scientific disagreement [101106]. As a
result, an accurate knowledge of those issues where there is
ongoing scientific dissensus (and why) is often missing from
the IPCC reports. This is concerning for policy makers relying
on the IPCC reports because, as van der Sluijs et al. (2010)
note, The consensus approach deprives policy makers of a
full view of the plurality of scientific opinions within and
between the various scientific disciplines that study the
climate problem [103]. From our perspective as members of
the scientific community, we are also concerned that this
suppression of open-minded scientific inquiry may be
hindering scientific progress into improving our
understanding of these challenging issues.
We argue that the Sun/climate debate is one of these issues
where the IPCC’s “consensus” statements were prematurely
achieved through the suppression of dissenting scientific
opinions. Indeed, van der Sluijs et al. (2010) specifically listed
it as a prime example: “Examples of such dissent are disputes
over the role of man compared to the role of the sun in the
observed and projected climate trends… [103].
We agree with Sarewitz (2011)’s argument that The very
idea that science best expresses its authority through
consensus statements is at odds with a vibrant scientific
enterprise. Consensus is for textbooks; real science depends
for its progress on continual challenges to the current state of
always-imperfect knowledge. Science would provide better
value to politics if it articulated the broadest set of plausible
interpretations, options and perspectives, imagined by the best
experts, rather than forcing convergence to an allegedly
unified voice [105].
The co-authors of this article each have quite different
views on the Sun/climate debate, and many of us plan on
continuing our research into this challenging topic through
independent ways. However, we believe that it is timely to
convey to the rest of the scientific community the existence of
several unresolved problems, as well as establish those points
where there is general agreement. Therefore, while not strictly
an “empirical adversarial collaboration” as described by e.g.,
Refs. [107109], this review shares some of the same
philosophy in that we have agreed not to take the “consensus-
driven” approach of the IPCC [101106], but rather to
emphasize where dissenting scientific opinions exist as well
as where there is scientific agreement. As Bacon (1605) noted,
"If a man will begin with certainties, he shall end in doubts;
but if he will be content to begin with doubts he shall end in
certainties." - Francis Bacon, The Advancement of Learning,
Book 1, Chapter 5, Section 8 (1605).
In Section 2, we will provide a historical review of the
Sun/climate debate and a discussion of some of the key
ongoing debates. We will attempt to estimate how much of the
long-term Northern Hemisphere temperature trends since the
19th century (or earlier) can be explained in terms of solar
variability assuming a simple linear relationship between
Northern Hemisphere surface air temperatures and Total Solar
Irradiance (TSI). We will demonstrate that even this rather
simple hypothesis has not yet been satisfactorily addressed.
The IPCC (2013) argued that TSI has been decreasing since
the 1950s, and this seems to have been one of the primary
reasons why they concluded that the observed warming since
the 1950s was “extremely likely” to be due to human-caused
greenhouse gas emissions [2]. However, Soon et al. (2015)
[56] and Scafetta et al. (2019) [60] have noted that the IPCC
(2013) reports had only considered a small subset of the TSI
estimates available in the literature, and that other TSI
estimates imply different trends. Therefore, we compile and
consider a more complete set of 16 different estimates of TSI.
This includes the 4 estimates considered by IPCC (2013) [2],
as well as the larger set of 8 estimates considered by Soon et
al. (2015) [56] and Scafetta et al. (2019) [60]. It also includes
the new estimate which Matthes et al. (2017) [110] have
recommended for use in the upcoming IPCC 6th Assessment
Aside from these debates over a direct linear relationship
between TSI and surface air temperatures, we note that there
are many studies arguing that the Sun/climate relationships are
probably more subtle than that. For instance, some have
argued that the relationship is non-linear, e.g., involving
thresholds at which prevailing oceanic or atmospheric
circulation patterns might shift [63,111113]. Others note that
the solar effect on the climate should be dampened on short
time scales due to thermal inertia [3234,40,41]. Others
suggest that the Sun/climate relationships might be more
pronounced in some geographical regions than others
[36,40,64,65,71,86,87,91,93,96,114,115]. For simplicity, the
primary focus in this paper will be on evaluating the relatively
simple hypothesis of a direct linear relationship between TSI
and surface air temperatures. However, we encourage readers
to follow up on the debates over the possibilities of more
subtle sun/climate relationships. With that in mind, in Sections
2.5-2.6, we briefly review some of these ongoing debates.
In Section 3, we will compile and generate several different
estimates of Northern Hemisphere temperature trends. We
will show that the standard estimates used by IPCC (2013) [2],
which include urban as well as rural stations, imply a much
greater long-term warming than most other estimates. This
suggests that the standard estimates have not adequately
corrected for urbanization bias [56,116118].
Journal XX (XXXX) XXXXXX Connolly et al
Our main analysis involves estimating the maximum solar
contribution to Northern Hemisphere temperature trends
assuming a linear relationship between TSI and temperature.
However, since IPCC (2013) concluded that the most
important factor in recent temperature trends is
“anthropogenic forcings” (chiefly from greenhouse gas
emissions), a useful secondary question we will consider is
how much of the trends unexplained by this assumed linear
solar relationship can be explained in terms of anthropogenic
forcings. Therefore, a second step of our analysis will involve
fitting the statistical residuals from the first step using the
anthropogenic forcings recommended by IPCC (2013) [1]. In
Section 4, we will describe the IPCC’s anthropogenic forcings
In Section 5, we will calculate the best fits (using linear
least-squares fitting) for each of the TSI and Northern
Hemisphere temperature reconstructions and then estimate the
implied Sun/climate relationship from each combination,
along with the implied role of anthropogenic (i.e., human-
caused) factors.
Finally, we will offer some concluding remarks and
recommendations for future research in Section 6. We
emphasise that the main research questions of this paper are
based on the debates over the role of the Sun in recent climate
change. Although we contrast this with the role of
anthropogenic factors, we do not explicitly investigate the
possible role of other non-solar driven natural factors such as
internal changes in oceanic and/or atmospheric circulation, as
this is beyond the scope of the paper. However, we encourage
further research into these possible factors, e.g., Refs. [119
2. Estimating Total Solar Irradiance changes
2.1. Challenges in estimating multi-decadal changes in
Total Solar Irradiance
Because most of the energy that keeps the Earth warmer
than space comes from incoming solar radiation, i.e., Total
Solar Irradiance (TSI), it stands to reason that a multi-decadal
increase in TSI should cause global warming (all else being
equal). Similarly, a multi-decadal decrease in TSI should
cause global cooling. For this reason, for centuries (and
longer), researchers have speculated that changes in solar
activity could be a major driver of climate change
[7,17,18,24,39,56,124127]. However, a challenging question
associated with this theory is, “How exactly has TSI changed
over time?
One indirect metric on which much research has focused is
the examination of historical records of the numbers and
types/sizes of “sunspots” that are observed on the Sun’s
surface over time [101,102,105110]. Sunspots are
intermittent magnetic phenomena associated with the Sun’s
photosphere, that appear as dark blotches or blemishes on the
Sun’s surface when the light from the Sun is shone on a card
with a telescope (to avoid the observer directly looking at the
Sun). These have been observed since the earliest telescopes
were invented, and Galileo Galilei and others were recording
sunspots as far back as 1610 [125,128131,134]. The Chinese
even have intermittent written records since 165 B.C. of
sunspots that were large enough to be seen by the naked eye
[135,136] Moreover, an examination of the sunspot records
reveals significant changes on sub-decadal to multi-decadal
timescales. In particular, a pronounced Sunspot Cycle” exists
over which the number of sunspots rises from zero during the
Sunspot Minimum to a Sunspot Maximum where many
sunspots occur, before decreasing again to the next Sunspot
Minimum. The length of this “Sunspot Cycle” or “Solar
Cycle” is typically about 11 years, but it can vary between 8
and 14 years. This 11-year cycle in sunspot behaviour is part
of a 22-year cycle in magnetic behaviour known as the Hale
Cycle. Additionally, multi-decadal and even centennial trends
are observed in the sunspot numbers. During the period from
1645 to 1715, known as the “Maunder Minimum” [125,128
130,134], sunspots were very rarely observed at all.
Clearly, these changes in sunspot activity are capturing
some aspect of solar activity, and provide evidence that the
Sun is not a constant star, but one whose activity shows
significant variability on short and long time scales. Therefore,
the sunspot records initially seem like an exciting source of
information on changes in solar activity. However, as will be
discussed in more detail later, it is still unclear how much of
the variability in TSI is captured by the sunspot numbers. The
fact that sunspot numbers are not the only important measure
of solar activity (as many researchers often implicitly assume,
e.g., Gil-Alana et al. (2014) [21]) can be recognized by the
simple realisation that TSI does not fall to zero every ~11
years during sunspot minima, even though the sunspot
numbers do. Indeed, satellite measurements confirm that
sunspots actually reduce solar luminosity, yet paradoxically
the average TSI increases during sunspot maxima and
decreases during sunspot minima [137140].
We will discuss the current explanations for the apparently
paradoxical relationship between sunspots and TSI in Sections
2.2 and 2.3. In any case, the fact that there is more to solar
activity than sunspot numbers was recognized more than a
century ago by Maunder and Maunder (1908) [124] (for whom
the “Maunder Minimum” is named) who wrote,
“…for sun-spots are but one symptom of the sun’s
activity, and, perhaps, not even the most important
symptom- Maunder and Maunder (1908), pp189-190
A [‘great’] spot like that of February, 1892 is enormous
of itself, but it is a very small object compared to the sun;
and spots of such size do not occur frequently, and last but
a very short time. We have no right to expect, therefore, that
Journal XX (XXXX) XXXXXX Connolly et al
a time of many sun-spots should mean any appreciable
falling off in the light and heat we have from the sun.
Indeed, since the surface round the spots is generally bright
beyond ordinary, it may well be that a time of many spots
means no falling off, but rather the reverse.- Maunder and
Maunder (1908), p183 [124]
At the start of the 20th century, Langley, Abbott and others
at the Smithsonian Astrophysical Observatory (SAO)
recognized that a more direct estimate of the variability in TSI
was needed [141143]. From 1902 until 1962, they carried out
a fairly continuous series of measurements of the “solar
constant”, i.e., the average rate per unit area at which energy
is received at the Earth’s average distance from the Sun, i.e.,
1 Astronomical Unit (AU). The fact they explicitly considered
the solar constant to understand climate change is apparent
from the title of one of the first papers describing this project,
Langley (1904) [141], i.e., On a possible variation of the
solar radiation and its probable effect on terrestrial
temperatures”. However, they were also acutely aware of the
inherent challenges in trying to estimate changes in solar
radiation from the Earth’s surface:
The determination of the solar radiation towards the
Earth, as it might be measured outside the Earth’s
atmosphere (called the “solar constant”), would be a
comparatively easy task were it not for the almost
insuperable difficulties introduced by the actual existence
of such an atmosphere, above which we cannot rise, though
we may attempt to calculate what would be the result if we
could.” (Langley, 1904) [141].
The true extent of this problem of estimating the changes in
TSI from beneath the atmosphere became apparent later in the
program. Initially, by comparing the first few years of data, it
looked like changes in TSI of the order of 10% were occurring.
However, it was later realized that, coincidentally, major
(stratosphere-reaching) volcanic eruptions occurred near the
start of the program: at Mt. Pelée and La Soufrière (1902) and
Santa Maria (1903). Hence, the resulting stratospheric dust
and aerosols from these eruptions had temporarily reduced the
transmission of solar radiation through the atmosphere [143].
2.2. The debate over changes in Total Solar Irradiance
during the satellite era (1978-present)
It was not until much later in the 20th century that
researchers overcame this ground-based limitation through the
use of rocket-borne [144], balloon-borne [145] and spacecraft
measurements [146]. Ultimately, when Hoyt (1979)
systematically reviewed the entire ~60 year-long SAO solar
constant project, he found unfortunately that any potential
trend in the solar constant over the record was probably less
than the accuracy of the measurements (~0.3%) [143].
However, with the launch of the Nimbus 7 Earth Radiation
Budget (ERB) satellite mission in 1978 and the Solar
Maximum Mission (SMM) Active Cavity Radiometer
Irradiance Monitor 1 (ACRIM1) satellite mission in 1980, it
finally became possible to continuously and systematically
monitor the incoming TSI for long periods from above the
Earth’s atmosphere [137,140,147,148].
Although each satellite mission typically provides TSI data
for only 10 to 15 years, and the data can be affected by gradual
long-term orbital drifts and/or instrumental errors that can be
hard to identify and quantify [149], there has been an almost
continuous series of TSI-monitoring satellite missions since
those two initial U.S. missions, including European missions,
e.g., SOVAP/Picard [150] and Chinese missions [151,152] as
well as international collaborations, e.g., VIRGO/SOHO
[153], and further U.S. missions, e.g., ACRIMSAT/ACRIM3
[154] and SORCE/TIM [155]. Therefore, in principle, by
rescaling the measurements from different parallel missions so
that they have the same values during the periods of overlap,
it is possible to construct a continuous time series of TSI from
the late-1970s to the present.
Therefore, it might seem reasonable to assume that we
should at least have a fairly reliable and objective
understanding of the changes in TSI during the satellite era,
i.e., 1978 to present. However, even within the satellite era,
there is considerable ongoing controversy over what exactly
the trends in TSI have been [42,52,56,60,68,156158]. There
are a number of rival composite datasets, each implying
different trends in TSI since the late-1970s. All composites
agree that TSI exhibits a roughly 11-year cycle that matches
well with the sunspot cycle discussed earlier. However, the
composites differ in whether additional multidecadal trends
are occurring.
The composite of the ACRIM group that was in charge of
the three ACRIM satellite missions (ACRIM1, ACRIM2 and
ACRIM3) suggests that TSI generally increased during the
1980s and 1990s but has slightly declined since then
[52,60,154,159]. The Royal Meteorological Institute of
Belgium (RMIB)’s composite implies that, aside from the
sunspot cycle, TSI has remained fairly constant since at least
the 1980s [160]. Meanwhile, the Physikalisch-
Meteorologisches Observatorium Davos (PMOD) composite
implies that TSI has been steadily decreasing since at least the
late-1970s [157,161]. Additional TSI satellite composites
have been produced by Scafetta (2011) [42]; de Wit et al.
(2017) [156] and Gueymard (2018) [158].
The two main rival TSI satellite composites are ACRIM
and PMOD. As we will discuss in Section 3, global
temperatures steadily increased during the 1980s and 1990s
but seemed to slow down since the end of the 20th century.
Therefore, the debate over these three rival TSI datasets for
the satellite era is quite important. If the ACRIM dataset is
correct, then it suggests that much of the global temperature
trends during the satellite era could have been due to changes
in TSI [29,35,41,42,52,60,154,159]. However, if the PMOD
dataset is correct, and we assume for simplicity a linear
Journal XX (XXXX) XXXXXX Connolly et al
relationship between TSI and global temperatures, then the
implied global temperature trends from changes in TSI would
exhibit long-term global cooling since at least the late-1970s.
