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The challenges of trying to reconstruct changes in Total Solar Irradiance (TSI) since 1700: A response to Chatzistergos (2024)’s remake of Hoyt & Schatten (1993)

Recently (February 15, 2024), a paper was published by Dr. Theodosios Chatzistergos at the Max Planck Institute for Solar System Research (MPS) that claims to have undermined the findings of several papers involving the CERES team. The paper, Chatzistergos (2024), is open access and so can be downloaded for free from the journal website:


Chatzistergos claims to have “updated” one of the first attempts in the satellite era to quantify the changes in the annual solar energy reaching the Earth (Total Solar Irradiance, or TSI for short). The TSI reconstruction he claims to have “updated” is Hoyt & Schatten (1993) or HS93 for short:


As the first part of his analysis, Chatzistergos first tried to replicate the HS93 reconstruction using the same data as Hoyt & Schatten (1993). His replication was fairly similar to the original. However, he claims that when he “updated” the reconstruction, his new version of the reconstruction looked very different from the original HS93.


He also noted that it was visually very similar to one of the MPS team’s reconstructions, SATIRE-T (Wu et al., 2018 and references there-in) that was co-developed by Chatzistergos’s PhD supervisors at the MPS (i.e., Prof. Sami K. Solanki and Dr. Natalie A. Krivova).


Key references on the SATIRE-T reconstruction (and SATIRE-M extension for Holocene)


Cheekily, Chatzistergos mocked Hoyt & Schatten (1993)’s open-minded title of “A discussion of plausible solar irradiance variations, 1700-1992” by changing their cautious wording of “plausible” to “implausible”.


As we will discuss in this post, Chatzistergos has not actually “updated” HS93.

Instead, he has created a “remake” of what he thinks Hoyt & Schatten (1993) should have done.


Below, we compare the original HS93 reconstruction and Chatzistergos’s replication using the same data (left hand side) and Chatzistergos’s “remake” (right hand side):



Moreover, it becomes clear from reading his paper that he doesn’t even think Hoyt & Schatten (1993) should have bothered to develop their TSI series in the first place – he thinks their approach was “implausible” from the beginning. So, he doesn’t seem to think his so-called “update” is of much use as a TSI reconstruction – despite the fact that he notes his remake matches quite well to the MPS’s SATIRE-T TSI reconstructions.


He seems to have created it as a parody of a TSI reconstruction. Instead, he argues that the scientific community should stick to using the SATIRE reconstructions of the MPS group or reconstructions that are similar, e.g., the NRL TSI reconstructions developed by Dr. Judith Lean at the Naval Research Laboratory (NRL) and colleagues, e.g., Lean (2018).


Perhaps this satirical approach to science could be a factor in why the MPS team chose to name their range of TSI reconstructions with the acronym “SATIRE”. “Satire” is a word that the Oxford dictionary defines as “the use of humour, irony, exaggeration, or ridicule to expose and criticize people’s stupidity or vices, particularly in the context of contemporary politics and other topical issues.” Apparently it stands for “Spectral And Total Irradiance Reconstructions”, but it is a name they have been using for more than 20 years, e.g., see Solanki et al. (2005) (pdf version available from MPS here) and references therein. So, they seem to like the name.


Nonetheless, a recurring theme in Chatzistergos’s papers seems to be the repeated use of the logical fallacy known as the “appeal to novelty” (argumentum ad novitatem):

“Appeal to Novelty (argumentum ad novitatem)
Description: Claiming that something that is new or modern is superior to the status quo, based exclusively on its newness.” – LogicallyFallacious.com

So, the main goal of this paper seems to be to try to convince researchers that anybody still using HS93 for their analysis is foolish because it’s older than the MPS’s latest reconstructions.


For example, in Chatzistergos (2024), he claims, “Notwithstanding all the advances briefly summarised here, several old and outdated TSI reconstructed series are still frequently used in the literature”, while in a recent review paper with other MPS team members, Chatzistergos et al. (2023, preprint version available here) asserts, “Figure 4 shows various TSI reconstructions extending back to at least 1700s. Some of these models have regularly been revised, refined, and updated. Nevertheless, often older versions are used in the literature ignoring the fact that newer versions, overriding the earlier ones, are available. We caution against using outdated reconstructions.


By this logic, if a film studio does a “remake” of a film or a “reboot” of a franchise, we should never look back at the originals.


We disagree – while sometimes a remake can be good, often the originals are better.

In this post, we will have a look at Chatzistergos’s remake of HS93 and see if it is better than the original. Our conclusion is that it is not. Read on to find out why.


We warn you that this post is a very long read.


But, to properly understand both HS93 and Chatzistergos’s remake, you need to get quite deep into the weeds. As they say, the devil is in the details.


However, we hope that this discussion will be helpful for readers who are genuinely curious about the challenges involved in trying to reconstruct the changes in TSI since 1700.


For those who just want to know what we think of Chatzistergos (2024)’s remake, feel free to skip to the conclusions section.


For the rest of you, maybe first get a tea or coffee or whatever beverage you prefer. Then, pull up a chair and dive in…


The significance of the debates over TSI reconstructions for the IPCC’s “mostly human-caused” claim

First, it may be useful to know why this debate over which TSI reconstructions are most reliable is such a big deal.


For their last four Assessment Reports, the UN’s Intergovernmental Panel on Climate Change (IPCC) has confidently asserted that the global warming since the 19th century is mostly human-caused (“anthropogenic”) – specifically due to increasing greenhouse gas emissions (chiefly carbon dioxide, or CO2). See links to each of these reports below:


In order to support this claim, they have repeatedly insisted with each report that it is (allegedly) not possible to simulate the long-term global warming in terms of naturally-occurring climate change drivers.


This is mostly done by comparing estimates of the global temperature changes to computer model “hindcasts” (opposite of a forecast) of what the models predict should have happened. They then compare the observed warming to the modelled warming expected in terms of either “natural forcings only” or “anthropogenic and natural forcings”. 


According to the IPCC, when these hindcasts are run using “natural forcings only”, then they cannot simulate much warming over the last century or so. However, they argue that when the hindcasts are re-run with “anthropogenic and natural forcings”, they can get a reasonable match to the observed warming.


This is, in a nutshell, the basis for the claim that modern global warming (and hence climate change) is “mostly human-caused”. You can find similar claims on popular webpages such as https://climate.nasa.gov/causes/ that was created by Daniel Bailey and colleagues at the Earth Science Communications Team of NASA Jet Propulsion Laboratory.


There are many logical flaws in that computer model-based claim. In particular, it relies on the assumption that the current computer climate models are accurate. However, for the purposes of this post, it is sufficient to note that these models only consider two “natural forcings”:

  1. Volcanic forcing – Temporary 2-3 year cooling events after a major volcanic eruption that reaches into the stratosphere (“stratospheric volcanoes”). One of the biggest of these was the eruption of Mount Pinatubo in 1991, but they occur several times per century. The recent underwater Hunga Tonga–Hunga Haʻapai eruption (“the Tonga eruption”) in December 2021 has led to some debate over whether volcanic eruptions might sometimes also cause some warming. This is because the Tonga eruption released large amounts of water vapor into the stratosphere instead of just dust/soot particles and related gases – since it erupted underwater. However, for now, the current computer models assume that stratospheric volcanoes only cause temporary cooling events. So, they cannot simulate a long-term global warming trend from volcanic activity – just temporary cooling.

  2. Solar forcing – If there is a long-term change in the annual Total Solar Irradiance (TSI) reaching the Earth, then this could cause either global warming or global cooling, depending on whether TSI was increasing (leading to warming) or decreasing (leading to cooling).


Since the first factor can only lead to a temporary 2-3 year cooling period, the only way in which the current global climate models (GCMs) can simulate a “natural global warming” that lasts more than a few years is through a long-term increase in TSI.


This is a key point to remember throughout this post: according to the current computer climate models, the only way in which any period of “global warming” lasting more than a few years could occur naturally is through a long-term increase in TSI.


The current computer climate models also assume that increasing greenhouse gas concentrations are the main climate driver. That is, they assume that the average global temperature has a very high “climate sensitivity” to increases in greenhouse gases. So, according to the current computer climate models, increasing CO2 concentrations since the industrial revolution should be causing unusual “anthropogenic global warming”.


As you probably gathered from the introduction there is considerable ongoing debate among the scientific community about which TSI reconstructions are most realistic and representative of the changes in TSI over the centuries. Chatzistergos (2024) claims that the HS93 reconstruction is unreliable and insists that the community only consider TSI reconstructions such as those developed by his colleagues at MPS or the NRL TSI reconstructions developed by Dr. Judith Lean of the US Naval Research Laboratory (NRL) and colleagues. So, it is useful background information to consider which TSI reconstructions the IPCC considered for their various reports.


TSI reconstructions used by the IPCC Assessment Reports

IPCC 3rd Assessment Report (AR3, 2001)

For AR3, the IPCC had not yet started using model hindcasts to evaluate the causes of climate change. That approach came later.