Therefore, the PMOD dataset implies that none of the
observed warming since the late-1970s could be due to solar
variability, and that the warming must be due to other factors,
e.g., increasing greenhouse gas concentrations. Moreover, it
implies that the changes in TSI have been partially reducing
the warming that would have otherwise occurred; if this TSI
trend reverses in later decades, it might accelerate “global
warming” [161,161,162].
The PMOD dataset is more politically advantageous to
justify the ongoing considerable political and social efforts to
reduce greenhouse gas emissions under the assumption that
the observed global warming since the late-19th century is
mostly due to greenhouse gases. Indeed, as discussed in Soon
et al. (2015) [56], Dr. Judith Lean (of the PMOD group)
acknowledged in a 2003 interview that this was one of the
motivations for the PMOD group to develop a rival dataset to
the ACRIM one by stating,
The fact that some people could use Willson’s [ACRIM
dataset] results as an excuse to do nothing about
greenhouse gas emissions is one reason we felt we needed
to look at the data ourselves Dr. Judith Lean, interview
for NASA Earth Observatory, August 2003 [163]
Similarly, Zacharias (2014) argued that it was politically
important to rule out the possibility of a solar role for any
recent global warming,
A conclusive TSI time series is not only desirable from
the perspective of the scientific community, but also when
considering the rising interest of the public in questions
related to climate change issues, thus preventing climate
skeptics from taking advantage of these discrepancies
within the TSI community by, e.g., putting forth a presumed
solar effect as an excuse for inaction on anthropogenic
warming. Zacharias (2014) [164]
We appreciate that some readers may share the sentiments
of Lean and Zacharias and others and may be tempted to use
these political arguments for helping them to decide their
opinion on this ongoing scientific debate. In this context,
readers will find plenty of articles to use as apparent scientific
justification, e.g., Refs. [22,150,156,157,160162,164166].
It may also be worth noting that the IPCC appears to have
taken the side of the PMOD group in their most recent 5th
Assessment Report see Section 8.4.1 of IPCC (2013) [1] for
the key discussions. However, we would encourage all readers
to carefully consider the counter-arguments offered by the
ACRIM group, e.g., Refs. [29,52,60,154,159]. In our opinion,
this was not satisfactorily done by the authors of the relevant
section in the influential IPCC reports, i.e. Section 8.4.1 of
IPCC (2013) [1]. Matthes et al. (2017)’s recommendation that
their new estimate (which will be discussed below) should be
the only solar activity dataset considered by the CMIP6
modelling groups [110] for the IPCC’s upcoming 6th
Assessment Report is even more unwise due to the substantial
differences between various published TSI estimates. This is
aside from the fact that Scafetta et al. (2019) [60] have argued
that the TSI proxy reconstructions preferred in Matthes et al.
(2017) (i.e., NRLTSI2 and SATIRE) contradict important
features observed in the ACRIM 1 and ACRIM 2 satellite
measurements. We would also encourage readers to carefully
read the further discussion of this debate in Soon et al. (2015)
2.3. Implications of the satellite era debate for pre-
satellite era estimates
The debate over which satellite composite is most accurate
also has implications for assessing TSI trends in the pre-
satellite era. In particular, there is ongoing debate over how
closely the variability in TSI corresponds to the variability in
the sunspot records. This is important, because if the match is
very close, then it implies the sunspot records can be a reliable
solar proxy for the pre-satellite era (after suitable scaling and
calibration has been carried out), but if not other solar proxies
may need to be considered.
In the 1980s and early 1990s, data from the
NIMBUS7/ERB and ACRIMSAT/ACRIM1 satellite missions
suggested a cyclical component to the TSI variability that was
highly correlated to the sunspot cycle. That is, when sunspot
numbers increased, so did TSI, and when sunspot numbers
decreased, so did TSI [137140,147,167,168]. This was not
known in advance, and it was also unintuitive because
sunspots are “darker”, and so it might be expected that more
sunspots would make the Sun “less bright” and therefore lead
to a lower TSI. Indeed, the first six months of data from the
ACRIM1 satellite mission suggested that this might be the
case because two large decreases in irradiance of up to 0.2
percent lasting about 1 week [were] highly correlated with the
development of sunspot groups Willson et al. (1981) [148].
However, coincidentally, it appears that the sunspot cycle is
also highly correlated with changes in the number of “faculae”
and in the magnetic network”, which are different types of
intermittent magnetic phenomena that are also associated with
the Sun’s photosphere, except that these phenomena appear as
“bright” spots and features. It is now recognized that the Sun
is currently a “faculae-dominated star”. That is, even though
sunspots themselves seem to reduce TSI, when sunspot
numbers increase, the number of faculae and other bright
features also tend to increase, increasing TSI, and so the net
result is an increase in TSI. That is, the increase in brightness
from the faculae outweighs the decrease from sunspot
dimming (i.e., the faculae:sunspot ratio of contributions to TSI
is greater than 1). For younger and more active stars, the
relative contribution is believed to be usually reversed (i.e.,
Journal XX (XXXX) XXXXXX Connolly et al
the ratio is less than 1) with the changes in stellar irradiance
being “spot-dominated” [169171].
At any rate, it is now well-established that TSI slightly
increases and decreases over the sunspot cycle in tandem with
the rise and fall in sunspots (which coincides with a roughly
parallel rise and fall in faculae and magnetic network features)
[137140,147,167,168]. Many of the current pre-satellite era
TSI reconstructions are based on this observation. That is, a
common approach to estimating past TSI trends includes the
following three steps:
1. Estimate a function to describe the inter-relationships
between sunspots, faculae and TSI during the satellite
2. Assume these relationships remained reasonably
constant over the last few centuries at least.
3. Apply these relationships to one or more of the sunspot
datasets and thereby extend the TSI reconstruction
back to 1874 (for sunspot areas [139,172]); 1700 (for
sunspot numbers [132,133]; or 1610 (for group
sunspot numbers [128,129]).
Although there are sometimes additional calculations
and/or short-term solar proxies involved, this is the basic
approach adopted by, e.g., Foukal and Lean (1990) [139];
Lean (2000) [173]; Solanki et al. (2000,2002) [174,175];
Wang et al. (2005) [172]; Krivova et al. (2007,2010)
[176,177]. Soon et al. (2015) noted that this heavy reliance on
the sunspot datasets seems to be a key reason for the
similarities between many of the TSI reconstructions
published in the literature [56].
However, does the relationship between faculae, sunspots
and TSI remain fairly constant over multidecadal and even
centennial timescales? Also, would the so-called “quiet” solar
region remain perfectly constant despite multidecadal and
secular variability observed in the sunspot and faculae cycles?
Is it reasonable to assume that there are no other aspects of
solar activity that contribute to variability in TSI? If the
answers to all these questions are yes, then we could use the
sunspot record as a proxy for TSI, scale it accordingly and
extend the satellite record back to the 17th century. This would
make things much simpler. It would mean that, effectively,
even Galileo Galilei could have been able to determine almost
as much about the changes in TSI of his time with his early
16th-century telescope as a modern (very high budget) Sun-
monitoring satellite mission of today. All that he would have
been missing was the appropriate scaling functions to apply to
the sunspot numbers to determine TSI.
If the PMOD or similar satellite composites are correct,
then it does seem that, at least for the satellite era (1978-
present), the sunspot cycle is the main variability in TSI and
that the relationships between faculae, sunspots and TSI have
remained fairly constant. This is because the trends of the
PMOD composite are highly correlated to the trends in
sunspot numbers over the entire satellite record. However,
while the ACRIM composite also has a component that is
highly correlated to the sunspot cycle (and the faculae cycle),
it implies that there are also additional multidecadal trends in
the solar luminosity that are not captured by a linear relation
between sunspot and faculae records. Recent modelling by
Rempel (2020) is consistent with this in that his analysis
suggests even a 10% change in the quiet-Sun field strength
between solar cycles could lead to an additional TSI variation
comparable in magnitude to that over a solar cycle [178].
Therefore, if the ACRIM composite is correct, then it would
be necessary to consider additional proxies of solar activity
that are capable of capturing these non-sunspot number-
related multidecadal trends.
Over the years, several researchers have identified several
time series from the records of solar observers that seem to be
capturing different aspects of solar variability than the basic
sunspot numbers [24,179185]. Examples include the average
umbral/penumbral ratio of sunspots [181], the length of
sunspot cycles [49,68,182,183,186189], solar rotation rates
[184], the “envelope” of sunspot numbers [185], variability in
the 10.7cm solar microwave emissions [65,190], solar plage
areas (e.g., from Ca II K spectroheliograms) [190193], polar
faculae [61,62,194], and white-light faculae areas [195,196].
Another related sunspot proxy that might be useful is the
sunspot decay rate. Hoyt and Schatten (1993) have noted that
a fast decay rate suggests an enhanced solar convection, and
hence a brighter Sun, while a slower rate indicates the opposite
[179]. Indeed, indications suggest that the decay rate during
the Maunder Minimum was very slow [179], hence implying
a dimmer Sun in the mid-to-late 17th century. Owens et al.
(2017) developed a reconstruction of the solar wind back to
1617 that suggests the solar wind speed was lower by a factor
of two during the Maunder Minimum [197]. Researchers have
also considered records of various aspects of geomagnetic
activity, since the Earth’s magnetic field appears to be strongly
influenced by solar activity [194,198202].
There are many other solar proxies that might also be
capturing different aspects of the long-term solar variability,
e.g., see Livingston (1994) [180], Soon et al. (2014) [203] and
Soon et al. (2015) [56]. In particular, it is worth highlighting
the use of cosmogenic isotope records, such as 14C or 10Be
[204], since they are used by several of the TSI reconstructions
we will consider. Cosmogenic isotope records have been used
as long-term proxies of solar activity since the 1960s [205
209]. Cosmogenic isotopes such as 14C or 10Be are produced
in the atmosphere via galactic cosmic rays. However, when
solar activity increases, the solar wind reaching the Earth also
increases. This tends to reduce the flux of incoming cosmic
rays, thus reducing the rate of production of these isotopes and
their quantity. These isotopes can then get incorporated into
various long-term records, such as tree rings through
photosynthesis. Therefore, by studying the changes in the
relative concentrations of these isotopes over time in e.g., tree
Journal XX (XXXX) XXXXXX Connolly et al
rings, it is possible to construct an estimate of multidecadal-
to-centennial and even millennial changes in average solar
activity. Because the atmosphere is fairly well-mixed, the
concentration of these isotopes only slowly changes over
several years, and so the 8-14 year sunspot cycle can be
partially reduced in these solar proxies. However, Stefani et
al. (2020) still found a very good match between 14C or 10Be
solar proxies and Schove’s (1955) [131] estimates of solar
activity maxima, which were based on historical aurora
borealis observations back to 240 A.D. [210]. Moreover, the
records can cover much longer periods, and so are particularly
intriguing for studying multi-decadal, centennial and
millennial variability.
We note that several studies have tended to emphasize the
similarities between various solar proxies
[13,17,18,22,158,190]. We agree that this is important, but we
argue that it is also important to contrast as well as compare.
To provide some idea of the effects that solar proxy choice, as
well as TSI satellite composite choice, can have on the
resulting TSI reconstruction, we plot in Figure 1 several
different plausible TSI reconstructions taken from the
literature and/or adapted from the literature. All 9
reconstructions are provided in the Supplementary Materials.
Foukal (2012) [193] and Foukal (2015) [196] used a similar
approach to the Wang et al. (2005) [172] reconstruction but
used slightly different solar proxies for the 20th century pre-
satellite era. Foukal (2012) used 10.7cm solar microwave
emissions for the 1947-1979 period and solar plage areas
(from Ca II K spectroheliograms) for the 1916-1946 period.
Foukal (2015) used the faculae areas (from white light images)
for the 1916-1976 period. In contrast, Wang et al. (2005)
predominantly relied on the group sunspot number series for
the pre-satellite era (after scaling to account for the
sunspot/faculae/TSI relationships during the satellite era).
These three different reconstructions are plotted as Figure
1(a), (c) and (i) respectively. All three reconstructions have a
lot in common, e.g., they all have a very pronounced ~11 year
Solar Cycle component, and they all imply a general increase
in TSI from the 19th century to the mid-20th century, followed
by a general decline to present. However, there are two key
differences between them. First, the Wang et al. (2005)
reconstruction implies a slightly larger increase in TSI from
the 19th century to the 20th century. On the other hand, while
Foukal (2012) and Wang et al. (2005) imply the maximum TSI
occurred in 1958, the Foukal (2015) reconstruction implies a
relatively low TSI in 1958 and suggested two 20th century
peaks in TSI one in the late 1930s and another in 1979, i.e.,
the start of the satellite era. All three reconstructions imply
that none of the global warming since at least 1979 could be
due to increasing TSI, and in the case of the Foukal (2012) and
Wang et al. (2005) reconstructions, since at least 1958.
Meanwhile, all three of those reconstructions were based
on the PMOD satellite composite rather than the ACRIM
composite. Therefore, in Figure 1(b) and (d), we have
modified the Foukal (2012) and (2015) reconstructions using
the ACRIM series for the 1980-2012 period instead of PMOD.
We did this by rescaling the ACRIM time series to have the
same mean TSI over the common period of overlap, i.e., 1980-
Because the ACRIM composite implies a general increase
in TSI from 1980 to 2000 followed by a general decrease to
present, while the PMOD composite implies a general
decrease in TSI over the entire period, this significantly alters
the long-term trends. The modified version of Foukal (2012)
implies that the 1958 peak in TSI was followed by an
equivalent second peak in 2000. This suggests that at least
some of the global warming from the 1970s to 2000 could
have been due to increasing TSI, i.e., contradicting a key
implication of Foukal (2012). The modified Foukal (2015)
reconstruction is even more distinct. It implies that TSI
reached an initial peak in the late 1930s, before declining until
1958, and then increasing to a maximum in 2000. As we will
discuss in Section 3, this is broadly similar to many of the
Northern Hemisphere temperature estimates. Therefore, the
modified Foukal (2015) is at least consistent with the
possibility of TSI as a primary driver of global temperatures
over the entire 20th century.
That said, while these plausible modifications can alter the
relative magnitudes and timings of the various peaks and
troughs in TSI, all these reconstructions would still be what
Soon et al. (2015) [56] and Scafetta et al. (2019) [60] refer to
as “low variability” reconstructions. That is, the multi-decadal
trends in TSI appear to be relatively modest compared to the
rising and falling over the ~11-year Solar Cycle component.