However, in Figure 6.8 in Chapter 6 of the Working Group 1 report, they compared the radiative forcings of two TSI reconstructions (and two estimates of volcanic forcings) to the modelled radiative forcings for anthropogenic factors. Both reconstructions implied a substantial role for solar activity in the global warming since the Little Ice Age, but less than from anthropogenic factors – in terms of radiative forcings at least. It was on this basis of comparing “radiative forcing” estimates, that they concluded that the warming was “mostly human-caused”.




The two TSI reconstructions they considered were HS93 and another reconstruction developed by Dr. Judith Lean and colleagues – Lean et al. (1995) or L95 for short:

  • Judith Lean, Juerg Beer, Raymond Bradley (1995). Reconstruction of solar irradiance since 1610: Implications for climate change. Geophysical Research Letters, 22(23). 3195-3198. https://doi.org/10.1029/95GL03093.


In Figure 6.5, they also compared these two TSI reconstructions to another two reconstructions (Solanki & Fligge, 1998 and Lockwood & Stamper, 1999) as well as Hoyt & Schatten’s Group Sunspot Number (GSN) record (Hoyt & Schatten, 1998).


IPCC 4th Assessment Report (AR4, 2007)

In advance of AR4, multiple climate modelling groups were invited to contribute climate model hindcast simulations as part of the so-called “CMIP3” project. The IPCC authors used these CMIP3 model hindcasts for their analysis. Details on the forcings used by these models are provided in the Supplementary Materials for Chapter 9 of the Working Group 1 report.

  • No natural forcings - 9 of the 23 computer models (39%) that contributed to CMIP3 did not include any natural forcings (no solar or volcanic, just anthropogenic forcings).

  • L95 – 8 models (35% of all CMIP3 models) used Lean et al. (1995). One of these models (ECHO-G) used a modified version of L95 that had been extended backwards by Crowley (2000) for the pre-1610 period.

  • HS93 – 2 models used the Hoyt & Schatten (1993) reconstruction

  • L02 – 2 models used the Lean et al. (2002) reconstruction – an early version of NRL TSI version 1.

  • L00 – One model used the Lean (2000) reconstruction, which was an even earlier version of NRL TSI version 1.

  • SK03 – One model used Solanki & Krivova (2003) – an early attempt by the MPS team that preceded the SATIRE reconstructions.


So, L95 and HS93 were still being used as TSI reconstructions in the 2007 report. But, some modelling groups were also starting to use the predecessors of what would later evolve into the current reconstructions of the NRL and MPS groups.


IPCC 5th Assessment Report (AR5, 2013/2014)

For the 5th Assessment Report, the CMIP project skipped straight from CMIP3 to CMIP5 for two reasons. One was because of potential confusion with a subproject of the CMIP project called the “Coupled Climate–Carbon Cycle Model Intercomparison Project” (Friedlingstein et al., 2006) which was given the acronym, “C4MIP” because of the four C-words in the title. The other reason was to tie together the numbering systems going forward so that CMIP5 contributed to IPCC AR5, CMIP6 to AR6, etc.


All the modelling groups were recommended to use WLS2005 for their 1850-2005 hindcasts – see here. This is the Wang, Lean & Sheeley (2005) reconstruction. This was a reconstruction co-developed by Lean who had earlier co-developed the L95 reconstruction. WLS2005 is now commonly referred to as version 1 of the NRL TSI reconstruction – because Lean was based at the US’s Naval Research Laboratory (NRL):

  • Y.-M. Wang, J. L. Lean and N. R. Sheeley, Jr. (2005). Modeling the Sun's Magnetic Field and Irradiance since 1713. The Astrophysical Journal, 625(1), 522. https://doi.org/10.1086/429689.


Like L95, NRL TSI version 1 uses Hoyt & Schatten (1998)’s group sunspot number (GSN) record as its primary solar proxy. However, unlike L95, they substantially reduced the variability in the inter-cycle “quiet sun” contribution. So, NRL TSI is a much “flatter” TSI reconstruction than either L95 or HS93.


Some of the modelling groups contributing to CMIP5 also were contributing hindcasts to the IPCC’s “Paleoclimate Modelling Intercomparison Project (PMIP)”. These PMIP hindcasts had to be longer and cover at least the past millennium. Because the WLS2005 reconstruction only covers the period from 1610 onwards, these groups used alternative TSI reconstructions for the earliest parts of their hindcasts – see Schmidt et al., 2011 and Schmidt et al., 2012. Specifically, five of the CMIP5 modelling groups used MPS’s SATIRE-M TSI reconstruction (Vieira et al., 2011) for the pre-1850 period and NRL TSI for the post-1850 period – see Table 2 of Schurer et al. (2013) for details.


IPCC 6th Assessment Report (AR6, 2021-2023)

For the CMIP6 project for AR6, all the modelling groups were recommended to use Matthes et al. (2017) for their 1850-2014 hindcasts – see here.


Matthes et al. (2017) is the simple average of (a) version 2 of NRL TSI (Coddington et al., 2016) and (b) MPS’s SATIRE-T reconstruction (Krivova et al., 2010). One modification was first made to the SATIRE-T reconstruction – instead of using Hoyt & Schatten (1998)’s daily GSN record as the primary solar proxy, the SATIRE-T version used for Matthes et al. (2017) was based on the annual SSN record (ISN v1).


As for CMIP5, the modelling groups also contributing to the paleoclimate hindcasting project used longer reconstructions for the pre-1850 period. However, for the post-1850 period, all of the model hindcasts contributing to IPCC AR6 used this simple average of the SATIRE-T and NRL TSI 2 reconstructions for their solar forcing.


Current plans for IPCC 7th Assessment Report (AR7, c. 2028-2029)

The TSI reconstructions to be used for the upcoming CMIP7 project, to go into the next IPCC report, AR7 (currently scheduled for c. 2028/2029) have not yet been decided. However, currently, it is being suggested that a similar average of the latest SATIRE and NRL TSI reconstructions should be used for AR7 – see Funke et al. (2024).


Hence, we can understand why Dr. Chatzistergos (currently at MPS) might feel frustrated at researchers (like us) who are interested in looking at alternative TSI reconstructions.

Different philosophies in developing a solar-proxy based TSI reconstruction

Much of the debates over the various proxy-based TSI reconstructions (including much of Chatzistergos’s apparent complaints of HS93) can be traced back to different scientific opinions on the relative importance of each of the following five points:

  1. The sunspot numbers (SSN) rise to a maximum and then fall to zero every 11 years or so. It is not an exact cycle since the exact period varies from 8 to 14 years each “cycle”, but it is usually about 11 years. And it is such a recurring phenomenon that we refer to this repeated rising and falling in sunspot activity as a “sunspot cycle” or “Solar Cycle”.

  2. During the satellite era, it quickly became clear that – over timescales of one sunspot cycle – TSI rises and falls in sync with the rises and falls of sunspot numbers. The correlation is not exact but is quite strong over timescales from months to years.

  3. This correlation between sunspot numbers and TSI over each cycle is not a causal correlation, because sunspots are actually associated with a decrease in TSI. Instead it is what Soon et al. (2015) (preprint available here) describe as a “commensal correlation”, i.e., it is an indirect correlation due to the two factors both being correlated to other common factors. In this case, it is generally agreed that the rise and fall of sunspots closely tracks the rise and fall of various “bright features” (including “faculae”) over a sunspot cycle. Unlike sunspots, these bright features are associated with an increase in TSI. And when averaged over a few months, the increase in TSI from the extra bright features outweighs the decrease in TSI from increased sunspot activity. This seems to be why sunspot activity is indirectly correlated to TSI activity over the course of a sunspot cycle.

  4. There has been considerable debate over whether there are also additional underlying trends in TSI between sunspot cycles. In particular, the first satellite TSI composite (“ACRIM composite”, e.g., Willson 1997; Willson & Mordvinov, 2003) suggested a noticeable increase in TSI of the first and second sunspot minima of the satellite era. However, the second TSI composite (“PMOD composite”, e.g., Fröhlich & Lean, 1998; Fröhlich & Lean, 2002) applied multiple sets of adjustments to the satellite data that removed most of the differences in TSI between these first two sunspot minima. [Note that the Lean in the PMOD team is the same Dr. Judith Lean involved in the L95 and NRL TSI reconstructions.]

  5. There have been periods when sunspot activity was dramatically reduced, including the Maunder Minimum (1645-1715) when sunspots almost disappeared for several “cycles” (e.g., Soon & Yaskell, 2003, pdf here; Usoskin et al., 2015).


Broadly, at present, there seem to be three main scientific paradigms in how to interpret the above.


Paradigm A – “The calm Sun”

Within this paradigm, it is believed that there is almost no variability in the TSI between solar minima. A corollary of this is that TSI satellite composites based on the original satellite observations are unreliable – the data must be adjusted until any apparent TSI trends between solar minima have been removed. The exact nature of these adjustments is debatable, but it is considered essential to adjust the data in some way to remove any inter-cycle trends.


It is recognized that sunspot numbers (SSN) and group sunspot numbers (GSN) are only an indirect proxy for TSI. However, in this paradigm it is believed that proxy models based on SSN or GSN capture most of the monthly and annual variability in TSI over the satellite era.


For this reason, it is assumed that once such proxy-based models have been calibrated to the adjusted satellite data, the models can be extended back in time over the entire SSN (1700 to present) or GSN record (1610 to present) by suitably scaling the sunspot data series.