As we will discuss in Section 2.6, many researchers have
identified evidence for a significant ~11-year temperature
variability in the climate of the mid-troposphere to
stratosphere [6567,7678,91,211216], which has been
linked to the more pronounced ~11-year variability in
incoming solar ultraviolet irradiance [8,217225]. However,
in terms of surface temperatures, the ~11-year component
seems to be only of the order of 0.02-0.2°C over the course of
a cycle [40,226230]. Some researchers have argued that the
relatively large heat capacity of the oceans could act as a
“calorimeter” to integrate the incoming TSI over decadal time
scales, implying that the multidecadal trends are more relevant
for climate change than annual variability [40,48,69,231
233], and others have argued that these relatively small
temperature variations could influence the climate indirectly
through e.g., altering atmospheric circulation patterns
[92,93,95,96,111,234]. However, this observation appears to
have convinced many researchers (including the IPCC reports
[1]) relying on “low variability” reconstructions that TSI
cannot explain more than a few tenths of a °C of the observed
surface warming since the 19th century, e.g., [1,5,7
9,11,12,1618,21,22]. We will discuss these competing
Journal XX (XXXX) XXXXXX Connolly et al
hypotheses and ongoing debates (which several co-authors of
this paper are actively involved in) in Section 2.6, as these
become particularly important if the true TSI reconstruction is
indeed “low variability”, i.e., dominated by the ~11-year
Figure 1. Examples of different TSI reconstructions that can be created by varying the choice of solar proxies used for the pre-satellite era
and the choice of TSI composite used for the satellite era. The Foukal (2012, 2015) [193,196] series using PMOD were downloaded from (Accessed 20/06/2020). The equivalent ACRIM series were rescaled using the annual means of
the ACRIM TSI composite which was downloaded from (Accessed 01/07/2020). The two
Solanki & Fligge (1998) series were digitized from Figure 3 of that paper [183] and extended up to 2012 with the updated ACRIM annual
means. The Hoyt and Schatten (1993) [179] series was updated to 2018 by Scafetta et al. (2019) [60]. The Wang et al. (2005) [172] and
Lean et al. (1995) [185] series were taken from the Supplementary Materials of Soon et al. (2015) [56]
On the other hand, let us consider the possibility that the
true TSI reconstruction should be “high variability”. In Figure
1(e)-(h), we consider four such “high variability”
combinations, and we will discuss more in Section 2.4. All
four of these reconstructions include a ~11-year solar cycle
component like the “low variability” reconstructions, but they
imply that this quasi-cyclical component is accompanied by
substantial multidecadal trends. Typically, the ~11-year cycle
mostly arises from the solar proxy components derived from
the sunspot number datasets (as in the low variability
reconstructions), while the multidecadal trends mostly arise
from other solar proxy components.
Solanki and Fligge (1998) [183] considered two alternative
proxies for their multidecadal component and treated the
envelope described by the two individual components as a
single reconstruction with error bars. Solanki and Fligge
Journal XX (XXXX) XXXXXX Connolly et al
(1999) [235] also suggested that this reconstruction could be
extended back to 1610 using the Group Sunspot Number time
series of Hoyt and Schatten (1998) [128] as a solar proxy for
the pre-1874 period. However, in Figure 1(e) and (f), we
treated both components as separate reconstructions, which
we digitized from Solanki and Fligge (1998)’s Figure 3, and
extended up to 2012 with the updated ACRIM satellite
composite. Both reconstructions are quite similar and, unlike
the low variability estimates, imply a substantial increase in
TSI from the end of the 19th century to the end of the 20th
century. They also both imply that this long-term increase was
interrupted by a decline in TSI from a mid-20th century peak
to the mid-1960s. However, the reconstruction using Ca II K
plage areas (Figure 1e) implies that the mid-20th century peak
occurred in 1957, while the reconstruction using Solar Cycle
Lengths (Figure 1f) implies the mid-20th century peak
occurred in the late 1930s and that TSI was declining in the
1940s up to 1965. In terms of the timing of the mid-20th
century peak, it is worth noting that Scafetta (2012) found a
minimum in mid-latitude aurora frequencies in the mid-1940s,
which is indicative of increased solar activity [236].
Figure 1(g) plots the updated Hoyt and Schatten (1993)
[179] TSI reconstruction. Although the original Hoyt and
Schatten (1993) reconstruction was calibrated to the satellite
era using the NIMBUS7/ERB time series as compiled by Hoyt
et al. (1992) [147], it has since been updated by Scafetta and
Willson (2014) [52] and more recently by Scafetta et al.
(2019) [60] using the ACRIM composite until 2013 and the
VIRGO and SORCE/TIM records up to present. The Hoyt and
Schatten (1993) reconstruction is quite similar to the two
Solanki and Fligge (1998) reconstructions, except that it
implies a greater decrease in TSI from the mid-20th century to
the 1960s, and that the mid-20th century peak occurred in
We note that there appear to be some misunderstandings in
the literature over the Hoyt and Schatten (1993)
reconstruction, e.g., Fröhlich and Lean (2002) mistakenly
reported that “…Hoyt and Schatten (1993) is based on solar
cycle length whereas the others are using the cycle amplitude
[162]. Therefore, we should stress that, like Lean et al. (1995)
[185], the Hoyt and Schatten (1993) reconstruction did include
both the sunspot numbers and the envelope of sunspot
numbers, but unlike most of the other reconstructions, they
also included multiple additional solar proxies [179]. We
should also emphasize that the Hoyt and Schatten (1998) [128]
paper describing the widely-used “Group Sunspot Number”
dataset is a completely separate analysis, although it was
partially motivated by Hoyt and Schatten (1993).
The Lean et al. (1995) [185] reconstruction of Figure 1(h)
also implies a long-term increase in TSI since the 19th century
and a mid-20th century initial peak this time at 1957, i.e.,
similar to Figure 1(e). The Lean et al. (1995) reconstruction
was based on Foukal and Lean’s (1990) reconstruction [139],
and itself evolved into Lean (2000) [173], which evolved into
Wang et al. (2005) [172], which in turn has evolved into the
Coddington et al. (2016) [237] reconstruction, which as we
will discuss in Section 2.4 is a major component of the recent
Matthes et al. (2017) [110] reconstruction. However, Soon et
al. (2015) [56] noted empirically (in their Figure 9) that the
main net effect of the evolution from Lean et al. (1995) [185]
to Lean (2000) [173] to Wang et al. (2005) [172] has been to
reduce the magnitude of the multi-decadal trends, i.e., to
transition towards a “low variability” reconstruction. We note
that Coddington et al. (2016) [237] and Matthes et al. (2017)
[110] has continued this trend. Another change in this family
of reconstructions is that the more recent ones have used the
PMOD satellite composite instead of ACRIM (which is
perhaps not surprising given that Lean was one of the PMOD
team, as mentioned in Section 2.2, as well as being a co-author
of all of that family of reconstructions).
Therefore, a lot of the debate over whether the high or low
variability reconstructions are more accurate relates to the
question of whether or not there are multi-decadal trends that
are not captured by the ~11-year solar cycle described by the
sunspot numbers. This overlaps somewhat with the ACRIM
vs. PMOD debate since the PMOD implies that TSI is very
highly correlated to the sunspot number records (via the
correlation between sunspots and faculae over the satellite
era), whereas the ACRIM composite is consistent with the
possibility of additional multidecadal trends between solar
cycles [42,52,56,60,156158].
This has been a surprisingly challenging problem to
resolve. As explained earlier, the ~11-year cyclical variations
in TSI over the satellite era are clearly well correlated to the
trends in the areas of faculae, plages, as well as sunspots over
similar timescales [137140,147,167,168]. However, on
shorter timescales, TSI is actually anti-correlated to sunspot
area [148,238]. Therefore, the ~11-year rise and fall in TSI in
tandem with sunspot numbers cannot be due to the sunspot
numbers themselves, but appears to be a consequence of the
rise and fall of sunspot numbers being commensally correlated
to those of faculae and plages. However, Kuhn et al. (1988)
argued that, “…solar cycle variations in the spots and faculae
alone cannot account for the total [TSI] variability” and that,
“… a third component is needed to account for the total
variability [239]. Therefore, while some researchers have
assumed, like Lean et al. (1998) that there is “…[no] need for
an additional component other than spots or faculae [240],
Kuhn et al. [241245] continued instead to argue that
sunspots and active region faculae do not [on their own]
explain the observed irradiance variations over the solar
cycle [244] and that there is probably a third component of
the irradiance variationthat is a nonfacular and nonsunspot
contribution [241]. Work by Li, Xu et al. is consistent with
Kuhn et al.’s assessment, e.g., Refs. [246249], in that they
have shown: that TSI variability can be decomposed into
Journal XX (XXXX) XXXXXX Connolly et al
multiple frequency components [246]; that the relationships
are different between different solar activity indices and TSI
[247,249]; and that the relationship between sunspot numbers
and TSI varies between cycles [248]. Indeed, in order to
accurately reproduce the observed TSI variability over the two
most recent solar cycles using solar disk images from ground-
based astronomical observatories, Fontenla and Landi (2018)
[250] needed to consider nine different solar features rather
than the simple sunspot and faculae model described earlier.
In summary, there are several key debates ongoing before
we can establish which TSI reconstructions are most accurate:
1. Which satellite composite is most accurate? In
particular, is PMOD correct in implying that TSI has
generally decreased over the satellite era, or is ACRIM
correct in implying that TSI increased during the 1980s
and 1990s before decreasing?
2. Is it more realistic to use a high variability or low
variability reconstruction? Or, alternatively, has the
TSI variability been dominated by the ~11-year solar
cycle, or have there also been significant multi-decadal
trends between cycles?
3. When did the mid-20th century peak occur, and how
much and for how long did TSI decline after that peak?
The answers to these questions can substantially alter our
understanding of how TSI has varied over time. For instance,
Velasco Herrera et al. (2015) used machine learning and four
different TSI reconstructions as training sets to extrapolate
forward to 2100 AD and backwards to 1000 AD [251]. The
results they obtained had much in common, but also depended
on whether they used PMOD or ACRIM as well as whether
they used a high or low variability reconstruction. As an aside,
the forecasts from each of these combinations implied a new
solar minimum starting in 2002-2004 and ending in 2063-
2075. If these forecasts are correct, then in addition to the
potential influence on future climate change, such a deficit in
solar energy during the 21st century could have serious
implications for food production; health; in the use of solar-
dependent resources; and more broadly could affect many
human activities [251].
2.4. Sixteen different estimates of changes in Total
Solar Irradiance since the 19th century and earlier
Soon et al. (2015) identified eight different TSI
reconstructions (see Figure 8 in that paper) [56]. Only four of
these reconstructions were used by the CMIP5 modelling
groups for the hindcasts that were submitted to the IPCC 5th
Assessment Report: Wang et al. (2005) [172] described above,
as well as Krivova et al. (2007) [176]; Steinhilber et al. (2009)
[252]; and Vieira et al. (2011) [253]. Coincidentally, all four
implied very little solar variability (and also a general decrease
in TSI since the 1950s). However, Soon et al. (2015) also
identified another four TSI reconstructions that were at least
as plausible including the Hoyt and Schatten (1993) [179]
and Lean et al. (1995) [185] reconstructions described above.
Remarkably, all four implied much greater solar variability.
These two sets are the “high solar variability” and “low solar
variability” reconstructions discussed in Section 2.3 which
both Soon et al. (2015) [56] and more recently Scafetta et al.
(2019) [60] have referred to.
Since then, eight additional estimates have been proposed
four low variability and four high variability. Coddington et
al. (2016) [237] have developed a new version of the Wang et
al. (2005) [172] estimate that has reduced the solar variability
even further (it uses a sunspot/faculae model based on
PMOD). Recently, Matthes et al. (2017) [110] took the mean
of the Coddington et al. (2016) [237] estimate and the
(similarly low variability) Krivova et al. (2010) [176,177]
estimate, and proposed this as a new estimate. Moreover,
Matthes et al. (2017) recommended that their new estimate
should be the only solar activity dataset considered by the
CMIP6 modelling groups [110]. Clearly, Matthes et al.’s
(2017) recommendation to the CMIP6 groups goes against the
competing recommendation of Soon et al. (2015) [56] to
consider a more comprehensive range of TSI reconstructions.
In Figure 2, we plot the four “low solar variability”
reconstructions from Soon et al. (2015) [56] as well as these
two new “low variability” estimates along with another two
estimates by Dr. Leif Svalgaard (Stanford University, USA),
which have not yet been described in the peer-reviewed
literature but are available from Svalgaard’s website
[, last accessed
27/03/2020], and have been the subject of some discussion on
internet forums.
Recently, Egorova et al. (2018) [254] proposed four new
“high variability” estimates that built on the earlier Shapiro et
al. (2011) [255] estimate. The Shapiro et al. (2011) [255]
estimate generated some critical discussion [256258] (see
Section 2.5.4). Egorova et al. (2018) [254] have taken this
discussion into account and proposed four new estimates
using a modified version of the Shapiro et al. (2011) [255]
methodology. Therefore, in Figure 3, we plot the four “high
solar variability” reconstructions from Soon et al. (2015) [56]
as well as these four new “high variability” estimates.
This provides us with a total of 16 different TSI
reconstructions. Further details are provided in Table 1 and in
the Supplementary Information. For interested readers, we
have also provided the four additional TSI reconstructions
discussed in Figure 1 in the Supplementary Information.
Figure 2. Eight low variability estimates of Total Solar Irradiance changes relative to 1901-2000 average.
Journal XX (XXXX) XXXXXX Connolly et al
Figure 3. Eight high variability estimates of the Total Solar Irradiance changes relative to the 1901-2000 average. Note the y-axis scales
are the same as in Figure 2.
Table 1. The sixteen different estimates of the changes in solar output, i.e., Total Solar Irradiance (TSI), analyzed in this study.
20th Century
mean TSI (W/m2)
Journal XX (XXXX) XXXXXX Connolly et al
Wang et al. (2005)
Krivova et al. (2007); updated by Krivova et al. (2010)
Steinhilber et al. (2009)
7362 BCE
Vieira et al. (2011)
Matthes et al. (2017)
Coddington et al. (2016)
Svalgaard (2014) "LASP" estimate
Svalgaard (2014) "SSN" estimate
Hoyt & Schatten (1993); updated by Scafetta et al. (2019)
Bard et al. (2000); updated by Ammann et al. (2007)
Shapiro et al. (2011); adapted by Schmidt et al. (2012)
Lean et al. (1995)
Egorova et al. (2018) "PHI-MC17" estimate
6000 BCE
Egorova et al. (2018) "PHI-US16" estimate
6000 BCE
Egorova et al. (2018) "PHI-MU16" estimate
Egorova et al. (2018) "SSR11" estimate
2.5. Arguments for a significant role for solar variability
in past climate change
The primary focus of the new analysis in this paper (Section
5) is on evaluating the simple hypothesis that there is a direct
linear relationship between incoming TSI and Northern
Hemisphere surface air temperatures. As will be seen, even for
this simple hypothesis, a remarkably wide range of answers
are still plausible. However, before we discuss in Section 3
what we currently know about Northern Hemisphere surface
air temperature trends since the 19th century (and earlier), it
may be helpful to briefly review some of the other frameworks
within which researchers have been debating potential
Sun/climate relationships.
The gamut of scientific literature which encompasses the
debates summarised in the following subsections (2.5 and 2.6)
can be quite intimidating, especially since many of the articles
cited often come to diametrically opposed conclusions that are
often stated with striking certainty. With that in mind, in these
two subsections, we have merely tried to summarise the main
competing hypotheses in the literature, so that readers
interested in one particular aspect can use this as a starting
point for further research. Also, several of the co-authors of
this paper have been active participants in each of the debates
we will be reviewing. Hence, there is a risk that our personal
assessments of these debates might be subjective. Therefore,
we have especially endeavoured to avoid forming definitive
conclusions, although many of us have strong opinions on
several of the debates we will discuss here.
The various debates that we consider in this subsection
(2.5) can be broadly summarised as being over whether
variations in solar activity have been a major climatic driver
in the past. We stress that a positive answer does not in itself
tell us how much of a role solar activity has played in recent
climate change. For instance, several researchers have argued
that solar activity was a major climatic driver until relatively
recently, but that anthropogenic factors (chiefly anthropogenic
CO2 emissions) have come to dominate in recent decades
[5,1317,22,68,80,185]. However, others counter that if solar
activity was a major climatic driver in the past, then it is
plausible that it has also been a major climatic driver in recent
climate change. Moreover, if the role of solar activity in past
climate change has been substantially underestimated, then it
follows that its role in recent climate change may also have
been underestimated [28,33,36
2.5.1. Evidence for long-term variability in both solar
activity and climate
Over the years, numerous studies have reported on the
similarities between the timings and magnitudes of the peaks
and troughs of various climate proxy records and equivalent
solar proxy records [28,30,37
39,54,55,80,182,186,189,209,262,268277]. Most climate
proxy records are taken to be representative of regional
climates, and so these studies are often criticised for only
representing regionalised trends and/or that there may be
reliability issues with the records in question [12,18,100,278]
(see also Section 2.6.3). However, others note that similar
relationships can be found at multiple sites around the world
[30,38,39,54,55,189,262,275,277]. And, it has been argued
that some global or hemispheric paleo-temperature
reconstructions show similar trends to certain solar
reconstructions [39,54,55,262].
Journal XX (XXXX) XXXXXX Connolly et al
These studies are often supplemented by additional studies
presenting further evidence for substantial past climatic
variability (with the underlying but not explicitly tested
assumption that this may have been solar-driven)
[30,39,54,55,262]. Other studies present further evidence for
substantial past solar variability (with the underlying but not
explicitly tested assumption that this contributed to climate
changes) [112,261,279,280].
Studies which suggest considerable variability in the past
for either solar activity or climate provide evidence that is
consistent with the idea that there has been a significant role
for solar variability in past climate change. However, if the
study only considers the variability of one of the two (solar
versus climate) in isolation from the other, then this is mostly
qualitative in nature.
For that reason, “attribution” studies, which attempt to
quantitatively compare specific estimates of past climate
change to specific solar activity reconstructions and other
potential climatic drivers can often seem more compelling
arguments for or against a major solar role. Indeed, this type
of analysis will be the primary focus of Section 5. However,
in the meantime, we note that the results of these attribution
studies can vary substantially depending on which
reconstructions are used for past climate change, past TSI, and
any other potential climatic drivers that are considered.
Indeed, Stott et al. (2001) explicitly noted that the amount of
the 20th century warming they were able to simulate in terms
of solar variability depended on which TSI reconstruction they
used. [6]
For instance, Hoyt and Schatten’s (1993) TSI
reconstruction was able to explain ~71% of the [temperature]
variance during the past 100 years and ~50% of the variance
since 1700” [179]. Soon et al. (1996) confirmed this result
using a more comprehensive climate model-based analysis,
and added that if increases in greenhouse gases were also
included, the percentage of the long-term temperature
variance over the period 1880-1993 that could be explained
increased from 71% to 92% [23], although Cubasch et al.’s
(1997) equivalent climate model-based analysis was only able
to explain about 40% of the temperature variability over the
same period in terms of solar activity [281]. More recently,
Soon et al. (2015) argued that if Northern Hemisphere
temperature trends are estimated using mostly rural stations
(instead of using both urban and rural stations), then almost all
of the long-term warming since 1881 could be explained in
terms of solar variability (using Scafetta and Willson (2014)’s
update to 2013 of the same TSI reconstruction [52]), and that
adding a contribution for increasing greenhouse gases did not
substantially improve the statistical fits [56].
On the other hand, using different TSI reconstructions, a
number of studies have come to the opposite conclusion, i.e.,
that solar variability cannot explain much (if any) of the
temperature trends since the late-19th century [5,1316,19,21].
For instance, Lean and Rind (2008) could only explain 10%
of the temperature variability over 1889-2006 in terms of solar
variability [15], while Benestad and Schmidt (2009) could
only explain 7±1% of the global warming over the 20th century
in terms of solar forcing [16].
Meanwhile, other studies (again using different TSI
reconstructions) obtained intermediate results, suggesting that
solar variability could explain about half of the global
warming since the 19th century [32,68,199] and earlier
2.5.2. Similarity in frequencies of solar activity metrics
and climate changes
Another popular approach to evaluating possible
Sun/climate relationships has been to use frequency analysis
to compare and contrast solar activity metrics with climate
records. The rationale of this approach is that if solar activity
records show periodic or quasi-periodic patterns and if climate
records show similar periodicities, it suggests that the
periodic/quasi-periodic climate changes might have a solar
origin. Given that the increase in greenhouse gas
concentrations since the 19th century has been more continual
in nature, and that the contributions from stratospheric
volcanic eruptions appear to be more sporadic in nature (and
temporary with aerosol cooling effects typically lasting only
2-3 years), solar variability seems a much more plausible
candidate for explaining periodic/quasi-periodic patterns in
climate records than either greenhouse gases or volcanic
Hence, much of the literature investigating potential
Sun/climate relationships has focused on identifying and
comparing periodicities (or quasi-periodicities) in climate,
solar activity and/or geomagnetic activity records. For
example, Le Mouël et al.
[50,61,62,90,98,194,194,201,282,283]; Ruzmaikin and
Feynman et al. [7375]; Scafetta et al. [126,127,259
261,284,285]; White et al. [226,227]; Baliunas et al.
(1997)[286]; Lohmann et al. (2004)[287]; Dobrica et al. [86
89]; Mufti and Shah (2011)[288]; Humlum et al. [47,63];
Laurenz, Lüdecke et al. [64,289]; Pan et al. (2020)[99]; Zhao
et al. (2020) [267].
Although the exact frequencies of each of the periodicities
and their relative dominance vary slightly from dataset to
dataset, the authors argue that the periodicities are similar
enough (within the uncertainties of the frequency analyses) to
suggest a significant role for solar and/or geomagnetic activity
in past climate change, albeit without explicitly quantifying
the exact magnitude of this role or the exact mechanisms by
which this solar influence manifests.
Again, it should be stressed that identifying a significant
solar role in past climate change does not in itself rule out the
possibility of other climate drivers and therefore does not
necessarily imply that recent climate change is mostly solar.
Journal XX (XXXX) XXXXXX Connolly et al
Indeed, the authors often explicitly state that the relative
contributions of solar, anthropogenic factors as well as other
natural factors in recent climate change may need to be
separately assessed [47,62,126,259,287]. However, they
typically add that the solar role is probably larger than
otherwise assumed [47,62,126,259]. In particular, Scafetta
(2013) notes that current climate models appear to be unable
to satisfactorily simulate the periodicities present in the global
temperature estimates, suggesting that the current climate
models are substantially underestimating the solar
contribution in recent climate change [259].
That said, one immediate objection to this approach is that
one of the most striking quasi-periodic patterns in many solar
activity records is the ~11 year solar cycle (sometimes called
the “Schwabe cycle”) described in previous sections, yet such
~11 year cycles are either absent or at best modest within most
climate records [21]. We will discuss the various debates over
this apparent paradox in Section 2.6. However, several
researchers have countered that there are multiple periodicities
other than the ~11 year Schwabe cycle present in both solar
activity and climate datasets
[62,73,88,99,126,182,194,259,284]. Moreover, many studies
have suggested there are indeed climatic periodicities
associated with the ~11 year cycle [62,64,73,86
A common limitation of these analyses is that the longer the
period of the proposed frequency being evaluated, the longer
a time series is required. The datasets with high resolution
typically only cover a relatively short timescale (of the order
of decades to centuries), meaning that they cannot be used for
evaluating multi-centennial cycles [62,99,126,194], while
studies using the longer paleoclimate records tend to be
focused on longer periodicities [261,262], although some
studies combine the analysis of long paleoclimate records with
shorter instrumental records [259]. That said, some records
can be used for studying both multi-decadal and centennial
timescales. For instance, Ruzmaikin et al. (2006) analysed
annual records of the water level of the Nile River spanning
the period 622-1470 AD. They found periodicities of ~88
years and one exceeding 200 years and noted that similar
timescales were present in contemporaneous auroral records,
suggesting a geomagnetic/solar link [73]. Interestingly,
although they also detected the 11-year cycle, it was not as
pronounced as their two multi-decadal/centennial cycles this
is consistent with the 11-year cycle being less climatically
relevant than other cycles [73].
Another criticism is the debate over whether the
periodicities identified in each of the datasets are genuine, or
merely statistical artefacts of applying frequency analysis
techniques to “stochastic” data. One problem is that even with
the relatively well-defined ~11 year Schwabe cycle, the cycle
is not strictly periodic, but quasi-periodic, i.e., the exact period
for each “cycle” can vary from 8 to 14 years. Meanwhile, there
are clearly non-periodic components to both climate and solar
activity datasets.
Indeed, some argue that many of the apparent
“periodicities” in these datasets are not actually periodic
patterns, but rather arise sporadically through stochastic
processes [290,291], e.g., Cameron and Schüssler (2019)
argue that all “periodicities beyond 11 years are consistent
with random forcing” in the various solar activity datasets
[291]. Others argue that we should not be expecting strict
periodicities but rather quasi-periodic patterns, and therefore
we should use frequency analysis techniques that are designed
to distinguish between pseudo-periodic components and
genuinely periodic (or quasi-periodic) components [61,62,99].
In any case, in recent years, several groups have begun
revisiting an old hypothesis that, if valid, could explain
genuine multidecadal-to-centennial periodic patterns in solar
activity. We will briefly review this hypothesis in Section
2.5.3. Sun-Planetary Interactions as a plausible
mechanism for long-term solar variability
From studying the variability of sunspot cycles in the
sunspot record and apparent similarities to estimates of past
climate changes over the last millennium, Dicke (1978) was
prompted to ask, “Is there a chronometer hidden deep in the
Sun?” [292]. That is, he wondered whether the variability
between solar cycles might not be “random”, but rather due to
various periodic but long-term processes that could lead to
various periodicities in solar activity on timescales greater
than the ~11 year cycle. If Dicke was right, then this would be
very consistent with many of the studies described in the
previous section. It would imply that many of the quasi-
periodicities identified by those studies could be genuine
periodicities (not necessarily linear in nature) and not just
statistical artifacts as their critics argued. It would also imply
that, in principle, it should be possible to reliably predict
future solar activity as well as retrospectively determine past
solar activity. Over the years, some researchers have even
suggested that long-term processes internal to the Sun might
be on a long-enough timescale to offer an alternative
explanation to the prevailing orbital-driven ice age theory
(which we will briefly discuss in Section 2.6.5) [293,294].
Dicke’s hypothesis has been disputed by others who argue
that the variability in solar activity between solar cycles is
strictly due to stochastic processes, i.e., that there are no
longer-term cyclical periodicities other than the ~11-year
cycle [290,291]. However, in recent years, several groups
have begun revisiting an old hypothesis to explain long-term
solar variability that Wolf had originally proposed in the mid-
19th century, which would prove that Dicke was correct
[63,126,210,259261,295306]. This is the hypothesis that
the gravitational effects of the planets orbiting the Sun can in
some manner (various mechanisms have been proposed)
Journal XX (XXXX) XXXXXX Connolly et al
interact with some of the mechanisms driving solar activity.
Note that we will discuss the related, but distinct, issue of the
influence that the other planets have on the Earth’s orbit of the
Sun [307,308] in Section 2.6.5. Here, we are referring to the
possibility that the changes in the orbits of each of the planets
over time might have an influence on solar activity, including
Although these Sun-Planetary Interactions (SPI) theories
can initially sound more astrological than scientific in nature,
many groups have noted that many of the periodicities in solar
activity (and climate) records discussed in the previous section
are intriguingly similar to the periodicities with which specific
planetary alignments occur. Indeed, even the ~11 year cycle
might potentially be related to planetary alignments such as
the 11.07-year Venus/Earth/Jupiter alignment cycle
[210,304,309,309] or harmonics associated with the
interactions between Jupiter, Saturn and the Sun that have
periodicities of about 10-12 years [127,259,310].
If any of these SPI theories transpire to be valid, then it
could have important implications for our understanding of
past solar variability, as well as offering us the potential to
predict future solar variability [261,300302,306]. It could
also be a powerful vindication of many of the studies
described in the previous section. As a result, it is not
surprising that the theories have generated significant interest
in recent years. However, studies considering these theories
have also generated a lot of criticism [311314], although
these critiques have in turn been addressed [127,285,303,315].
Even among proponents of the theory, there is considerable
ongoing debate over which combinations of orbitals are most
relevant, e.g., if the 2100-2500 year “Bray-Hallstatt
oscillation” is driven by SPI, which is more relevant: the 2318-
year periodicity involving Jupiter, Saturn, Uranus and
Neptune [260,261] or the 2139-year periodicity involving just
Jupiter and Saturn [301]?
At any rate, any discussion of the theory appears to be
highly controversial and often moves beyond the realm of
purely scientific debate. This can be seen from some of the
reactions that have occurred when articles considering the
concept are published. We give two examples to illustrate the
contentiousness of this theory, and how non-scientific
arguments often get invoked in a discussion of this theory. We
provide the following examples not because we believe the
theory is beyond scientific critique (far from it), but rather to
emphasise that readers who are interested in the scientific
validity of the theory (or otherwise) should recognise that
much of the criticism of the articles promoting SPI often
moves beyond the realm of pure scientific debate.
As a first example, in 2014, a special issue dedicated to
investigations into SPI theory was published in a new journal,
“Pattern Recognition in Physics”. In response, the managing
director of Copernicus Publications terminated the entire
journal for reasons that are still not entirely clear, but
apparently included the facts that one of the editors of the
journal was a “climate skeptic” and that the concluding article
in the special issue criticised some of the interpretations and
conclusions of “the IPCC project” regarding future climate
change trends. Interested readers can find the managing
director’s full statement on his decision as well as links to an
archive of the journal at https://www.pattern-recognition-in- One of the editors in question, the late Nils-Axel
Mörner, has also responded in Mörner (2015) [316]. To
clarify, we are not arguing here that the articles in that special
issue should somehow have been protected from scientific
critique or scrutiny. On the contrary, we are noting that the
managing director’s decision to terminate the journal did not
seem to be based on any of the scientific evidence and
arguments for SPI which were presented in the articles.