Further, it is also believed that cosmogenic isotope records can be used as “proxies for sunspot activity” over longer timescales (reaching several millennia back in time). Once these proxies have been converted into a longer sunspot activity record than the actual sunspot records, they can then be used to reconstruct TSI back for millennia.


While Paradigm A acknowledges that sunspot activity was lower during the Maunder Minimum and other solar minima, Paradigm A believes that the TSI variation over one sunspot cycle in the current satellite era is essentially the same as that between the Maunder Minimum and present, e.g., Yeo et al. (2020).


TSI reconstructions developed within this paradigm imply that there has been very little variability in TSI other than the short-term rises and falls over the course of the roughly 11-year sunspot cycle. Hence, researchers who believe in this paradigm find it highly unlikely that changes in TSI are a substantial factor in climate change in either direction (neither warming nor cooling).


Some of the current TSI reconstructions from this paradigm include MPS’s SATIRE reconstructions and Lean et al.’s NRL TSI reconstructions. That is, the TSI reconstructions used for CMIP5, CMIP6 and being proposed for CMIP7, are all developed within this paradigm. Chatzistergos (2024)’s remake of HS93 was also developed from this paradigm.


Hoyt and Schatten (1993) referred to this perspective early on as “the constant quiet Sun model”:

“The constant quiet Sun model postulates that the solar irradiance has only an 11-year cycle and all radiation changes can be explained by active features. Since all solar minima are the same in these models, it is called the constant quiet Sun model.”

Paradigm B – “The bright modern Sun”

This paradigm agrees with Paradigm A that the adjusted satellite composites showing little variability between solar minima are accurate. Therefore, within this paradigm, it is considered unlikely that changes in TSI could be a substantial factor to any global warming within the satellite era, i.e., the last 45 years (late-1978 to present).


However, they consider it very likely that TSI has varied substantially over the centuries and that TSI was substantially lower during periods of low sunspot activity such as the Maunder Minimum (1645-1715).


In contrast to Paradigm A, it is believed that increases in TSI from Grand Solar Minima such as the Maunder Minimum to Grand Solar Maxima such as that during the 20th century can explain a substantial component of the global warming since the Little Ice Age (a cold period reaching its coldest during the 16th-18th centuries) up to the mid-20th century. However, it is agreed with Paradigm A that TSI has not increased since the start of the satellite era – and might even have slight decreased.


Some of the TSI reconstructions within this paradigm include Shapiro et al. (2011) and three of the four Egorova et al. (2018) reconstructions. These reconstructions suggest that TSI has increased substantially over the centuries, but has been relatively constant since the mid-20th century (although Egorova et al.’s “PHI-MU16” reconstruction suggests a possible increase during the satellite era).


Prof. Shapiro is a co-author of both Shapiro et al. (2011) and also Egorova et al. (2018) and is currently working with the MPS group.


Paradigm C – “The variable Sun”

This paradigm agrees with Paradigm B that TSI has varied substantially over the centuries and that TSI was much lower during Grand Solar Minima like the Maunder Minimum.


However, the belief of the other two paradigms that the TSI variability within the satellite era has been largely settled is strongly disputed.


Within this paradigm, it is considered very plausible that there is significant TSI variability between solar minima as well as solar maxima – and more generally that there are multi-decadal trends in TSI between solar cycles that are not captured by the simpler “calm Sun” models.


Indeed, the satellite TSI composites that are constructed without applying artificial adjustments to the data seem to support this paradigm.


This paradigm agrees with the other two paradigms that – over the course of a sunspot cycle – TSI rises and falls in line with the rise and fall of sunspot activity. However, it is argued that TSI also shows significant inter-cycle variability that is not captured by the sunspot numbers.


Given that those in this paradigm believe that the TSI trends within the satellite era have still not been satisfactorily resolved, proponents of this paradigm believe that establishing the longer-term trends in TSI also has not been satisfactorily resolved.


The HS93 TSI reconstruction was developed from this paradigm, as was the Scafetta (2023) paper that recently extended the HS93 reconstruction to 2022 using satellite data (including ACRIM).


 

Once we recognize that different scientists in the TSI community belong to these three distinct paradigms, we can better understand why individual scientists can so wholeheartedly agree with some scientists and vehemently disagree with others. Scientists in Paradigm A cannot easily fathom the research of those in Paradigm C, and vice versa! They are effectively talking at cross purposes to each other.


On the other hand, scientists in Paradigm B can often find common ground with researchers from either of the other paradigms. They are in agreement with Paradigm A on the TSI changes within the satellite era, but they are also in agreement with Paradigm C in believing that there have been substantial TSI changes over the centuries and millennia. They also disagree with some views within the other paradigms. But, they are still able to work with scientists from either paradigm - on at least some aspect of their common work!


As an example, Usoskin et al., 2015 was a collaborative paper that involved researchers from all three paradigms – including CERES co-team leader, Dr. Soon, and Dr. Chatzistergos’s two PhD advisors, Dr. Krivova and Prof. Solanki:

  • Ilya G. Usoskin, Rainer Arlt, Eleanna Asvestari, Ed Hawkins, Maarit Käpylä, Gennady A. Kovaltsov, Natalie Krivova, Michael Lockwood, Kalevi Mursula, Jezebel O’Reilly, Matthew Owens, Chris J. Scott, Dmitry D. Sokoloff, Sami K. Solanki, Willie Soon and José M. Vaquero (2015). The Maunder minimum (1645–1715) was indeed a grand minimum: A reassessment of multiple datasets. Astronomy & Astrophysics. 581, A95. https://doi.org/10.1051/0004-6361/201526652


As another example, Prof. Shapiro (whose Shapiro et al., 2011 and Egorova et al., 2018 TSI reconstructions strongly support Paradigm B) is a colleague of Dr. Chatzistergos, yet Dr. Chatzistergos’s research is very much in Paradigm A.


Hoyt & Schatten (1993)’s approach to reconstructing past TSI changes (Paradigm C)

Hoyt & Schatten (1993) was definitely a Paradigm C TSI reconstruction.


By 1993, the authors were already well aware that over the course of the sunspot cycle, TSI rises and falls in sync with the rise and fall of sunspot activity. Doug Hoyt was on the team in charge of the first TSI satellite mission, NIMBUS7/ERB – see Hoyt et al. (1992) for details. And one of the aims of this mission was to establish the relationships between sunspot activity and TSI.


Ken Schatten had even co-developed one of the first Paradigm A TSI reconstructions that suggested that almost all of the TSI variability was captured by sunspot number proxies, i.e., Schatten & Orosz (1990).


However, they also believed it was very probable that there were additional underlying long-term (“secular”) trends in TSI between solar cycles that were not being captured by simply measuring the solar photospheric features (sunspots, faculae, etc.) They speculated that these long-term trends could be due to “changes in the Sun’s convective energy transport”.


They argued that it was important to separately model these long-time multi-decadal TSI trends from the short-term year-to-year TSI changes associated with the sunspot cycles.


The challenge, however, was (and still is!) how to measure the long-term TSI variability that is not already captured by the sunspot number record. They identified several relatively long and complete records of solar variability that each suggested slightly different multi-decadal trends over the centuries.


Each of them pointed to a different aspect of the long-term variability of the Sun that was not captured by the short-term rises and falls in sunspot activity over the course of an 11-year solar cycle. So, they decided to treat each of these records as proxies of some aspect of solar variability that could potentially also be contributing to long-term shifts in TSI.


They noted that the precise trends implied by each record were different but that they also had several features in common. They decided to use each record as an independent proxy model for some different aspect of the “real solar variations” that collectively they proposed were contributing to long-term TSI variability over the centuries:

“Each model is taken to be a different and somewhat imperfect measurement of an underlying ‘true’ variations.”

Again, they also saw that these trends were independent from the short-term rises and falls in TSI over the course of a solar cycle that are associated with the rise and then fall in activity of the various solar photospheric features (sunspots, faculae, etc.). They decided to calculate these short-term and long-term components separately.


They then used the direct satellite observations of TSI by the NIMBUS7/ERB satellite mission to separately convert the short-term and long-term components of solar variability into TSI values (in units of Watts per m2).


They intentionally used a different approach for converting the two components into TSI values.


They were careful to only use the satellite observations for converting the records into TSI values – they wanted to preserve as much of the independence of each proxy record as possible.


In contrast, for his remake, Chatzistergos rescaled all of his proxy records to best match the trends of the current PMOD satellite composite. As we will see, this different approach in converting the proxy records into TSI values is a big factor in the differences between the original HS93 and Chatzistergos’s remake.


Chatzistergos’s approach makes perfect sense from the point of view of Paradigm A, but is a major mistake from the point of view of Paradigm C. This is why it is important to be aware of these differences in paradigms – whichever paradigm you personally find more compelling.


At any rate, for the original HS93 reconstruction, Hoyt & Schatten took the following approach:


Part 1. Cycle component

For the short-term TSI variability component they used the annual sunspot numbers as a proxy for the rises and falls in TSI over each cycle due to the “contributions from facular emission and sunspot blocking”. To convert this proxy into TSI values, they calculated the difference between the maximum and minimum satellite measured TSI over one sunspot cycle and the corresponding sunspot numbers.