Further, now that the journal has been terminated, it is likely
that many of those who might have otherwise debated for or
against the scientific arguments presented in any of those
articles will simply dismiss the articles out of hand.
As another example, Zharkova et al. (2019) [317] was
retracted (despite the objections of three of the four authors
[318]) because, in one of the subsections in the paper, the
authors appear to have made a mistake in their interpretation
of SPI theory. Specifically, in their penultimate subsection,
they appear to have mistakenly overlooked the fact that as the
barycenter of the solar system moves, the Earth mostly moves
in tandem with the Sun, i.e., the Earth-Sun distance does not
fluctuate as much as they had assumed. This was indeed a
mistake as noted by, e.g., Scafetta (2020) [260]. Also, much
of the rest of the article built on earlier analysis that has been
separately criticised, e.g., Usoskin (2018) [319] (although
defended by the authors [320]). However, given that the
mistake in question only really related to a subsection of the
paper and one sentence in their conclusions, it is surprising
that the reaction of the journal was to retract the article rather
than encourage the authors to issue a corrigendum.
Most of the researchers currently publishing works that are
considering SPI (which includes some of us) appear to be open
to the fact that the field is still somewhat speculative and
ongoing, and that the theory that SPI significantly influences
solar activity has not yet been satisfactorily proven. In
particular, most SPI researchers explicitly acknowledge that
the direct vertical tides induced on the Sun by the planets are
very small (millimeters), and that a more compelling
mechanism by which the planetary motions could
significantly influence solar activity (including TSI) needs to
be established [63,126,210,259261,295,298305].
Nonetheless, several such mechanisms have now been
proposed in the literature which seem plausible and worthy of
further investigation [260,302]. For instance, perhaps the
changes in the strength and spatial distribution of potential
energy induced by the planetary orbits could influence solar
irradiance [298,300,302]. Abreu et al. have proposed that the
Journal XX (XXXX) XXXXXX Connolly et al
time-varying torque exerted by the planets on the a non-
spherical tachocline could significantly influence solar
activity [299,315]. Scafetta (2012) has proposed that the very
modest planetary tidal effects implied by classical physics
might be substantially amplified in modern physics by
modulating the nuclear fusion rates in the Sun and therefore,
TSI. He therefore calculates that planetary tides could
theoretically induce an oscillating luminosity increases in TSI
of between 0.05 and 1.63 W/m2, i.e., a range consistent with
the observed variations in TSI during the satellite era [309].
Meanwhile, Stefani et al. have developed a solar dynamo
model in which tidal synchronisation amplifies the weak
individual effects during “beat periods” [210,304,306].
Scafetta (2020) notes that the various hypotheses should still
be treated speculatively especially since often the proposed
mechanisms are at least partially inconsistent with each other
[260]. However, often the proposed mechanisms are
complementary with each other, e.g., Yndestad & Solheim
(2017) proposed a hypothesis that combined features of four
different mechanisms [302].
2.5.4. Analogies of solar variability with the variability
of other “Sun-like” stars
Another approach that several researchers have taken to try
and estimate the magnitude of past solar variability is by
analogy with variability of other stars that are “Sun-like” (a
somewhat loose term, as will be discussed). Stellar variability
does not directly tell us about the exact timings of historic
solar activity trends. However, given that the Sun is itself a
star, by comparing the behaviour of other stars to what we
know of the Sun, we can provide a better context for how we
should expect the Sun to behave, including the range of
variability in TSI we should expect to see over multi-decadal
to multi-centennial time-scales. Of particular relevance for our
discussion is the potential help it could provide in resolving
the debate over whether the “low variability” or “high
variability” TSI reconstructions (Section 2.3-2.4) are more
This field of studying “Sun-like stars” was largely
pioneered by the astronomer, Olin Wilson (1909-1994),
working at the Mount Wilson Observatory (CA, USA the
similarity in names was coincidental). To determine which
stars are most Sun-like and properly compare the long-term
variability of the Sun with other stars, it is important to
systematically record measurements of a large sample of
potentially “Sun-like stars” over as long a period as possible.
Therefore, in 1966, he began a spectroscopic program of
regularly recording the relative fluxes of two frequency bands
in the stellar emissions from a sample of 91 main-sequence
stars [321]. The two frequency bands were those associated
with the Ca II “H” and “K” emission lines, as it was known
that the ratio in the emission from these two narrow (i.e., about
1 Å) bands varies with solar magnetic activity. The program
became known as “the Mount Wilson HK project” and was
continued by Baliunas et al. until funding ran out in 2003
[169,265,322324]. A later program consisted of a
collaboration between Fairborn Observatory (AZ, USA) and
Lowell Observatory (AZ, USA) to acquire Strömgren b and y
photometry (a different estimate of stellar activity using very
broad wavelength bands) of a large sample of stars to
approximate their TSI variability [169,264,323,325328].
In the context of our paper, one of the first points noted
from the Mount Wilson HK project as the records for each star
increased to about a decade or longer was that many stars (but
not all) appear to undergo cyclical variations in the combined
fluxes of the H and K lines on timescales similar to those of
the Sun’s sunspot cycle [265,321,325]. For some stars, the
emission fluxes seemed to be mostly constant, while for
others, the fluxes seemed to be undergoing a long-term
increase or decrease.
Initially, to compare these stellar measurements to those of
the Sun, Wilson (1978) used equivalent lunar measurements
of the reflected sunlight from the Moon [321]. Others have
used Ca II spectroscopic measurements from the National
Solar Observatory Sacramento Peak (NM, USA) of the “Sun-
as-a-star” program [329331]. Egeland et al. (2017) has
recently compared both approaches and found good
agreement between them [324].
These HK measurements of “the Sun as a star” show
cyclical changes that closely correspond to the rise and fall in
sunspot numbers over a solar cycle [265,324,326,329331].
Similarly, the variability in Strömgren b and y photometry also
seems to capture much of the variability in TSI over a solar
cycle, although surprisingly there is some controversy over
whether (b+y)/2 is anti-correlated with TSI [332,333] or
correlated [169,264,328,334,335]. The controversy appears to
arise because solar observations from the Earth are from the
ecliptic plane (where the amplitude of the 11-year variability
in TSI is relatively low) whereas stellar observations could be
from any angle [328,334336].
At any rate, several studies have suggested that the
variability of solar activity for the Sun during the satellite era
has been relatively low compared with other stars
[169,258,264,265,323,325,326,336338]. This would be
consistent with high solar variability reconstructions.
However, other studies have argued that the low solar
variability estimates are more plausible, e.g., Hall and
Lockwood (2004) [327]; Judge and Saar (2007) [339].
Meanwhile, Judge et al. (2020) using an analysis of a sample
of 72 Sun-like stars calculated an upper bound for the solar
forcing since 1750 which was much larger than the IPCC’s
low variability estimate of solar variability, although the
IPCC’s estimate also fell within the bounds of their analysis
[264]. As a result, their analysis is compatible with either low
or high variability reconstructions.
Journal XX (XXXX) XXXXXX Connolly et al
A major challenge with using Sun-like star data to evaluate
long-term solar variability is the difference in timescales,
given that we have hundreds of years of sunspot records and
proxies covering millennia of solar activity, while only several
decades at most for our Sun-like star data.
One approach has been to compare the ranges of the multi-
decadal variability in the HK and/or b+y measurements of the
stellar data to the equivalent measurements for the Sun during
recent decades. Many of these studies have suggested that the
solar variability in recent decades has been relatively low
compared with other Sun-like stars [169,187,257,258,264
266,323,326,328330]. This would be consistent with high
solar variability reconstructions in that it would imply that the
solar variability could be greater over longer time-scales.
However, other studies disagree and argue that the solar
variability in recent decades overlaps quite well with the range
of stellar variability for Sun-like stars [170,327,339,340]. This
would be consistent with the low solar variability
A major reason for the conflicting conclusions seems to be
due to the relatively small samples of suitable stars with large
amounts of data and deciding on which stars are most “Sun-
like”. For instance, in an early analysis of the data, Baliunas
and Jastrow (1990) identified 13 stars with relatively long
records that appeared to be suitable Sun-like stars. As part of
their analysis, they noted that four of these stars (~30%) were
non-cycling and that these stars implied much lower activity
[265]. Later studies with larger sample sizes have suggested
that “non-cycling” stars only represent 10-15% of the Sun-like
stars [169,170,341,342]. Nonetheless, Baliunas and Jastrow
speculated that maybe these “non-cycling” stars might
correspond to Sun-like stars that had entered a “Maunder
Minimum”-like state. Lean et al. combined this hypothesis
with measurements from the “Sun-as-a-star” program to
estimate that the TSI during the Maunder Minimum had been
0.24% lower than present-day [329,330]. This result was later
used for calibrating the Lean et al. (1995) TSI reconstruction
of Figure 3(d) [185].
However, since then, several studies have suggested that
identifying Sun-like stars in “Maunder Minimum”-like states
is probably more challenging [327,339,342344]. Hall and
Lockwood (2004) [327] found that 17% of a larger sample of
57 Sun-like stars were “non-cycling”, but the distribution of
stellar activities was not as neatly divided as Baliunas and
Jastrow’s original sample. While some have argued that this
is an argument in favour of the low-variability reconstructions,
e.g., Schmidt et al. (2012) [256], others have noted that we still
do not know whether these “non-cycling” stars were genuinely
in a Maunder Minimum state, rather than being not as Sun-
like as assumed [342,343]. Therefore, there is some interest
[339,344] in using more nuanced methods for identifying
genuinely Sun-like stars that are currently in a Maunder
Minimum-like state than Baliunas and Jastrow’s simple first
approximation of dividing stars into “cycling” or “non-
If Sun-like star monitoring programs like the early Mount
Wilson, Lowell and Fairborn Observatory programs could be
expanded to include a larger sample of potential Sun-like stars
(ideally a minimum of several hundred candidates), and these
programs were continued for multiple decades, then it is
plausible that we could identify samples of Sun-like stars
transitioning from a cycling state to a non-cycling state (or
vice versa).
In the meantime, other studies have taken different
independent approaches to using the Sun-like stars data to
distinguish between high and low-variability reconstructions.
For instance, Zhang et al. (1994) estimated the relationship
between stellar brightness (analogous to TSI) and stellar
magnetic activity (analogous to sunspot/faculae activity) by
comparing the HK and b+y measurements[266]. Importantly,
they found a reasonably linear relationship. By extrapolating
this relationship to zero magnetic activity, and assuming that
this was similar to the Maunder Minimum, they calculated that
TSI had probably increased by something between 0.2% and
0.6% since the Maunder Minimum. This would be consistent
with the high variability reconstructions. Soon et al. (1994)
also noted that, like solar activity, the stellar activity of cyclic
stars seemed to be inversely proportional to the cycle length,
and this offered another metric for comparing solar activity to
that of the Sun-like stars [187].
More recently, controversy over the high solar variability
in the TSI reconstruction of Shapiro et al. (2011) [255] in
Figure 3(c) has led to some interesting comparisons with the
Sun-like star data [254,257,258]. Judge et al. (2012) argued
that the model “A” for the irradiance from the quiet Sun’s
photosphere used for generating the Shapiro et al. (2011)
reconstruction led to certain unrealistic results, and that using
a replacement “model B” reduced the variability of the
reconstruction by a factor of two [257]. This would still make
the reconstruction a high variability reconstruction, but
obviously less high. However, they also noted that when they
split the original reconstruction into a series of 15 year
segments (for comparison with the various 10-20 year stellar
records), the distribution of trends was actually quite
consistent with that implied by the Sun-like star data [257].
This was later confirmed by Shapiro et al. (2013) [258] and
Judge et al. (2020) [264], suggesting that perhaps the high
variability implied by the original reconstruction was
coincidentally correct. Egorova et al. (2018) [254] developed
an equivalent “model B” that was able to replicate the results
of Judge et al. (2012), but they noted that by varying the choice
of which solar modulation potential dataset to use, they could
get four different TSI reconstructions Figure 3(e)-(h).
Coincidentally, one of these (“PHI-MU16”) implied a similar
difference between the Maunder Minimum and present to the
original Shapiro et al. (2011) reconstruction [254], suggesting
Journal XX (XXXX) XXXXXX Connolly et al
a possible explanation for the apparent contradictions between
the two separate analyses of Judge et al. (2012). On the other
hand, Yeo et al. (2020) disputes whether any of the models of
the quiet solar photosphere considered by Shapiro et al. (2011)
[255], Judge et al. (2012) [257] or Egorova et al. (2018) [254]
are reliable and argues for a different model which implies a
rather modest difference between the Maunder Minimum and
present [345]. Although, Rempel (2020) clarifies that Yeo et
al.’s model does not completely rule out the high TSI changes
implied by these reconstructions, but rather suggests that they
would “require substantial changes in the quiet-Sun field
strength (about a 50% reduction)” between the Maunder
Minimum and present [178].
Unfortunately, carrying out multi-decadal monitoring of a
large sample of Sun-like stars requires considerable effort and
resources, and many of these projects have been discontinued
due to lack of funding. However, some recent projects such as
the Kepler space mission (2009-2013) or the Chinese ground-
based Large Sky Area Multi-Object Fiber Spectroscopic
Telescope (LAMOST) surveys (2012-present) have provided
important additional data for the short-term variability of Sun-
like stars [336338,346349]. The relatively short
observational timespans of these projects mean that they
cannot be used for studying the multi-decadal variability.
However, the data can be used for comparing the short-term
variability of the Sun to other stars on timescales less than a
few years [336338,346349]. Additionally, the data can
improve our understanding of the relationships between the
faculae:starspot ratios which we discussed in Section 2.1-2.3.
E.g., why are some stars “faculae-dominated” (like the Sun is
currently) and others “spot-dominated” [171,335,347,350]?
2.6. The apparent paradoxes from the 11 year
“Schwabe” quasi-cyclical component
If you consider all of the TSI reconstructions among the
“low variability estimates” (Figure 2), except for the
Steinhilber et al. (2009) reconstruction which is based on
cosmogenic isotope proxies, it could appear that the most
significant feature is the short-term maximum-minimum
Sunspot Cycle fluctuations which occur with a roughly-11
year period (i.e., the “Schwabe cycle”). Therefore, initially, it
might be supposed that the influence of solar variability on the
Earth’s climate should be most obvious over the course of
each Sunspot Cycle. This applies even more so if you treat the
raw Sunspot Number (SSN) record as a proxy for TSI, since
the SSN falls to zero during every cycle [21].
This has been a puzzle for the community since the
beginning of modern research into possible sun/climate
connections, since the fluctuations in global surface air
temperature (for instance) over a Sunspot Cycle are relatively
small at best [17,41], and often quite ambiguous [100].
Typically, the peak-to-trough variability in global surface
air temperatures over a sunspot cycle is estimated empirically
at about 0.1°C [17,41], although Scafetta (2009) notes that the
estimates of this “11-year solar cycle signature” in the
literature vary from about 0.05°C to about 0.2°C [41]. He also
notes that typical climate models are unable to simulate even
this modest temperature variability over a solar cycle, with
some climate models predicting the solar cycle signature to be
as low as 0.02-0.04°C [41]. Partly on this basis, he suggests
that there are, …reasons to believe that traditional climate
models cannot faithfully reconstruct the solar signature on
climate and are significantly underestimating it[41].
In any case, if you assume that (a) the low variability TSI
estimates are more reliable than the high-variability estimates,
and (b) there is a linear relationship between TSI and global
(or hemispheric) surface air temperatures, these relatively low
11-year solar cycle signature estimates would initially appear
to put a very modest upper bound on the maximum
contribution of solar variability to the Northern Hemisphere
surface temperature trends since the 19th century. In Section 5,
we will compare and contrast the linear fits using the high and
low-variability TSI estimates, i.e., we will be implicitly
evaluating the first assumption. However, there is also a
considerable body of literature critically evaluating the second
assumption from several different avenues. Therefore, in this
section, we will briefly review some of the main attempts to
resolve this apparent “11-year paradox”.
The apparent paradox could indicate that the Sun affects the
climate by other covarying aspects of solar variability
(changes in the ultraviolet (UV) component, galactic cosmic
ray fluxes, etc.) rather than just TSI changes. Indeed, much of
the literature over the last few decades has suggested that we
should not be only looking for a direct linear relationship
between TSI and global surface air temperatures, but rather
considering the possibility of more indirect and/or subtle
Sun/climate relationships. Some of the main hypotheses are
summarized schematically in Figure 4.
Figure 4. Schematic illustrating the domains of proposed action for
three distinct sets of current hypotheses for how the Sun indirectly
influences the Earth’s climate. Type (a) notes that there is greater
variability in the ultraviolet region of the incoming solar irradiance,
but that this is mostly absorbed in the stratosphere. Therefore, it is
Journal XX (XXXX) XXXXXX Connolly et al
argued that the main Sun/climate relationships originate in the
stratosphere but may be propagated down to the troposphere and
surface (“top-down”). Type (b) suggests that there are direct effects
within the troposphere from variations in Total Solar Irradiance,
but that these are either subtle (e.g., through changes in circulation
patterns), or involve heating the oceans which then indirectly alter
the tropospheric climate (“bottom-up”). Type (c) notes that solar
variability reduces the flux of incoming galactic cosmic rays (GCR)
when the solar wind is strong, and that suggests that this GCR flux
influences the climate in the troposphere and/or stratosphere.
2.6.1. “Top-down” vs. “bottom-up” mechanisms
As a surface-dwelling species, we are most interested in the
climate at or near ground level, e.g., the surface air
temperature. Moreover, most of our climate records similarly
describe climate at or near the surface. However, as Dines
(1919) noted in the early 20th century from analysis of early
weather balloon measurements [351], the variabilities in
temperatures and pressures at the surface are somewhat
connected to those in the troposphere and stratosphere. Indeed,
the temperature variability throughout the troposphere is
partially correlated to that at the surface and boundary layer
and partially anti-correlated to that in the stratosphere [352].
With that in mind, several researchers looking for Sun/climate
relationships have identified potential “top-down”
mechanisms whereby a relatively strong ~11-year solar cycle
signature in the stratosphere might, in turn, propagate
downwards to indirect influence surface climate perhaps in
a subtle and nuanced manner, that could explain the apparent
“11-year paradox”.
Notably, Labitzke and van Loon (1988) [65] noticed
intriguing correlations between Northern Hemisphere winter
temperatures (and also the geopotential heights at particular
atmospheric pressure levels) and the 11-year solar cycle in the
stratosphere, particularly in the polar regions. They found that
these correlations were most apparent when they split the data
into two halves based on whether the so-called “quasi-biennial
oscillation” (QBO) wind was in its west phase or east phase.
The QBO is a stratospheric circulation pattern, whereby the
prevailing stratospheric winds near the equator appear to
alternate from being mostly westerly to mostly easterly
roughly every two years. Later work by this group extended
these relationships to include the tropics, sub-tropics and both
hemispheres as well as other seasons [66,67,211].
Although some of the relationships identified by Labitzke
et al. also seem to be partially present within the troposphere,
the relationships appear to be most pronounced for the
stratosphere. In that context, several researchers noted that
most of the ultraviolet (UV) component of the incoming solar
irradiance is absorbed within the stratosphere, and the
variability of this UV component over the ~11-year cycle
seems to be much greater than for TSI [217219,333,353].
This has led to one of the main sets of current hypotheses for
an indirect Sun/climate relationship illustrated schematically
as Figure 4(a). That is, it is argued that the relationships
initially identified by Labitzke et al. and built upon by others
[76,213,215,222225] are in some way driven by UV
irradiance and therefore originate in the stratosphere, rather
than in the troposphere [76,213,217,219,222225].
These “top-down” mechanisms imply that the Sun/climate
relationships identified in the troposphere or at the surface
occur indirectly through coupling of the stratosphere and
troposphere. From this perspective, one solution to the
apparent 11-year paradox is that there are Sun/climate
relationships, but they are mostly confined to the stratosphere,
and, by the time the “solar signal” has reached the surface,
only a modest signal remains. Indeed, climate models that
attempt to incorporate these “top-down” mechanisms
generally simulate a relatively small and diffused “solar
signal” at surface level [217,219221,225]. For example,
Haigh and Blackburn’s (2006) model simulations suggest that
solar heating from increased UV irradiance took at least 50
days to heat the stratosphere but up to 500 days to reach the
troposphere [219]. Some studies have found solar signals in
the troposphere, but argued that they are less pronounced than
in the stratosphere, i.e., consistent with the “top-down”
hypothesis [213,215,216,224].
That said, other studies have also found evidence for a
strong solar signal for temperature variability within the
troposphere [27,78,89,91,354]. In particular, Soon et al.
(2000) found intriguing correlations between a specific
measure of solar activity (the area of the Sun covered by
coronal holes) and air temperatures in the lower troposphere
(as derived from satellite measurements) [27]. Their results
suggested that most of the temperature variability within the
lower troposphere (over the satellite era at least) could be
explained in terms of solar variability, volcanic activity and El
Niño/La Niña periods [27]. As can be seen from the schematic
in Figure 4, the lower troposphere nominally includes the
surface. Therefore, the results of Soon et al. (2000) might
initially appear to contradict the apparent 11-year paradox
[27]. However, we note here an additional nuance in that the
satellite-based estimates of “lower troposphere” temperature
trends mostly describe the temperatures above the boundary
layer, i.e., above the first few kilometers. Ongoing work by
some of us (RC, MC and WS) suggests that the temperature
variability within the regions of the troposphere that are above
the boundary layer is more closely related to that of the
stratosphere than within the lowest parts of the troposphere
closest to the surface. With that in mind, we suggest future
research into possible Sun/climate relationships considering
the troposphere should distinguish between the boundary layer
part of the troposphere and the tropospheric region above the
boundary layer (as well as separately considering the
“tropopause” transition between the troposphere and
Meanwhile, others have argued for a more nuanced solar
signal at the surface/within the troposphere, whereby solar
Journal XX (XXXX) XXXXXX Connolly et al
variability directly influences the surface and tropospheric
climate, but in more subtle ways that become amplified via
positive feedbacks and/or changes in oceanic or atmospheric
circulation patterns [214,229]. For instance, van Loon et al.
have argued for solar signals that alter circulation patterns
associated with, in turn: Hadley and Walker circulations
[234,355]; El Niño Southern Oscillation (ENSO) [92,234,356]
and the North Atlantic Oscillation (NAO) [93]. Changes in
these circulation patterns themselves could alter regional and
even hemispheric surface temperatures. Similarly, Ruzmaikin
et al. found evidence for a solar signal in the North Annular
Mode (NAM), which in turn appears to influence Northern
Hemisphere surface temperatures [71,72]. Many other
relationships along these lines have now been proposed
Thereby, these “bottom-up” mechanisms Figure 4(b) -
offer an alternative solution to the apparent 11-year paradox,
in which the 11-year cycle only has a modest direct influence
on surface temperatures but also indirectly influences the
climate (perhaps on multi-decadal timescales) by altering
prevailing circulation patterns especially those associated
with key “centers of action” [111].
In terms of Sun/climate relationships at the surface, some
researchers have argued that it is difficult to establish whether
the “top-down” or “bottom-up” mechanisms are more
important [78,212,214]. Others have suggested that both sets
of mechanisms are important [9597,362], with Roy et al.
proposing that a complex series of interconnected mechanisms
from both sets could be involved [9597]. Meanwhile, Dima
and Voiculescu (2016) suggest that both the “top-down” and
“bottom-up” mechanisms might also combine with a third
mechanism involving solar-driven variability in cloud cover
[362]. They suggest this could be driven by one of the
proposed Galactic Cosmic Ray mechanisms, which we will
discuss in Section 2.6.4. In that case, their Sun/climate
relationships would involve all three of the sets of mechanisms
described in Figure 4.
2.6.2. “The ocean as a buffer”: Ocean heat capacity as
a “filter capacitor”-based buffering mechanism
Reid (1987; 1991; 2000) [69,231,232] noticed that the
global Sea Surface Temperature (SST) time series was
intriguingly similar to the multi-decadal trends of the Sunspot
Number (SSN) record once the 11-year cycle had been
removed by either smoothing both series with an 11-year
running mean [231] or by using the “envelope” of the SSN
record, i.e., the time series generated by connecting the
maxima from each solar cycle [232]. He argued that variability
in TSI was influencing ocean temperatures on multi-decadal
timescales but not as much over the 11-year cycle due to the
relatively short time frame and the fact that it was (quasi)-
cyclical: “The cyclical nature of the solar [11-year cycle]
forcing, however, substantially reduces its climatic impact,
since the thermal inertia of the ocean is large enough to
dampen an 11-year cycle considerably- Reid (2000) [69] .
Hence, Reid’s solution for the apparent “11-year paradox”
described above was that the heat capacity of the oceans
effectively acts as a buffer that filters out much of the short-
term cyclical solar variability of the incoming TSI over the 11-
year cycle but captures much of the longer multi-decadal to
centennial trends and cycles in TSI. If the ocean temperatures
are influenced by solar variability on these longer timescales,
this could in turn influence oceanic and/or atmospheric
circulation patterns, which in turn could influence land surface
If this hypothesis is valid, it would imply we need to
separately consider TSI variability on multiple timescales
(dovetailing with the types of analysis in Section 2.5.2 and
2.5.3) [41]. Indeed, Dima and Lohmann (2009) have proposed
that solar variability on millennial time scales could combine
with variability in oceanic thermohaline circulations to create
a possible combined solar-thermohaline circulation origin
for the ~1,500-year [climate change] cycle[112]. Soon and
Legates have proposed an analogous solar/thermohaline
mechanism that could also operate on multidecadal-to-
centennial timescales [113,233].
White et al. (1997; 1998) [226,227] attempted to do such
an assessment of the influence of TSI variability on ocean
temperatures using the Lean et al. (1995) TSI reconstruction
of Figure 3(d). White et al. (1997) used an SST dataset
covering the period 1900-1991 and an upper-ocean
temperature profile dataset covering the period 1955-1994
[226]. In a second paper, White et al. (1998) repeated the
analysis using a time series of the depth-weighted average
temperatures (DVT) of the upper oceans for 1955-1996 [227].
Both studies found that the solar influence on ocean
temperatures was different on decadal timescales (9-13 years)
compared with interdecadal timescales (18-25 years) and for
the longer dataset in the first paper, probably multi-decadal to
centennial scales (although the dataset was only 92 years
long). In principle, this is consistent with Reid’s hypothesis
that the solar influences on ocean temperatures are different
on different timescales. Indeed, the first paper concluded that
solar variability could explain between 0.2-0.3°C (i.e., 50-
75%) of the 0.4°C global SST warming over the preceding
century which at the time had occurred, i.e., largely agreed
with Reid. However, in the second paper, they clarified that
the long-term increase in TSI in recent decades implied by the
Lean et al. (1995) [185] TSI reconstruction was insufficient to
explain the rate of warming and argued that a greenhouse gas
component was needed. We note Lean was a co-author of both
White et al. papers.
More recently, Scafetta (2009) has argued empirically that
the global temperature trend estimates of the last 400 years are
best fit in terms of solar variability by assuming that solar
forcing from changes in TSI act on both fast (less than 0.5
Journal XX (XXXX) XXXXXX Connolly et al
year) and slower, multidecadal time-scales [41]. Although that
analysis was empirical in nature, and therefore did not
postulate a definitive mechanism for why, this would also be
consistent with the “ocean as a buffer” mechanism described
above. Indeed, many energy balance climate models (EBMs)
compartmentalize the oceans into two or more layers with
different time-scales in each layer to explicitly model this
buffering mechanism, e.g., Lindzen & Giannitsis (1998)
[363]; Held et al. (2010) [364]; Ziskin & Shaviv (2012) [48];
Geoffroy et al. (2013)[365]; Rohrschneider et al. (2019) [366].
Moreover, Wang et al. (2020) suggest that the relationships
between TSI and ocean heat content may vary between oceans
and on different timescales [367].
The “ocean as a buffer” mechanism on its own could
potentially resolve the apparent “11-year cycle paradox” and
imply that investigations into a solar influence on the climate
should probably prioritise looking at TSI and climate
variabilities on timescales longer than the ~11 year cycle, i.e.,
multidecadal-to-centennial or longer. However, we note that
even in terms of the ~11-year component, there is considerable
debate over the magnitude of the solar influence. Within the
literature, estimates of the solar-induced variability on ocean
temperatures over the course of a cycle vary from 0.02-0.2°C
[40,226230,368]. Therefore, further investigation into the
role of TSI on the ~11-year timescale does still seem
warranted. Shaviv (2008) found evidence for a solar influence
over the 11-year cycle on ocean temperatures that was 5-7
times greater than what he would have expected from the
changes in TSI alone [40]. He suggested that this indicated
that some form of solar amplification mechanism, such as the
ones we will review in Section 2.6.4, might be involved. This
has support from Solheim (2013) who noted a tight correlation
between global annual-averaged sea level changes and
annually-averaged sunspot numbers [51]
2.6.3. Sun-climate effects are more pronounced in
certain regions
In Section 2.6.1, we showed that several studies have
argued that solar variability could indirectly influence
regional temperature trends, e.g., via altering atmospheric
circulation patterns. However, other studies have argued for a
more direct relationship between solar variability and regional
climate trends.
Using one of the high variability TSI estimates (Hoyt and
Schatten (1993) [179]), Soon found a striking correlation
between TSI and Arctic surface air temperatures since at least
1875, i.e., the entire length of the then-available temperature
dataset [31,113]. This suggested that most of the Arctic
temperature trends since at least the 19th century (including the
Arctic warming since the 1970s) was due to solar variability
rather than anthropogenic factors. Interestingly, Callendar
(1938) also argued against an anthropogenic role in Arctic
temperature trends in his original case for a CO2-driven global
warming [369]. Soon et al. (2011) later found a similar result
for China [370], while Scafetta et al. found the same for the
Central England Temperature dataset from at least 1700 to the
present [52,259,284]. Soon et al. (2015) noted that after
accounting for urbanization bias in the Northern Hemisphere
temperature data, the same TSI estimate could explain most of
the long-term temperature trends since at least 1881 for the
entire hemisphere (but not for urban areas) [56]. Soon and
Legates (2013) also found evidence that the same TSI estimate
could explain much of the trends in the so-called Equator-to-
Pole Temperature Gradient [233]. In other words, the Hoyt
and Schatten (1993) TSI estimate implies a very strong
correlation between surface air temperatures and TSI. Indeed,
this was already noted by Hoyt and Schatten (1993) [179].