This implied a relationship between TSI and sunspot numbers of 0.01 Watts per metre squared for an increase in sunspot number of 1. They then applied this relationship to the entire sunspot number record (1700-1992) to estimate the short-term solar cycle contribution from the solar photospheric features.


Somewhat confusingly by modern terminology, they referred to this as the “solar activity component” as opposed to the “solar irradiance” components. This terminology made sense at the time since the cyclic component was due to the rises and falls of the “active regions” on the Sun’s photosphere (sunspots, faculae, etc.) They used “solar irradiance” to describe the multi-decadal trends between solar cycles. However, it can be a bit confusing today since the terms solar activity and solar irradiance are often used interchangeably. Indeed, we do so in this post.


Chatzistergos (2024) refers to this component as HS93’s “cycle component”. We think this term is easier to understand by current terminology and so we will also use this term.


Part 2. Inter-cycle components

For the longer-term inter-cycle TSI variability, Hoyt & Schatten considered and discussed in turn five different proxy models each of which was based on a different aspect of solar variability:

  1. The fraction of the sunspots that were “penumbral”, i.e., didn’t contain a dark “umbra” center. They discussed on theoretical and experimental grounds how this fraction seems to increase during less active cycles.

  2. The decay rate of the solar cycle. Hoyt & Schatten noted (again on theoretical and experimental grounds) that the decay rates of individual sunspots tended to be faster during periods of high solar luminosity. They noted that this is part of the reason why penumbral spots tend to be more common during less active cycles. Indeed, they found that these two proxies showed generally similar tendencies over time. However, they were not identical, and so they treated both metrics as independent models.

  3. The solar cycle length. As we mentioned, the solar cycle length is usually about 11 years, but can vary as short as 8 years or as long as 14 years. Several studies have suggested that shorter solar cycles tend to be more active than longer cycles.

  4. The equatorial rotation rate of the Sun. Everybody knows that the entire Earth rotates on its axis every 24 hours. However, because the Sun is not a solid body, its rate of rotation varies from the equator to the poles. It also seems to vary over time and some studies have suggested that these subtle changes in rotation rates could potentially be contributing to changes in TSI over inter-cycle time scales.

  5. The “mean level of solar activity”, i.e., the 11-year running average of the sunspot number record. As we discussed above, they used the annual sunspot number records for approximating the short-term changes in TSI during each sunspot cycle. However, they also used an 11-year running average to calculate the inter-cycle changes in sunspot activity. They explained that periods where the sunspot activity for each cycle increases are an indicator of long-term inter-cycle trends in solar variability over multiple cycles. They suggested that this could be due to inter-cycle changes in solar convection. Therefore, they felt it was important to include two different solar proxies based on the sunspot number record – the short term “cycle component” based on the annual data and a second “inter-cycle component” that was based on the smoothed record (to capture the inter-cycle trends). Experimentally they noted that the inter-cycle changes implied by this second proxy seemed to be delayed by roughly one solar cycle relative to the other inter-cycle proxies. They noted that this was consistent with theoretical models of solar convection activity that suggested the inter-cycle changes in solar convection might occur years before manifesting on the photosphere. Therefore, they applied an 11-year shift to this particular proxy model.


Each of these proxy models implied different solar variabilities over time but they also shared common features. In particular, all five proxies implied a long-term increase in solar irradiance from a minimum during the late-19th century (1880s) to a maximum during the mid-20th century (1930s/40s). Hoyt & Schatten decided to use this commonality as a baseline for converting the proxies into absolute TSI values.


They calculated four different estimates for how much TSI had increased over this period. Two of these estimates were calculated directly for this period. These suggested an increase of either 0.30% or 0.38% in irradiance over the 1880-1940 period.


They also found two competing estimates of the increase in TSI from the Maunder Minimum (1645-1715) to the 1986 solar minimum (which was the most recent solar minimum at the time). Lean et al. (1992) estimated this to be 2.7 W/m2, i.e., a 0.19% increase since the Maunder Minimum, while Nesme-Ribes & Manganey (1992) estimated an increase of 6.8 W/m2, i.e., a 0.50% increase since the Maunder Minimum. Hoyt & Schatten estimated that the TSI increase over their 1880s to 1930s-40s period was roughly 70% of the increase between the Maunder Minimum and the 1986 minimum. Therefore by rescaling those estimates by 70% they got an additional two estimates for the 20th century increase of 0.14% and 0.35% respectively.


They therefore had a range of four estimates of the 20th century increase from 0.14% to 0.38%. They decided to cautiously choose the lower bound – which happened to be the Lean et al. (1992) estimate. As we will see later, Chatzistergos (2024) disputes the validity of the Lean et al. (1992) estimate.


Therefore, they rescaled each of their proxy models to have a 0.14% increase from the late-19th century minimum to the 1930s/40s maximum. For 1979-1992, the NIMBUS7 satellite mission suggested an average TSI of 1372.1 W/m2. So, they converted each proxy model into a TSI estimate by rescaling them from units of % solar variability to absolute TSI values (in W/m2).


Part 3. Combining the inter-cycle components and the cycle component

Finally, they averaged the five proxy models into a single multiproxy estimate of the inter-cycle changes in TSI values and added the cycle component.


Since they were aware that some researchers preferred “the constant quiet Sun model” (Paradigm A), Hoyt & Schatten were conscious that people might be sceptical that each of the proxies considered could be contributing to inter-cycle trends not included in the constant quiet Sun model. However, in their summary section, they anticipated this scepticism and countered in advance,

There is plausible evidence for long-term changes in solar irradiance. Over the last two decades, diagnostic measurements of the equivalent width of lines, the limb darkening of the Sun, and line bisectors all indicate secular changes in solar convection, the photospheric temperature gradient, and solar irradiance are possible. Additional evidence for long-term irradiance changes come from such proxy measures as sunspot structure, sunspot decay rates, the length of solar cycles, the normalized solar cycle decay rate, the equatorial solar rotation rate, and the time rate of change of the solar diameter. The variations in these indices can plausibly be explained as arising from a common source, namely secular changes in solar convective energy transport or convective velocities. We recognize that such changes fall outside the domain of usual theories of stellar structure, but then all the observed solar variations do so too. Without any consideration of the arguments put forth in this paper, it seems more plausible for all these solar proxies to play some role in the varying solar irradiance than it would be for all these variations to exist with an invariant solar brightness.” – Hoyt & Schatten (1993); Emphasis added by us in bold.

Below, we plot the original HS93 TSI reconstruction (1700-1992):




The ACRIM team’s extensions of HS93 using the ACRIM satellite composite (Paradigm C)

As discussed earlier, the ACRIM satellite TSI composites were very consistent with Paradigm C in that they suggested that the average TSI during sunspot minima changes between solar cycles, e.g., Willson 1997; Willson & Mordvinov, 2003.


This contradicts the claims of groups such as Fröhlich & Lean (PMOD group) who insisted that any inter-cycle changes in the TSI minima must be flawed (since Paradigm A believes there are no inter-cycle changes in the TSI minima) and therefore the original data must be adjusted accordingly.


All of the satellite composites are obviously just describing the satellite era (1978 to present). However, the ACRIM team argued that if they were observing inter-cycle trends in the solar minima within the satellite era (in contradiction to the Paradigm A-based TSI reconstructions), then it seemed likely that trends between solar minima could similarly have occurred during the pre-satellite era.


Therefore, if Paradigm C is correct (as suggested by the ACRIM composite), then Paradigm C-based TSI reconstructions would be more plausible than the Paradigm A-based TSI reconstructions.


They saw that HS93 was one of the few TSI composites that suggested substantial inter-cycle TSI variability within the satellite era, but that it had ended in 1992. Therefore, in the appendices of Scafetta & Willson (2014) (pdf available here), they proposed a simple update to HS93 by using the ACRIM composite to extend the reconstruction up to 2013.


Although the final ACRIM composite only covers the period until the ACRIMSat /ACRIM3 satellite mission ended in early 2013, the ACRIM team have since then published several extensions to the composite using the averages of more recent satellite missions. Recently, Scafetta (2023) used such an extension to extend the HS93 reconstruction up to 2022.


In several studies, we have noted that this combined HS93+ACRIM composite TSI reconstruction matches quite well with Northern Hemisphere temperature records that are not contaminated by urban warming:



And even if you include urban stations (as the IPCC’s favored temperature records do), it still suggests a substantial role for the Sun in the warming since the 19th century up until the end of the 20th century:



E.g., see Connolly et al. (2020); Connolly et al. (2021); Soon et al. (2023) and Connolly et al. (2023). In contrast, we found that using the TSI reconstructions used by the CMIP5 or CMIP6 modelling groups, we got the same results as the IPCC, i.e., that TSI couldn’t explain much of the temperature changes.


In Connolly et al. (2021) and Connolly et al. (2023), we noted that we found substantial solar roles for multiple different TSI reconstructions – not just HS93 – but never when we used the SATIRE-T or NRL TSI reconstructions developed from Paradigm A.


However, Chatzistergos (2024) claims that our specific results related to the HS93 reconstruction are invalid because his HS93 remake is similar to the SATIRE-T and NRL TSI reconstructions.


So, let’s now look at Chatzistergos’s HS93 replication efforts and then his remake.


Chatzistergos (2024)’s replication of HS93 using digitized data

The first step he did was to digitize the various solar proxy records used by Hoyt & Schatten (1993) and then try to replicate the methodology they used to generate their TSI reconstruction. This was not such a trivial task because the paper was published in 1993 which was quite a different era from today.


All the scientific journals were hard-copy physical journals and the journals were much stricter on how many pages and figures you could include in your article. As a result, some of the specific details on some of the steps used by Hoyt and Schatten were quite terse (in order to meet journal word limits).


Unlike most modern on-line journals that allow users to upload data files as Supplementary Information, this was the era where data was usually stored and shared either on paper or if you were tech-savvy, with a 5.25” or 3.5” floppy disk that had a maximum memory capacity less than a typical modern e-mail attachment! So, “sharing data” was typically done by plotting the results in a figure, or sometimes in a table if there weren’t too many data points. Unfortunately, even these figures were usually of a lower quality and resolution than modern standards. Even including one color figure was very expensive and most figures were gray scanned-in versions of the original figures provided by the authors.


So, Chatzistergos first digitized the underlying solar proxy records and TSI reconstruction from the figures in the article. This is something we also did in Soon et al. (2015), a pre-CERES study by three members of the CERES team:


He seems to have done a reasonable job of digitizing the original solar proxy records used by HS93. See below:



Chatzistergos then tried to replicate the original HS93 TSI reconstruction using their data, the descriptions provided by Hoyt and Schatten (1993) and a bit of trial and error. He also seems to have done a fairly reasonable job of this. See below:


The red line is his digitized version of HS93 and the black line is his attempt to reconstruct HS93 using his digitized solar proxy records.


We agree with him that he seems to have done a fairly reasonable job of replicating how HS93 was originally constructed. If Chatzistergos were to publish these time series and calculations as Supplementary Information, then it might be useful for others trying to build on the analysis of Hoyt & Schatten (1993).


Given the fact that most journals are unfortunately not interested in publishing simple replications of previous papers, he probably wouldn’t have been able to publish this replication on its own. However, we think this was a positive feature of his paper that is useful and should be commended – especially if he decides to provide his replication data to the scientific community.


Unfortunately, the rest of Chatzistergos (2024)’s analysis, i.e., his attempts to “update HS93” are less impressive (in our opinion, at least). And, disappointedly, this is the aspect that he has focused on in his conclusions and his framing of his work.


Chatzistergos (2024)’s “remake” of HS93

As we saw, Chatzistergos was able to replicate the original HS93 series reasonably well when using the time series that he digitized from the graphs in HS93. The results were not identical but close enough to show that he was able to follow HS93’s methodology and rationale enough to reproduce their overall result – at least when using the time series compiled by HS93.


Chatzistergos (2024) then decided to generate his own versions of HS93’s time series using more recent datasets. He then claims to have “update(d) the HS93 model with new input data”. He claims that,

“… our result is consistent with more recent estimates such as those from the Spectral And Total Irradiance REconstruction (SATIRE) model and Naval Research Laboratory TSI (NRLTSI), which were used by the Intergovernmental Panel on Climate Change (IPCC).”

Below we compare his remake (left-hand side) to the SATIRE-T reconstruction (right-hand side) developed by his colleagues at MPS.



We agree with Chatzistergos that these two plots are pretty similar to each other. He seems to treat this as a vindication of the SATIRE-T reconstruction and he concludes, “updating the HS93 model with recent data results in TSI variations since 1700 that are consistent with those by SATIRE-T and NRLTSI, that is those used by IPCC.


We note that this apparent agreement between his remake and SATIRE-T introduces a bit of a paradox in his arguments in the paper. Throughout the article, as he dismisses each of the five inter-cycle proxy models chosen by HS93 in turn as “implausible” proxies for long-term solar irradiance variability. The only one of the proxy models he appears to endorse is the cycle component (based on the short-term TSI variability due to the rise and fall of photospheric features).


Yet, when he carries out his “update” using his extensions of these five proxy models, he ends up with almost the same results as the SATIRE-T reconstruction of his colleagues.


Therefore, if the proxies identified by HS93 truly are as implausible as Chatzistergos claims then how come they lead to the same results? And what does it say about the reliability of the SATIRE-T reconstruction when Chatzistergos can get the same results by throwing “implausible” proxies into his analysis?


The main reason why Chatzistergos’s remake looks so similar to SATIRE-T is that for his “updated” reconstruction, he refused to rigorously follow the methodology and philosophy of HS93 that he had used for his “replication”. A secondary reason is that he was quite selective in the data choices he made when deciding how to “update” each of the time series used by HS93.


We will demonstrate this by carrying out an alternative “update” by using the time series that Chatzistergos (2024) compiled as his “updates” – but processing them according to the methodology and rationale used by Hoyt & Schatten (1993). As we will discover, this leads to very different results than Chatzistergos’s remake!


Problems with Chatzistergos (2024)’s “remake” of HS93

The problem seems to be that Chatzistergos has very different scientific opinions on the variability of TSI than Hoyt & Schatten (1993). He believes in Paradigm A, while HS93 was developed from Paradigm C.


Therefore, Chatzistergos fundamentally disagrees with the rationale and methodology they used. He also disagrees with many of the decisions they made in developing their TSI reconstruction. So, when he claims he has “updated” HS93, he does not mean this.


Instead, he has replaced those arguments made by HS93 that he disagrees with with his own opinions. Apparently, he believes that the TSI reconstructions developed by the group he works for (MPS) are superior to HS93 and therefore for his “update”, he refuses to genuinely respect the rationale or methodology offered by Hoyt & Schatten (1993).


A separate issue is that there is considerable scientific debate over two of the key datasets he uses as “newer” equivalents of the datasets used by HS93:

  • HS93 used the NIMBUS7/ERB satellite data for their analysis, but Chatzistergos’s remake seems to be predominantly based on the PMOD satellite composites.

  • HS93 used the standard sunspot number (SSN) dataset for describing sunspot activity. Afterwards, Hoyt & Schatten (1998) developed an alternative dataset describing group sunspot numbers (GSN). This dataset has been widely used as a more consistent metric of sunspot activity by many groups and reconstructions – including most of the SATIRE and NRL reconstructions that Chatzistergos favors. Yet, he instead chose to “update” HS93 using a majorly altered new version of the SSN dataset called ISN v2 (Clette et al., 2023).


Chatzistergos has his personal scientific opinions on the debates over these two datasets. He has subjectively chosen his favored dataset choices and his updated time series are based accordingly.


Therefore, for our analysis in this post, we will use these two datasets for consistency with his analysis. However, we want to stress the caveats that we think both of these choices were debatable, as explained below.


Caveat 1: Concerns over Chatzistergos’s dataset choices for the satellite data

We note that Chatzistergos chose to “update” the NIMBUS7/ERB satellite data with the PMOD satellite composite (Fröhlich, 2012) and for his multilinear regression by using the current PMOD group’s satellite composite (Montillet et al., 2022). However, both of these composites apply Fröhlich’s various adjustments to the underlying satellite data in order to remove the changes in TSI between solar minima.


In the paper, he explains that he also repeated his updates using the ROB and ACRIM TSI composites and he tabulates some statistics on those fits. But, the final reconstructions he plots in Figures 11 and 12, he apparently only used the Montillet et al. (2022) PMOD composite. So, he seems to have decided that this is his “update” to HS93’s NIMBUS7/ERB satellite data.


While updating their ACRIM composite in 2013, Scafetta & Willson specifically reached out to Doug Hoyt (as a member of the NIMBUS7/ERB team) to see whether he thought the PMOD group’s adjustments to the NIMBUS7/ERB satellite data were justified. As described in the appendices of Scafetta & Willson (2014) (pdf available here), Hoyt strongly disagreed with Fröhlich’s adjustments to the data on multiple grounds and concluded, “there is no justification for Fröhlich’s adjustment in my opinion.”


Therefore, given Hoyt’s explicit disagreement with the adjustments applied to the various PMOD composites (original or current), we do not think that they are a suitable “update” to the NIMBUS7/ERB satellite data used by HS93. A satellite composite that used the original data, e.g., the ACRIM composite would be a more natural “update”.


Caveat 2: Concerns over Chatzistergos’s dataset choice for sunspot activity

Using ISN v2 is technically an “update” (Clette et al., 2023). However, a more genuine update would probably have been to switch to using Group Sunspot Numbers.


This is because, following Hoyt & Schatten (1993), they expressed considerable concern with the reliability of the SSN record. They developed a new Group Sunspot Number record (GSN) that they believed was a more consistent metric of sunspot activity than SSN:


Because Hoyt & Schatten (1998)’s GSN dataset provides a longer record (1610-present) than the SSN records (1700-present), many of the groups – including MPS – have used their data instead of SSN for their TSI reconstructions. This includes the original versions of SATIRE-T (Krivova et al., 2010) and SATIRE-T2 (Dasi-Espuig et al., 2016). Moreover, Chatzistergos himself has explicitly discussed the GSN data in his own work, e.g., Chatzistergos et al. (2017).


So, he is very familiar with the fact that following Hoyt & Schatten (1993), both co-authors have argued that the GSN data is a more robust record than the SSN data they had used for their 1993 study. In other words, rather than switching to ISN v2, a more authentic update would be to switch to using an updated GSN dataset.