One of us (JES) has noted (manuscript in preparation) this TSI
estimate is also well correlated with the 440-year long series
of estimated positions of the August ice edge in the Barents
Sea described in Mörner et al. (2020) [63].
On the other hand, if researchers use one of the low
variability TSI estimates of Figure 2, or even use the raw SSN
record as a proxy of solar activity, it is much harder to find a
strong relationship. Nonetheless, several researchers have
argued that significant correlations can still be identified
between solar activity and surface temperature and/or
precipitation for certain geographical regions [43
For instance, in a series of papers (independent of their
more recent work discussed in Section 2.5.2), Le Mouël and
colleagues argued that climatic trends in Europe [4345,115],
the United States [115,371] and possibly Australia [43] were
consistent with being at least partially solar-driven. These
studies were collectively disputed by Yiou et al. in two papers
[372,373], although Le Mouël et al. (2011) defended their
analysis [46].
Within the paradigm of the “11-year puzzle”, these studies
could potentially be interpreted in several distinct ways:
1. They could be case studies representative of much wider
global Sun/climate relationships that might be overlooked
in global analyses that smooth out subtle relationships
through averaging processes, for instance. Also, in some
cases, these studies are confined to certain regions simply
due to the limited availability of the relevant data for other
regions [43,52,56,284]. In other cases, the analysis may
be carried out as a case study [86,87,188,370]. This could
then potentially contradict the “11-year paradox” if the
relationships were later shown to be global in nature.
With that in mind, Dobrica et al. (2018) argue that the
Sun/climate relationships they identified in their early
case studies of Europe [86,87] can now also be extended
to much of the Northern Hemisphere, and for different
levels of the atmosphere from the surface to the
stratosphere [89].
Journal XX (XXXX) XXXXXX Connolly et al
2. On the other hand, it might be argued that these
relationships are strictly regional in nature. That is, the
studies may have just identified unique geographic
regions where the climatic trends have a particularly
pronounced solar influence [44,45,49,63,64,86,87,289].
This could then be consistent with the “11-year paradox”,
which refers to global trends.
3. Another interpretation offers a compromise between the
other two perhaps these regions represent important
climatic “centers of action” [111]. In that case, perhaps
the solar-induced climatic variability of these regions
could in turn lead to shifts in prevailing atmospheric
and/or oceanic circulation patterns. Christoforou and
Hameed (1997) [111] proposed that, in principle, this
could offer potential mechanisms whereby a relatively
small variability in TSI over the ~11-year cycle could
indirectly lead to multidecadal climatic trends on regional
or even global scales. Several examples of such potential
mechanisms have been proposed, e.g., Soon (2009) [113];
Mörner et al. (2020) [63]. As an aside, Mörner et al.
(2020) [63] proposed that it could be the solar wind and
not TSI which is the main climatic driver. They propose
that the solar wind interacts with the magnetosphere
affecting Earth’s rate of rotation (Length-of-Day or LOD
[198,202]), and that this alters the Earth’s centripetal
acceleration and in turn could alter prevailing oceanic
circulation patterns.
2.6.4. Galactic Cosmic Ray-driven amplification
In Section 2.6.1, we discussed how several researchers have
argued for Sun/climate relationships that are driven by the
larger variability in the UV component of the solar cycle,
rather than the more modest variability over the solar cycle in
Total Solar Irradiance (TSI). Since most of the incoming UV
irradiance is absorbed in the stratosphere, this has led to
various “top-down” mechanisms whereby the Sun/climate
relationships begin in the upper atmosphere before being
propagated downward, as schematically illustrated in Figure
4(a). However, other researchers have focused on a separate
aspect of solar variability that also shows considerable
variability over the solar cycle, i.e., changes in the numbers
and types of Galactic Cosmic Rays (GCRs) entering the
Earth’s atmosphere. Because the variability in the GCR fluxes
can be different at different altitudes, but some GCRs are
absorbed in both the troposphere and the stratosphere, such
mechanisms could potentially be relevant throughout the
atmosphere [70,374,375] Figure 4(c). Also, because both the
flux and the variability in the incoming GCR fluxes increase
with latitude (greatest at the geomagnetic poles [70,374,375]),
if such mechanisms transpire to be valid, this might mean that
the Sun/climate relationships are more pronounced in some
regions than others (Section 2.6.3).
Although some cosmic rays come from the Sun, GCRs are
believed to come from other stellar systems, especially from
the explosions of nearby supernovae. However, the solar wind
appears to reduce the flux of GCRs entering the Earth’s
atmosphere, and since the solar wind increases with solar
activity, the flux of GCRs appears to be inversely proportional
to solar activity. Even though the flux of GCRs is much
weaker than incoming TSI, GCRs are responsible for much of
the ionization that occurs in the atmosphere. Indeed, this is
why changes in the ratios of cosmogenic isotopes such as 14C
or 10Be are often used as proxies for solar activity (Section
For this reason, Ney (1959) [374] and Dickinson (1975)
[375] both hypothesised that changes in the GCR flux might
actually be climatically significant through ionization
processes and/or interactions with electric fields. For instance,
Ney suggested that changes in the GCR flux might lead to
changes in storminess (especially thunderstorms) [374].
Dickinson speculated that if GCRs were involved in a
significant Sun/climate mechanism, then a plausible candidate
mechanism would involve some connection between GCRs
and cloud formation. He openly admitted that his hypotheses
were strictly speculative and warned, I have so piled
speculation upon speculation that much further argument
does not seem profitable. However, he hoped, “…that this
discussion has provided some guidance as to fruitful avenues
for further research into physical connections between solar
activity and the lower atmosphere[375].
22 years later, Svensmark and Friis-Christensen (1997)
[25] noticed an intriguing result that appeared to have
vindicated Dickinson’s speculations. They noticed a striking
correlation between the GCR flux and satellite estimates of
global cloud cover, according to the ISCCP-C2 dataset over
the then-available period, 1983-1990. Although this was a
relatively short period, it captured a considerable portion of a
solar cycle and implied a strong and pronounced Sun/climate
mechanism that had not been considered by the climate
models. The study was criticised [376,377], but also defended
Kernthaler et al. (1999) reanalysed the ISCCP-C2 dataset
to distinguish between “high”, “medium” and “low” clouds
and also split the global data into latitudinal bands. They
argued that taking this more granular approach, the apparent
relationship between GCRs and cloud coverage disappeared
[376]. When the ISCCP dataset was updated to 1994 and
upgraded to version “D2”, the dataset providers included
similar granular breakdowns. Independently, both Pallé Bagó
and Butler (2000;2001) [379,380] and Marsh and Svensmark
(2000) [381] confirmed that the original relationship had
broken down but that a more nuanced relationship still
remained it appeared that there was a strong correlation
between GCR flux and the percentage of low cloud cover,
particularly for lower latitudes [379,381]. This appeared
Journal XX (XXXX) XXXXXX Connolly et al
counterintuitive, as it had been supposed that any such effect
would actually be greatest for high clouds and high latitudes.
Nonetheless, the correlation was quite striking and now
covered a longer period (1983-1994).
As before, this updated relationship was criticised
[7,9,382384] but also defended [385,386] and gained some
support from other researchers [70,387]. However, when the
ISCCP-D2 dataset was updated to 2001, Marsh and
Svensmark (2003) noticed that the apparent relationship
seemed to breakdown again [385]. Yet, they also noted that
there was a gap in the available ISCCP calibration satellites
between September 1994 and January 1995, and that if a
single step calibration adjustment was applied to the data
during this gap, the correlation between low cloud cover and
GCRs remained for the entire updated 1983-2001 period
[385]. Meanwhile, Sun and Bradley (2004) argued that the
entire ISCCP D2 time series was unreliable and that ground-
based time series (which appeared to contradict the
GCR/cloud hypothesis) were preferable [383], while Marsh
and Svensmark (2004) argued the opposite [386]. More
recently, Agee et al. (2012) argued that the GCR-cloud
hypothesis breaks down when the (unadjusted) ISCCP-D2
dataset was updated to 2008, as it implied unusually low cloud
cover during a period of unusually high GCR flux [388]. On
the other hand, Evan et al. (2007) had already argued that the
unusually low cloud cover values of the ISCCP dataset were
due to “satellite viewing geometry artifacts and […] not
related to physical changes in the atmosphere[389].
We sympathise with readers who find these controversies
over the reliability of the global cloud cover datasets
unsettling. At any rate, Kristjánsson et al. (2004) raised an
important additional challenge to the theory by noting that,
because GCR fluxes are quite well correlated to other metrics
of solar activity, similar correlations could be found between
TSI and cloud cover [384]. They also carried out spatial
correlations instead of just comparing the global time series
and found that some regions had stronger correlations than
others [384]. Pallé et al. (2004) also found similar results
In a series of papers, Voiculescu et al. have built on these
ideas and carried out regional analyses on the basis that the
cloud cover in different regions might be influenced by
different factors, including different solar drivers [362,391
393]. Voiculescu et al. found a solar influence on the cloud
cover in many regions but, in some regions and for different
types of clouds, the correlations were better with changes in
UV irradiance. For other regions, the correlations were better
with changes in GCR flux, while for others the cloud cover
seemed to be influenced by non-solar factors [391,392].
While less exciting than the original Svensmark and Friis-
Christensen (1997) result [25], these more nuanced analyses
where GCRs are just one of several potential drivers of
changes in cloud cover are still consistent with the overall
theory that changes in GCR fluxes could be a driver of global
temperature changes. However, it suggests that more subtle
regional effects need to be considered. It also confirms that it
is challenging to separate a specific GCR-driven mechanism
from other solar-driven mechanisms [70].
A potentially useful approach for trying to evaluate these
more nuanced proposed GCR/cloud connections is to look for
any significant cloud changes associated with Forbush
decrease (FD) events. These are occasional events (typically a
few each year) following a Coronal Mass Ejection (CME)
when the solar wind temporarily increases for a few hours,
substantially reducing the GCR flux for a few days. Although
CMEs also influence other aspects of solar activity, this
temporary effect on GCR flux is quite pronounced, and
therefore if the GCR/cloud mechanisms are valid, we would
expect that evidence for this could be identified by comparing
climatic conditions during the event to those of the days
immediately before and after the event.
Several studies taking this approach have reported
significant climatic changes associated with FD events. For
instance, analysing ground-based sunlight measurements at
several UK weather stations, Harrison and Stephenson (2006)
noted an average reduction in diffuse solar radiation (i.e.,
cloudier weather) during FD events [387]. Similarly,
Svensmark et al. (2009) found that the liquid water content of
low clouds could be reduced by up to 7% during FD events
[394]. However, again, these studies are typically contested,
e.g., Laken et al. (2009) [395] and Calogovic et al. (2010)
[396] disputed Svensmark et al.’s (2009) analysis and argued
that there was no statistically robust relationship between FDs
and cloud cover.
Part of the challenge is that some FD events are stronger
than others, and they are so sporadic that the number of strong
events over a relatively short period such as the satellite era is
quite limited. To overcome this limitation, Dragić et al. (2011)
used records of the “Diurnal Temperature Range” (DTR), i.e.,
the difference between the daily maximum and daily
minimum temperatures from 189 European weather stations,
as a proxy for cloud cover [397]. This allowed them to study
a much longer time period than the satellite era. They found
statistically significant changes in DTR for strong FDs with a
GCR reduction of at least 7% [397]. However, Laken et al.
(2012) [398] argued that the statistical averaging techniques
used by both Dragić et al. (2011) and Svensmark et al. (2009)
were inappropriate. On the other hand, after Svensmark et al.
(2016) carried out a more robust statistical analysis, they
concluded that “there is a real influence of FDs on clouds
probably through ions” [57].
An ongoing debate over the relevance of the GCR/cloud
theory has been over the exact physical mechanism by which
changes in GCRs could influence cloud coverage [70,79]. This
has prompted considerable laboratory work to try and replicate
in a closed (indoors) system the various steps involved in
Journal XX (XXXX) XXXXXX Connolly et al
cloud formation and evaluating the role of GCRs relative to
other factors. This includes cloud chamber experiments
carried out by Svensmark et al. in the “SKY” project
[58,399,400] and an independent CERN-based group as part
of the “CLOUD” project by Kirkby et al. [79,401403]. These
experiments have confirmed that ionization by GCRs does
appear to increase rates of cloud nucleation under certain
circumstances [58,399401]. However, there is debate over
whether there are substantial regions where cloud formation is
inhibited by a shortage of GCRs. In particular, computer
simulations using global aerosol models that have been
calibrated using some of the CLOUD results suggest that
GCRs are not a major contributor [402,403]. But, Kirkby et al.
(2011) had noted that these models are still not very good at
explaining the observed data [401]. Meanwhile, it has been
argued that at least for Antarctica, cloud cover appears to be
influenced by GCRs [404].
Although much of the discussion on potential links between
GCRs and climate have focused on Svensmark et al.’s theory,
other groups have argued for more subtle effects, e.g., by
influencing stratospheric ozone concentrations [405] or by
influencing cyclonic and anti-cyclonic activity [406]. In
particular, Tinsley et al. have argued that GCRs interact with
the climate by influencing the Global Electrical Circuit [81
83]. This builds on some of Ney’s (1959) [374] and
Dickinson’s (1975) original hypotheses [375]. Carslaw et al.
(2002) noted that such mechanisms could themselves
influence cloud cover making it hard to distinguish between
Svensmark et al.’s specific theory and other subtler
GCR/cloud/climate mechanisms [70]. Tinsley et al. have now
published multiple studies suggesting potential links between
GCRs and the climate through the intermediary of the Global
Electric Circuit, e.g., [8185]. Others have also provided
independent analysis that is somewhat consistent with such
mechanisms [70,387,393,407].
Regardless of the exact mechanism by which GCRs might
influence climate, Shaviv and Veizer (2003) noted that when
they compared estimates of past paleotemperatures and past
GCR fluxes over the last 500 million years, they found a much
better match than between paleotemperatures and estimates of
past CO2 [263]. This study was criticised by both Rahmstorf
et al. (2004a) [408] and Royer et al. (2004a) [409], with these
criticisms leading to rebuttals and counter-rebuttals from both
sides [410412]. A major challenge is that there is
considerable ongoing debate over which estimates of past
temperature, CO2 and solar activity on these timescales are
most reliable. As a result, some studies argue that Shaviv and
Veizer’s original analysis was broadly correct [36,413415],
while others disagree [416,417].