In terms of updated GSN records, there have been several recent attempts. As mentioned above, Chatzistergos has developed one version. However, Hoyt and Schatten have each worked with different groups in developing their own rival updates.


Schatten has been working with the team involved in ISN v2, e.g., Svalgaard & Schatten (2016) (preprint available here).


However, more recently Hoyt has been working with the CERES team on an alternative update to GSN that he argues is more reliable, e.g.,

  • Velasco Herrera, V.M., Soon, W., Hoyt, D.V. & Judit Muraközy (2022). Group Sunspot Numbers: A New Reconstruction of Sunspot Activity Variations from Historical Sunspot Records Using Algorithms from Machine Learning. Solar Physics, 297, 8. https://doi.org/10.1007/s11207-021-01926-x


In our opinion, this most recent GSN update involving Hoyt and the CERES team is probably a more fitting update than using ISN v2. Hoyt’s new GSN dataset can be downloaded from the CERES website here.


But, we recognize that debates are ongoing over which of the various rival SSN and GSN datasets are most reliable. Also, we appreciate that since Chatzistergos is involved in the ISN v2 project (Clette et al., 2023), he probably has a personal preference for using ISN v2 as an “update” to ISN v1.


 

Correcting Chatzistergos’s “remake” using his data

Now that those caveats are expressed, let us try to update HS93 in terms of Chatzistergos’s compiled data using the actual methodology and rationale of Hoyt & Schatten (1993).


Part 1. The cycle component

In terms of the cycle component, Chatzistergos (2024) calculated an equation for updating this in terms of PMOD and ISNv2 (his equation 5). Although he didn’t use this in his “multilinear regression” remake, he apparently used this for calculating his main remake. His equation 5 says that SSN can be converted into the cyclic TSI variability by multiplying the annual SSN by 0.0067.


There is some uncertainty in exactly how Chatzistergos made this calculation. He explains,

“The scaling of the sunspot number for the first component was determined by simply considering that over 1978 – 1992 ISNv1 changed by ≈150, while Nimbus-7 (Hoyt et al., 1992) TSI measurements changed by ≈1.5 W m−2. This led them to the approximate relationship
TSI = 0.01 ISNv1. (4)
Comparing ISNv2 and PMOD TSI composite we find a very similar scaling of
TSI = 0.0067 ISNv2, (5)
which equals 0.01 when brought to the scale of ISNv1 (divided by 0.6) and it is consistent with other more recent studies (Dewitte, Cornelis, and Meftah, 2022; Xu, Lei, and Li, 2021).”

We assume since the reconstruction is in annual resolution that this comparison was done with yearly data (as for HS93). However, when we calculate the scaling using the ISNv2 and PMOD TSI composite (Fröhlich, 2012) data we find several possible scaling factors:

  • HS93 method with HS93 time period (1979-1992) = 0.0047

  • HS93 method using full satellite record (1979-2017) = 0.0055

  • Linear regression over full satellite record (1979-2017) = 0.0049 (r2=0.888)


Alternatively, if we use the current PMOD composite (Montillet et al., 2022) over the full satellite record (1981-2022), we get the following scaling factors:

  • HS93 method with HS93 time period (1981-1992) = 0.0052

  • HS93 method using full satellite record (1981-2022) = 0.0061

  • Linear regression over full satellite record (1981-2022) = 0.0059 (r2=0.909)


Since Chatzistergos refers to the PMOD TSI composite as being distinct from the current PMOD composite (Montillet et al., 2022), we assume that he was using this composite for this step. Therefore, we apply the 0.0055 scaling since this is the closest of our PMOD-based factors to the value he calculated.


Part 2. The inter-cycle components

He attempts to extend each of the five solar proxy records to present using more recent sets of measurements made by different observatories from those originally used by Hoyt & Schatten (1993). Unfortunately, most of these attempts are quite subjective and his proposed “updates” don’t match very well with the original time series.


We sympathize with the challenges of finding suitable records for updating the individual proxies used by Hoyt & Schatten (1993). Unfortunately, most of the records they had originally used had been discontinued by the relevant observatories and more recent records for these types of measurements by different observatories seem to have taken different approaches to making these measurements. As a result, they are not always directly comparable to the records used by Hoyt & Schatten (1993).


Moreover, when Chatzistergos was trying to reproduce the individual HS93 indices from scratch using his newer datasets, none of his attempts matched perfectly with the original HS93 indices. This can be seen by comparing the red curves (which were his digitized versions of the HS93 records) to the other curves in Figures 1, 2, 3, 4 and 6. Nonetheless, he claims that,

“We replicated the indices used by HS93 to a rather reasonable degree. However, we find almost perfect agreement only for two out of five indices (smoothed sunspot-number series and penumbral-spot fraction)." – Chatzistergos (2024), p25.

So, let’s first consider those two indices he says he found “almost perfect agreement” for.


Proxy 1. Penumbral-spot fraction

In terms of the penumbral spot fraction index, Chatzistergos notes that the two records he identified as potential candidates for updating the HS93 series were not directly comparable datasets and that they each implied different trends – even after scaling one to match the others:

“Further aggravating this is that it is unclear how the umbra/penumbra separation was done in all archives. In RGO and Rome the identification was done manually, which then carries the extra uncertainty of potential variations of the selection criteria over time. In Debrecen this was most likely done in an automatic way with fixed intensity thresholds. Therefore, the observing conditions can significantly affect the measurements, e.g. when there is poor seeing the spots would appear smeared and the umbra will appear brighter and potentially indistinguishable from the penumbra.
[…]
It becomes very clear that the overall behaviour of penumbral spots is significantly different in the various databases. Rome and RGO report between 20 – 40% of spots having only penumbra, while this increases significantly for Debrecen to about 20 – 80%. The evolution of penumbral spots differs dramatically between the different archives, showing opposite behaviours over almost the entire overlapping periods. Peculiarly, around 1995 there is an increase in penumbral spots in the Rome database, at the same time of a decrease of penumbral spots in the Debrecen database. Similarly, between 1955 and 1965, when Rome shows a decrease in penumbral spots, RGO reports an increase. Overall, the level of penumbral spots is relatively stable in the Rome database, while the RGO one shows a consistent decrease until the 1940s, which is followed by an increase. Debrecen data show an increase since the 1990s.”

That is, for one of the only two proxies he claims he was successfully able to replicate with “almost perfect agreement”, he could see that the results “differ dramatically between the different archives”, making the choice of how to genuinely update the HS93 record to present very subjective.


Looking at his Figure 6b, which we have reproduced below with added labels, you can see that he “updated” the HS93 record (which he colored with a red dashed line) using the complex extenstion that he labelled “This work (Debrecen /3)” and colored with a purple dashed line.

 




He explains how he developed this purple dashed line as follows:

“For the following discussion we will use the series we produced by combining RGO and Rome data following HS93, extended to 2000 and then stitched to Debrecen data until 2018. We note that we do not simply stitch the Debrecen data to the other archives because it would introduce a sharp decrease in this index after 2000. In an attempt to reduce the bias in our results due to the archive inconsistencies, we produce two different versions of the penumbral-spot fraction index, where the Debrecen penumbral fractions were divided by three and seven (shown in orange and yellow in Figure 6b, respectively) and stitch these scaled series to the data from the other archives.”

However, if we look at the various curves he plotted, you can see that the most natural extension to the end of the HS93 record in 1989 is probably the “Debrecen ÷ 7 record” (which he colored in yellow).


Therefore, while we do not think that it has been satisfactorily resolved how to update HS93’s penumbral spot record past 1989, if we were to use Chatzistergos’s compiled potential updates, we think that the one he chose (purple) seems very arbitrary and the curve he colored in yellow would have been a more natural extension.


Hence, for our update, we have extended the original HS93 record using this yellow plot from the various possible updates he considered instead of using the purple plot he used (or the cyan plot he considers in a sub-analysis).

 

Proxy 2. Smoothed sunspot number proxy

We have already discussed our concerns over Chatzistergos’s decision to use the ISN v2 record instead of GSN for the sunspot activity data.


Another debatable point is whether the smoothed inter-cycle sunspot activity record should be shifted by 11 years or not. As explained earlier, Hoyt & Schatten (1993) used the SSN record in two ways. They used the unsmoothed SSN record “to approximate an 11-year solar activity component which includes contributions from facular emission and sunspot blocking”. Chatzistergos doesn’t seem to disagree with this aspect. Indeed, it is the dominant feature of his HS93 remake!


However, Hoyt & Schatten (1993) also used the 11-year running mean of the SSN record as an additional solar proxy for capturing aspects of the inter-cycle variability in irradiance. Specifically, they suggested that long-term changes in sunspot activity are related to changes in internal solar convection that could potentially influence the irradiance changes of future cycles. They argued on a combination of empirical and theoretical grounds that for this purpose, it was recommended to allow a delay time of 11 years to their running mean for this TSI proxy.


Chatzistergos disputes this hypothesis on the basis that a computer model developed at the MPS doesn’t consider this possibility by assuming all the irradiance variability is associated with changes that are visible on the photosphere, i.e., Yeo et al., 2017; Shapiro et al., 2017. This is the belief within Paradigm A.


He is entitled to have a different scientific opinion from Hoyt & Schatten (1993) on this. However, as Hoyt & Schatten (1993) explained in their paper, their reconstruction was explicitly not based on “the constant quiet Sun model” that Paradigm A assumes.


Therefore, if he were genuinely interested in “updating HS93”, then he would have applied this step to his update of this proxy – even if he personally disagreed with it. After all, he claimed to be updating Hoyt & Schatten (1993). Hence, for our update, we apply this shift to this index – as implemented by Hoyt & Schatten (1993).


Proxies 3. The solar cycle decay rate index

For his update of the solar cycle decay rate index, he explains that his attempts at replication only worked when he applied a 10-year offset. However, he refused to apply this step in his extensions.


We have not yet identified why there is this apparent lag between his replication and the original. However, from his Figure 3, we note that even with this offset to the HS93 data (his blue dashed line), his attempt to replicate the time series (his black solid line) doesn’t match very well.


Therefore, it seems to us that Chatzistergos has not yet succeeded in establishing how Hoyt & Schatten (1993) calculated their solar-cycle decay rate index. With that in mind, his “update” of this index needs to be treated with considerable caution. Nonetheless, since he found his best approximation of the HS93 series occurred when he applied a 10-year offset to his calculations, this seems a more authentic “update” of the original HS93 series.


Proxies 4 & 5. The other two proxies

For the remaining two proxies, we have used Chatzistergos’s proposed “updates” as-is. However, we note that he does not seem to have satisfactorily replicated either proxy yet:

  • For his Solar Cycle Length (SCL) index, he admits he couldn’t figure out exactly how Hoyt & Schatten had derived their SCL index. He experimented with a couple of ideas of how one might calculate the annualized index that HS93 developed, but none of his attempts seemed to match up consistently – see his Figure 2. We also note that the “two different interpretations” that he has proposed do not seem to have much in common with the actual description HS93 gave. Nonetheless, the curves he created seem to qualitatively capture much of the trends of HS93’s record.

  • For his equatorial solar rotation index, his attempt at replication led to a greater variability than HS93’s original index – see his Figure 4. Nonetheless, the two curves both seem to generally track each other over the period of overlap.


Part 3. The debate over the scaling of the inter-cycle components

As we explained earlier, when Hoyt & Schatten (1993) were scaling the five solar proxy models into TSI units they identified four different estimates for the increase in TSI from the late 19th century (1880s) minimum to the 1930s-40s maximum: 0.14%, 0.30%, 0.35% and 0.38%.


Although they noted that 0.30% provided the best correlation with climate, they chose to go with the lowest estimate, i.e., 0.14%. This estimate was taken from Lean et al. (1992).


Chatzistergos claims that a Sun-like star study that was used by Lean et al. (1992) as part of their calculations (Baliunas & Jastrow, 1990) was “later shown to be incorrect” by three studies:

  • J.C. Hall and G.W. Lockwood (2004). "The Chromospheric Activity and Variability of Cycling and Flat Activity Solar-Analog Stars". The Astrophysical Journal, 614 (2), 942. https://doi.org/10.1086/423926 

  • J.T. Wright (2004). "Do We Know of Any Maunder Minimum Stars?". The Astronomical Journal, 128, 1273-1278. http://dx.doi.org/10.1086/423221 

  • J.C. Hall, G.W. Henry, G.W. Lockwood, B.A. Skiff and S.H. Saar (2009). "The activity and variability of the Sun and Sun-like Stars. II. Contemporaneous Photometry and Spectroscopy of Bright Solar Analogs." The Astronomical Journal, 138 (1), 312. https://doi.org/10.1088/0004-6256/138/1/312


On the basis of these three studies, he argued that the 0.14% estimate that Hoyt & Schatten (1993) had chosen for their scaling was incorrect and outdated. One straightforward way to update the HS93 reconstruction in light of Chatzistergos’s dispute over this scaling factor would be to use the next lower estimate from Hoyt & Schatten (1993)’s estimates, i.e., 0.30%.


[As an aside, the Lean of Lean et al., 1992 is the same Dr. Judith Lean we discussed earlier who in later years co-developed the NRL TSI reconstructions and the initial PMOD adjustments for the satellite data.]


However, as it happens while those three papers published between 2004 and 2009 did indeed raise questions over some aspects of Baliunas & Jastrow (1990)’s estimates of the Maunder Minimum, many relevant Sun-like star papers have been published since, e.g.,

  • I. Shapiro, W. Schmutz, G. Cessateur and E. Rozanov (2013). The place of the Sun among the Sun-like stars. Astronomy & Astrophysics. 552, A114. https://doi.org/10.1051/0004-6361/201220512 

  • Ricky Egeland, Willie Soon, Sallie Baliunas, Jeffrey C. Hall, Alexei A. Pevtsov, and Luca Bertello (2017). The Mount Wilson Observatory S-index of the Sun. The Astrophysical Journal, Volume 835, Number 1 https://doi.org/10.3847/1538-4357/835/1/25 

  • R.R. Radick, G.W. Lockwood, G.W. Henry, J.C. Hall and A.A. Pevtsov (2018). "Patterns of Variation for the Sun and Sun-like Stars". The Astrophysical Journal, 855 (2), 75. https://doi.org/10.3847/1538-4357/aaaae3 

  • Timo Reinhold, Alexander I. Shapiro, Sami K. Solanki, Benjamin T. Montet, Natalie A. Krivova, Robert H. Cameron & Eliana M. Amazo-Gómez (2020). The Sun is less active than other solar-like stars. Science, 368 (6490), 518-521. https://doi.org/10.1126/science.aay3821

  • P.G. Judge, R. Egeland and G.W. Henry (2020). "Sun-like Stars Shed Light on Solar Climate Forcing". The Astrophysical Journal, 891 (1), 96. https://doi.org/10.3847/1538-4357/ab72a9 

  • A.C. Baum, J.T. Wright, J.K. Luhn and H. Isaacson (2022). "Five Decades of Chromospheric Activity in 59 Sun-like Stars and New Maunder Minimum Candidate HD 166620". The Astronomical Journal, 163 (4), 183. https://doi.org/10.3847/1538-3881/ac5683 

  • J.K. Luhn, J.T. Wright, G.W. Henry, S.H. Saar and A.C. Baum (2022). "HD 166620: Portrait of a Star Entering a Grand Magnetic Minimum". The Astrophysical Journal Letters, 936 (2), L23. https://doi.org/10.3847/2041-8213/ac8b13

  • Howard Isaacson, Stephen R. Kane, Brad Carter, Andrew W. Howard, Lauren Weiss, Erik A. Petigura, and Benjamin Fulton (2024). The California-Kepler Survey. XI. A Survey of Chromospheric Activity through the Lens of Precise Stellar Properties. The Astrophysical Journal. 961:85. https://doi.org/10.3847/1538-4357/ad077b


Dr. Willie Soon, CERES co-team leader, has been one of the leading researchers in the study of Sun-like stars for the last 30 years, and several of the above studies involve researchers who have been collaborating with the CERES team as well as the co-authors of the three papers cited by Chatzistergos. So, this is a topic we are very familiar with.


Baliunas & Jastrow (1990) was a seminal and valiant first attempt to try and compare the solar variability of the Sun over the sunspot record (1700-1989 at the time) to shorter records of multiple “Sun-like stars”.


One of the goals of studying Sun-like stars is to study the stellar variability of other stars that seem “Sun-like” and use them as an analogue for our Sun. Ideally, if we can identify several truly Sun-like stars and monitor them for several decades, then we can get independent estimates of how variable the Sun is.


Identifying and defining a “Sun-like star” is a challenging process and the scientific community has been evolving and refining this process over the years since that early study.


Baliunas & Jastrow (1990) were analyzing the observational data from a collection of 74 “Sun-like stars” that had been monitored for several decades. Most of these stars only had limited observations, but a subset of 13 of these stars had been studied monthly since 1966 and nightly since 1980.


While explicitly recognizing the limited sample sizes of their data, they found that four of the stars in their subset of 13 were “non-cycling” while the other 9 were “cycling”. They suggested these four “non-cycling” stars could be “tentative(ly)” treated as analogues for how the Sun might have behaved during the Maunder Minimum. They noticed that all four stars had an irradiance equivalent at the very low end of the binned observations from all 74 stars. They suggested that this was supporting evidence that the average irradiance during the Maunder Minimum was considerably lower than during the satellite era.


Lean et al. (1992) used Baliunas & Jastrow’s binned activity distribution of all 74 Sun-like stars to estimate that the TSI during the 1986 solar minimum was 0.30% higher than the “minimum possible Sun”. They also used the average of those four non-cycling stars as an estimate of the Maunder Minimum and concluded this was 0.19% lower than the 1986 solar minimum. This led to Hoyt & Schatten (1993)’s lower bound estimate.


Now, by the time of the three papers cited by Chatzistergos (2024), a lot more data on Sun-like stars had been collected. This allowed the three studies to look at those four non-cycling stars in more detail. The studies collectively suggested that ultimately, those four stars were probably not suitable analogues for “the Maunder Minimum”. This meant that they couldn’t be used to directly quantify the difference in TSI between the Maunder Minimum and the satellite era, as originally hoped.