Clearly, the evidence for and against a significant influence
of GCRs on the climate has been controversial and equivocal,
with many proponents [36,114,397,415,418] and critics
[20,398,403,417,419] of the theory, while others remain more
neutral [362,380,393,407,420]. There is also considerable
ongoing debate over what the net effects of changes in GCR
fluxes would be on climate. Indeed, it is worth noting that
Ney’s (1959) original hypothesis implied that increased solar
activity should lead to a net cooling effect [374], i.e., the
opposite of Svensmark et al.’s theory [25,36,114,385]. A
further complication is that the role of clouds appears to
depend on whether you are considering short or long
timescales, e.g., Young et al. (2019) propose that the net
climatic effect of clouds can change from a negative cloud-
temperature feedback to a positive cloud-temperature
feedback when considering different timescales [421].
Nonetheless, it is acknowledged by proponents of the
GCR/cloud/climate theory [36,114,385] that it is not as clear-
cut as the intriguing Svensmark and Friis-Christensen (1997)
result initially implied [25]. However, it is also acknowledged
by critics of the theory that GCRs do seem to have some
influence in cloud formation and that our understanding of
how and why cloud cover varies is still quite limited
[402,403]. It has also been conceded by critics of the theory
that interest in the theory has been valuable for the community
in that it has prompted more research into these challenging
topics, including the SKY and CLOUD projects [402,403].
2.6.5. Short-term orbital effects The difference between the average Earth-Sun
distance (1AU) and the daily Earth-Sun distance
It is also worth briefly distinguishing between changes in
the solar irradiance leaving the Sun and changes in the solar
irradiance reaching the Earth. Much of the interest in
understanding the changes in solar activity have focused on
the former. As a result, the TSI is typically described in terms
of the output reaching 1 Astronomical Unit (AU), i.e., the
average distance of the Earth from the Sun. This applies to
most of the TSI reconstructions discussed in this paper.
However, as discussed in Soon et al. (2015) [56], because the
Earth’s orbit of the Sun is elliptical rather than circular, the
physical distance of the Earth from the Sun varies quite a bit
over the course of the year. Currently, the Earth receives 6.5%
more TSI (88 W m-2) in January (i.e., the Northern
Hemisphere winter) during the perihelion (the Earth’s closest
point to the Sun) than in July (i.e., the Northern Hemisphere
summer) during the aphelion (the Earth’s furthest point from
the Sun). Therefore, if we are interested in the effects of
changes in the solar activity on the Earth’s climate, then
arguably we are more interested in the changes in TSI actually
reaching the Earth, rather than the changes in TSI reaching a
distance of 1 AU.
Because the seasonal cycles of the Earth’s orbit are almost
identical each year, it might initially be supposed that the
annual averages of the TSI reaching the Earth and that
reaching 1 AU should be perfectly correlated with each other.
Journal XX (XXXX) XXXXXX Connolly et al
If so, then this would mean that, when averaged over the year,
this difference between the TSI reaching the Earth compared
to that at 1 AU would be trivial. In that case, using 1 AU
estimates for evaluating the potential effects of varying TSI on
the Earth’s climate would be easier, since the variations in TSI
from year-to-year are easier to see in the TSI data at 1 AU
compared to that at Earth’s distance (as will be seen below).
This appears to be an implicit assumption within much of
the literature evaluating the effects of varying TSI on the
Earth’s climate. However, we note that there are subtle, but
often substantial, differences that can arise between the annual
averages at 1 AU versus Earth’s distance since most of the
trends in TSI (including the ~11-year cycle) are on timescales
that are not exact integer multiples of the calendar year.
We appreciate that mentally visualising the differences that
can arise between the two different estimates is quite tricky,
even if you have a high degree of visual spatial intelligence.
Therefore, in order to demonstrate that there are indeed subtle
but significant differences between the annual averages of TSI
at 1 AU versus the TSI reaching the Earth, we compare and
contrast the TIM/SORCE TSI datasets for 1 AU and Earth’s
distance in Figure 5. The TIM/SORCE datasets are the results
from a single satellite that operated from 2003 to 2020, and it
is particularly relevant because the data is reported for both 1
AU and that at the in-situ Earth’s orbit. This period covers
roughly 1.5 Solar Cycles Figure 5 (b).
Before describing the results in Figure 5, we should note
some technical points on this analysis. We downloaded the
daily-resolved datasets for both versions from (accessed
26/06/2020). Unfortunately, the full SORCE TSI data records
from February 25, 2003 through February 25, 2020 do not
have continuous daily measured values for either the in-situ
Earth’s orbit or the 1 AU distance adjusted data. On average
there are 11 missing days for all years except 2013, 2003 and
2020. 2013 was missing 160 daily values, and discounting
2013, the average for the full 2004-2019 period is 22.5 missing
days per year. To fill in the missing daily TSI values, we
applied a more sophisticated method than just a linear
interpolation. For the 1 AU TSI values, we use an artificial
intelligence algorithm that matched not only the amplitude of
the measured daily TSI values but also the spectral properties
of the measured SORCE TSI record. In addition, PMOD TSI
data were used and were calibrated to SORCE’s TIM daily
series using the method proposed by Soon et al. (2019) [422].
The PMOD data between 2003 and 2017 were standardized
with characteristics of the TIM and then added to the TIM
records. The data between 2018 and 2020 that were missing in
the TIM series were consecutively less than 5 days and
therefore were estimated using the method of Radial Basis
Function Artificial Neural Networks (RBFANN). Our
RBFANN has three layers of neurons: one input (objective
data in this case from TIM), one hidden and one output
(matching the high- or low- frequency spectral properties). For
the daily TSI values at Earth’s orbit, another set of RBFANN
was constructed to fill in the missing daily values. Therefore,
by applying these advanced and more elegant techniques than
interpolation per se, we can generate the complete daily
SORCE TIM’s TSI composite time series for both Earth orbit
and at 1 AU perspectives.
Figure 5. Comparison of the amount of Total Solar Irradiance (TSI) that reaches the Earth as opposed to 1 Astronomical Unit (AU), i.e., the
mean distance of the Earth from the Sun. (a) illustrates schematically (not to scale) how the Earth-Sun distance increases and decreases
over the calendar year due to the elliptical nature of the Earth’s orbit. The images of the Sun, Earth and Moon are public domain images
published by NASA. The Sun image was taken by the SOHO space craft on September 24, 2008 (Credit: SOHO Consortium, EIT, ESA, NASA, The Earth and Moon image is a composite created by Reto Stöckli, Nazmi El Saleous, and
Marit Jentoft-Nilsen, NASA GSFC ( (b)-(d) present the results of the
TIM/SORCE sun-monitoring satellite program (2003-2020), as downloaded from (accessed
26/06/2020). (b) plots the daily averages at 1 AU. (c) compares the daily averages at 1 AU and at the Earth’s actual distance from the Sun.
(d) compares the annual averages and (e) plots the differences between the annual means. A small number of days had missing data. We
interpolated these data points using the method described in the text. In (b) and (c), the interpolated points are indicated using dashed
lines. In (d), those years with some interpolated data are indicated by dashed lines.
The daily results are shown in Figures 5(b) and 5(c), with
the interpolated points indicated with dashed lines (and
slightly different colors). The annual means of both versions
are compared in Figure 5(d). Note that the y-axes each have a
different range. This is because, as noted above, the seasonal
cycle in the TSI reaching the Earth is of the order of 90 W/m2,
while the variability in TSI over the solar cycle is only of the
order of a few W/m2. As a result, the pronounced ~11 year
solar cycles that can be seen in the 1 AU plot of Figure 5(b)
are barely noticeable when viewed on the scale of Figure 5(c).
That said, when the annual averages of both time series are
calculated, this seasonal cycle is no longer an issue, and the
two time series can be directly compared, as in Figure 5(d).
However, as can be seen from Figure 5(e), while the two
annual time series are broadly similar, albeit with the 1 AU
values being slightly lower than that at Earth distance, the
differences between the two time series vary slightly from
year-to-year. Over the 16 year period, the differences between
the two annual averages varied from +0.35 W/m2 (2013) to -
0.06 W/m2 (2014), i.e., a range of 0.41 W/m2. It could be
argued that the 2014 estimate is anomalous in that this was the
year with the most data interpolation. But, even neglecting that
year, the differences between the two averages varied between
0.34 and 0.15 W/m2, i.e., a range of nearly 0.2 W/m2. For
Journal XX (XXXX) XXXXXX Connolly et al
comparison, the difference between the maximum and
minimum annual TSI at 1AU over the same period was 0.9
W/m2. So, while small as a percentage of the total TSI, these
subtle differences are not insignificant.
These differences between the annual averages for each
year might initially be surprising. For the analysis in Figure 5,
we are assuming that the SORCE datasets at both 1AU and the
Earth’s distance are reliable. We also are assuming that the
interpolations we have carried out (described earlier) are
reasonable. However, even if either of those assumptions are
problematic, we should stress that the fact that there are
differences between the annual means for both versions that
vary from year to year is actually to be expected on statistical
grounds. The general principle can be understood once we
recognise (a) the elliptical shape of the Earth’s orbit and (b)
that the ~11-year solar cycle does not fall exactly on the
calendar year. This means that the times of the year during
which a given rise or fall in TSI occurs can make a difference.
For instance, if the maximum of a solar cycle occurred during
January, then this will lead to a greater mean TSI for the year
than if it had occurred during July of the same year. This is
because the Earth is currently closer to the Sun in January than
in July.
To clarify, if the trends in TSI over a given calendar year
are reasonably linear statistically, i.e., it has a constant slope,
then this seasonality should not make much difference to the
annual mean TSI. This is regardless of the slope itself, i.e.,
whether the trend is rising, falling or near-zero. However, if
the trends for that year are non-constant, then the annual mean
may be slightly higher or lower depending on whether the
Earth is closer to perihelion or aphelion when the changes in
the trends in TSI occur.
More generally, the annual average TSI reaching the Earth
depends not just on the changes in TSI, but the times of the
year over which those changes occur. The SORCE data in
Figure 5 only covers roughly 1.5 Solar Cycles, but in
principle, the same could apply to any other multi-decadal
trends which might be occurring in addition to the ~11-year
Since all of the TSI reconstructions discussed in Sections
2.2-2.5 are calculated in terms of the annual averages at 1 AU,
for this paper we will limit our analysis to this. However, we
encourage researchers who have until now limited their
analysis of TSI variability to that at 1 AU to consider this extra
complication in future research.
As can be seen from Figure 5(e), the changing differences
between the annual average TSI at 1 AU versus that reaching
the Earth are subtle, but non-trivial. In addition to this
complication in terms of the annual averages, a
comprehensive analysis of the effects of TSI on the Earth’s
climate should consider the seasonal changes in the different
latitudinal distributions of the incoming TSI, due to the
seasonal orbital of the Earth. There are several different
aspects to this, but for simplicity they are collectively referred
to as “orbital forcings”. Comparison with long-term orbital forcing
The theory that changes in atmospheric CO2 are a primary
driver of climate change was originally developed by
Arrhenius in the late 19th century as a proposed explanation
for the transitions between glacial and interglacial periods
during the ice ages [423]. The existence of these dramatic
climatic changes on multi-millennial timescales was only
established in the 19th century and was one of the great
scientific puzzles of the time. [As an aside we note that
glaciologically speaking, an “ice age” is usually defined as a
period where large permanent ice sheets are present in both
hemispheres. These ice sheets can substantially expand during
“glacial periods” and retreat during “interglacial periods”. As
Greenland and Antarctica both currently have large ice sheets,
we are currently in an interglacial period (the “Holocene”)
within an ice age, even though colloquially, the term “ice age”
is popularly used just to describe the “glacial periods”.]
This CO2 driven explanation for the glacial/interglacial
transitions was later criticised by, e.g., Ångström (1901) [424]
and Simpson (1929) [425]. However, it was later revived by
Callendar (1938) who extended the theory to suggest that
anthropogenic CO2 emissions were also the primary driver of
the warming from the late-19th century to mid-1930s [369],
and Plass (1956) who speculatively proposed (anticipating
that this would encourage scientific debate) that atmospheric
CO2 was the primary driver of climate change on most
timescales [426].
A competing hypothesis that several 19th-century
researchers proposed, e.g., Adhémar, and later Croll
[308,427429], was that long-term cyclical changes in the
Earth’s orbit around the Sun were the driver of the
glacial/interglacial transitions. In the early 20th century,
Milankovitch carried out an extensive series of calculations
that demonstrated that there are several important cyclical
variations in the Earth’s orbit that vary over tens of thousands
of years and that these influence the incoming solar radiation
at different latitudes for each of the seasons [430,431].
In the 1970s, relatively high precision estimates of the
timings of the glacial/interglacial transitions from ocean
sediment cores appeared to vindicate the Milankovitch ice age
theory [427,432]. That is, when frequency analyses like those
in Sections 2.5.2 and 2.5.3 were carried out on the deep-sea
sediment cores, they suggested that the past climate changes
of the last few hundred thousand years were dominated by
periodicities of ~90,000-120,000 years and to a lesser extent
40,000-42,000 years, and also had peaks at 22,000-24,000
years and 18,000-20,000 years. These peaks were
approximately similar to the main astronomical cycles
calculated by Milankovitch: 41,000 years; 23,000 years;
19,000 years and to a lesser extent ~100,000 years. As a result,
analogous to the arguments described in Sections 2.5.2-2.5.3,
Journal XX (XXXX) XXXXXX Connolly et al
it was argued that the glacial/interglacial transitions were
indeed driven by orbital forcings [427,432]. Later analysis in
terms of ice core measurements also appeared to confirm this
theory [433435].
This appears to have convinced most of the scientific
community that the Milankovitch orbital-driven explanation
for the glacial/interglacial transitions is correct, and this
currently seems to be the dominant paradigm within the
literature [430,431,435440] including the IPCC reports [1].
Ironically, this means that the original CO2-driven theory for
the glacial/interglacial transitions as proposed by Arrhenius
(1896) [423]; Callendar (1938) [369]; Plass (1956) [426] has
been largely discarded even though the current theory that
recent climate change has been largely driven by changes in
CO2 was developed from that early theory. That said, we
emphasise that this is not necessarily a contradiction in that
several researchers argue that changes in atmospheric CO2
concentrations caused by orbitally-driven warming or cooling
might act as a positive feedback mechanism [1,430,435440].
We note that there are possible problems with the theory
that the Milankovitch orbitals are the primary driver of the
glacial/interglacial transitions. To clarify, the Milankovitch
orbital variations are clearly climatically significant as
discussed above. Also, the idea that some combination of
these variations could provide the explanation for the
glacial/interglacial transitions seems plausible and intuitive.
Indeed, the approximate similarity in the timings of both
phenomena is intriguing. However, as will be discussed
below, there is still considerable debate over the exact causal
mechanisms and over which specific aspects of the
Milankovitch orbital variations would drive such dramatic
long-term climate changes and why. That said, each of these
problems has been countered, and the current consensus
among the scientific community is