Work to try to identify and monitor more suitable Maunder Minimum candidates is ongoing, e.g., Luhn et al. (2022); Isaacson et al. (2024).


In the meantime, Judge et al. (2020) has taken a different approach to evaluating the potential increases in TSI since 1750 based on a much expanded version of the Sun-like stars used by the three papers cited by Chatzistergos (2024). They estimate that TSI could potentially have increased as much as 4.5 W/m2 since 1750, i.e., a 0.33% increase.


This implies an updated scaling factor for the HS93 reconstruction of 0.23% (70% of 0.33%), which is less than the factor of 0.30% discussed earlier.


Below we compare the updated reconstructions using either the original scaling (left) or the updated scaling of Judge et al. (2020) (right):


Since Chatzistergos (2024) disputes the validity of the original scaling, we use the updated scaling.


Below we show the number of proxies available for each year in our corrected version of Chatzistergos’s remake of HS93. We note that the number of proxies available is lower at the start and end of the record. These values should probably be treated more cautiously as a result. We have indicated the years with less than three proxies available with dashed lines:



Below, let us compare the different versions of HS93 we have discussed so far:



While our corrected version of Chatzistergos’s remake shows a reduced long-term increase in TSI to present compared to the original HS93 and the ACRIM extension, it shows more similarity to those reconstructions than Chatzistergos’s remake.


But, let us now turn to the question of how much of a role TSI can play in the temperature changes since the 19th century in terms of these old and new reconstructions.

 

How much of a role can TSI explain in global warming?

In Section 4 of Chatzistergos (2024), he tries to fit the global temperature records used by the IPCC in terms of TSI. The global temperature records he chooses to fit are surprising choices for somebody who claims to have something to say on our five papers that he criticizes, i.e., Soon et al. (2015) (preprint pdf here); Connolly et al. (2020); Connolly et al. (2021); Soon et al. (2023) and Connolly et al. (2023). If he has genuinely read those papers – as he seems to be implying through his criticism – then he should be aware that we have explicitly shown that the land component of those global temperature records is substantially affected by urban warming biases. This is because urbanized weather stations represent the majority of the longest and most complete records in the global temperature dataset, yet urban areas only account for 3-4% of the land surface and 1-2% of the global surface.

[As an aside, Doug Hoyt was a co-author on three of those studies.]


Therefore, a more genuine “Comparison to Earth’s Temperatures” would have been if he had used estimates unaffected by urban warming biases. Here, we use our Rural-only Northern Hemisphere temperature record that we originally published in Connolly et al. (2021). The dataset can be downloaded here.



 In each panel, the green curves show the rural-only temperature changes relative to the 20th century average. The red (and in one case blue) curves show the TSI plots after we have calibrated them into a Northern Hemisphere land temperature equivalent by rescaling each TSI series to have the same mean and standard deviation as the temperature record over the 20th century.


In the top-left panel we see that both the original HS93 (red curve) and Chatzistergos’s replication (blue dashed line) track the average rural-only land temperature (green dashed line with circles) remarkably well over the entire TSI record from the start of the temperature series in 1850 to the end of the original TSI record in 1992. This is quite a remarkable result given that our rural-only series was not developed until 2020 – 27 years after Hoyt & Schatten (1993) developed their TSI record.


We have already discussed a similar result for the top-right panel in detail in Soon et al. (2023) – there are some divergences at the start of the temperature record and for the post-20th century period. See the conclusions of Soon et al. (2023) for a detailed discussion.


However, overall, the long-term warming and cooling periods match quite well with the changes in TSI over most of the temperature record.


In the bottom two panels, we compare Chatzistergos’s remake of HS93 on the left with our corrected version of his updates on the right hand side. For his remake, the modelled temperature changes imply there should be a major warming/cooling pattern every solar cycle, yet this is not seen in the actual temperature record. This suggests that his remake has substantially overestimated the cyclical component of his reconstruction.


Meanwhile, for our corrected version of his update, the modelled solar contribution matches very well over most of the temperature record up until the late-1990s when the modelled temperature suggests a sharp cooling until the early 2000s, while the actual temperature record shows a warming.


If this corrected version is an accurate representation of TSI changes then it suggests that the post-1990s warming in the rural record is not due to TSI, but that most of the temperature changes from 1850 up to then can be explained in terms of TSI.


Moreover, in that case, because CO2 has been steadily increasing over the decades, the model-predicted anthropogenic warming should have been a steadily increasing warming over time, rather than zero anthropogenic warming up to the late-1990s followed by a sudden onset of warming. That is, if the warming up to the late-1990s is mostly due to TSI, then the apparent divergence between TSI and temperatures is probably due to other factors than CO2. In other words, despite Chatzistergos (2024)’s claim that his update, “…renders void arguments about the solar influence on Earth’s climate that were drawn based on the original HS93”, the corrected version of Chatzistergos’s HS93 update actually is consistent with a substantial solar influence on Earth’s climate – especially outside of urban areas (that only represent 1-2% of the Earth’s surface).


Furthermore, given that his remake of HS93 seems to show too large a “cycle component” relative to the inter-cycle component, it is worth briefly looking at the data using an 11-year running mean to reduce the magnitudes of the 11-year cycle components. See below:


Interestingly, while the top two panels (based on the original HS93 reconstruction) show a reasonable match between the smoothed temperature and solar activity curves from the 20th century onwards, the bottom two panels (based on Chatzistergos’s alternative proxy series) suggest a slightly better match for the period from the start of the temperature record to the end of the 19th century, i.e., 1850s-1890s.


The timings of the peaks and troughs in Chatzistergos’s remake (bottom left) don’t match as well as in the corrected version. However, nonetheless the smoothed plots of his remake suggests a plausible solar contribution that is not as obvious from the unsmoothed data. This is another indication that his remake probably overweighted the cycle component.


As an aside, this approach of applying an 11-year running mean to evaluate the non-cycle components has been quite popular over the years. Indeed, it was used by Hoyt & Schatten (1993) and has also sometimes been used by Dr. Chatzistergos’s former PhD supervisors, e.g., Solanki & Krivova (2003).

 

Conclusions

In terms of how variable the Sun’s Total Solar Irradiance (TSI) is, we saw that there are currently at least three scientific paradigms:

  • Paradigm A – “The calm Sun”

  • Paradigm B – “The bright modern Sun”

  • Paradigm C – “The variable Sun”


In terms of the causes of climate change, Paradigm A implies that humans are far more powerful than the Sun. Paradigm B implies that humans are about as powerful as the Sun.


In contrast, Paradigm C implies a much greater role for the Sun. Therefore, we can understand why those in Paradigm A are very frustrated by Paradigm C. Those in Paradigm A are frustrated that Paradigm C seems to be assigning much of the observed climate change to forces beyond our control - and, thereby, taking that control away from humanity.


However, many of those in Paradigm C believe that by truly understanding the complex nature of solar variability, we may be better able to predict and prepare for future climate changes, as well as gain a better understanding of the past.


In other words, from Paradigm C’s perspective, fully understanding how the climate has changed in the past will provide humans with a much greater power for dealing with future climate change. That is, it could help bring us better control over our fates.


The original Hoyt & Schatten (1993) TSI reconstruction (“HS93”) explicitly acknowledged that several reconstructions at the time were developed within Paradigm A, which they called “the constant quiet Sun model”. However, they argued that this model was failing to explain many of the historically observed aspects of solar variability as well as the ongoing satellite TSI missions.


In his latest paper, Chatzistergos has claimed to have firstly replicated (using digitized versions of the HS93 plots) and then “updated” the reconstruction to 2009. His “update” looks very different from the original. However, it looks quite similar to his MPS group’s rival “SATIRE-T” reconstruction, which is very much a Paradigm A approach.


Obviously, those who follow Paradigm A are quite chuffed with Chatzistergos's “HS93” remake, e.g., Dr. Gavin Schmidt, director of the NASA Goddard Institute for Space Studies, who has recently posted an article on the RealClimate blog promoting Chatzistergos (2024).


However, in this post, we showed that while his initial replication seems to have been reasonable, his “update” was not a genuine update, but rather a “remake” in terms of Paradigm A.


When we used Chatzistergos’s updates for the individual proxies but applied the original methodology and philosophy of Hoyt & Schatten (1993), we obtained a reconstruction that was quite similar to the original. Below we compare his remake on the left and our update on the right using the same proxy updates, but actually following the approach of HS93:



For each of the “updated” proxies that Chatzistergos used for his remake, we found they were not a great replication of the original series used by HS93. Qualitatively they showed similar trends, but in all cases there were significant divergences from the original HS93 records. In several cases, there was considerable subjectivity in what datasets he used to “update” these proxies and how to process them. Therefore, we are not necessarily endorsing his “updates” to the individual time series. Nor are we endorsing the “corrected” reconstruction we get when we apply the HS93 methodology correctly to his updates.


Nonetheless, we find the differences between his remake and our attempt to update HS93 explicitly relying on the datasets chosen and used by Chatzistergos to be quite substantial.


Therefore, we think that Chatzistergos’s enthusiasm in claiming to have objectively “updated” HS93 seems to have been a bit premature.