Nicola Scafetta Comments on “Solar Trends And Global Warming” by Benestad and Schmidt
From Climate Science — Roger Pielke Sr.
On July 22 2009 I posted on the new paper on solar forcing by Lean and Rind 2009 (see). In that post, I also referred to the Benestad and Schmidt 2009 paper on solar forcing which has a conclusion at variance to that in the Lean and Rind paper.
After the publication of my post, Nicole Scafetta asked if he could present a comment (as a guest weblog) on the Benestad and Schmidt paper on my website, since it will take several months for his comment to make it through the review process. In the interests of presenting the perspectives on the issue of solar climate forcing, Nicola’s post appears below. I also invite Benestad and Schmidt to write responses to the Scaftta contribution which I would be glad to post on my website.
GUEST WEBLOG BY NICOLA SCAFETTA
Benestad and Schmidt have recently published a paper in JGR. (Benestad, R. E., and G. A. Schmidt (2009), Solar trends and global warming, J. Geophys. Res., 114, D14101, doi:10.1029/2008JD011639).
This paper criticizes the mathematical algorithms of several papers that claim that the temperature data show a significant solar signature. They conclude that such algorithms are “nonrobust” and conclude that
“the most likely contribution from solar forcing a global warming is 7 ± 1% for the 20th century and is negligible for warming since 1980.”
By using the word “robust” and its derivates for 18 times, Benestad and Schmidt claim to disprove two categories of papers:
those that use the multilinear regression analysis [Lean and Rind, 2008; Camp and Tung, 2007; Ingram, 2006] and those that present an alternative approach [Scafetta and West, 2005, 2006a, 2006b, 2007, 2008]. (See the references in their paper.)
Herein, I will not discuss the limitation of the multilinear regression analysis nor the limits of Benestad and Schmidt’s critique to those papers. I will briefly focus on Benestad and Schmidt’s criticism to the papers that I coauthored with Dr. West. I found Benestad and Schmidt’s claims to be extremely misleading and full of gratuitous criticism due to poor reading and understanding of the data analysis that was accomplished in our works.
Let us see some of these misleading statements and errors starting with the less serious one and ending with the most serious one:
1. Since the abstract Benestad and Schmidt claim that they are rebutting several our papers [Scafetta and West, 2005, 2006a, 2006b, 2007, 2008]. Already the abstract is misleading. Indeed, their criticism focuses only on Scafetta and West [2005, 2006a]. The other papers used different data and mathematical methodologies.
2. Benestad and Schmidt claim that we have not disclosed nor detailed the mathematical methodology and some parameters that we use. For example:
a) In paragraph 39 Benestad and Schmidt criticize and dismiss my paper with Willson [2009] by claiming that we “did not provide any detailed description of the method used to derive their results, and while they derived a positive minima trend for their composite, it is not clear how a positive minima trend could arise from a combination of the reconstruction of Krivova et al. [2007] and PMOD, when none of these by themselves contained such a trend).” However, the arguments are quite clear in that paper and in the additional figures that we published as supporting material. Moreover, it is not clear to me how Benestad and Schmidt could conclude that our work is wrong if Benestad and Schmidt acknowledge that they have not understood it. Perhaps, they just needed to study it better.
b) In paragraph 41 Benestad and Schmidt claim that: “It is not clear how the lagged values were estimated by Scafetta and West [2006a]“. However, in paragraph 9 of SW06a it is written “we adopt the same time-lags as predicted by Wigley’s [1988, Table 1] model.” So, again, Benestad and Schmidt just needed to study better the paper that they wanted to criticize.
c) In paragraph 48 Benestad and Schmidt claim that: “over the much shorter 1980-2002 period and used a global surface temperature from the Climate Research Unit, 2005 (they did not provide any reference to the data nor did they specify whether they used the combined land-sea data (HadCRUT) or land-only temperatures (CRUTEM).” However, it is evident from our work SW05 that we were referring to the combined land-sea data which is properly referred to as “global surface temperature” without any additional specification (Land or Ocean, North or South). We also indicate the webpage where the data could be downloaded.
d) In paragraph 57 Benestad and Schmidt claim that: “The analysis using Lean [2000] rather than Scafetta and West’s own solar proxy as input is shown as thick black lines.” However, in our paper SW06a it is crystal clear that we too use Lean’s TSI proxy reconstruction. In particular we were using Lean 1995 which is not very different from Lean 2000. Benestad and Schmidt apparently do not know that since 1978 Lean 1995 as well as Lean 2000 do not differ significantly from PMOD because PMOD was build (by altering the published TSI satellite data) by using Lean 1995 and Lean 2000 as guides. Moreover, we also merge the Lean data with ACRIM since 1978 to obtain an alternative scenario, as it is evident in all our papers. The discontinuity problem addressed by Benestad and Schmidt in merging two independent sequences (Lean’s proxy model and the ACRIM) is not an issue because it is not possible to avoid it given the fact that there are no TSI satellite data before 1978.
3. In Paragraphs 48-50 Benestad and Schmidt try to explain one of our presumed major mathematical mistakes. Benestad and Schmidt’s states: “A change of 2*0.92 W/m2 between solar minimum and maximum implies a change in S of 1.84 W/m2 which amounts to 0.13% of S, and is greater than the 0.08% difference between the peak and minimum of solar cycle 21 reported by Willson [1997] and the differences between TSI levels of the solar maxima and minima seen in this study (~1.2 W/m2; Figure 6).” Benestad and Schmidt’s are referring to our estimate of the amplitude of the solar cycle referring to the 11-year modulation that we called A7,sun = 0.92 W/m2 in SW05. Benestad and Schmidt are claiming that our estimate is nor reasonable because in their opinion according to our calculations the change of TSI between solar maximum and solar minimum had to be twice our value A7,sun , so they write 2*0.92=1.84 W/m2, and this would be far too large. However, as it is evident from our paper and in figure 4a in SW05 the value A7,sun refers to the peak-to-trough amplitude of the cycle, so it should not be multiplied by 2, as Benestad and Schmidt misunderstood. This is crystal clear in the factor ½ before the equation f(t)= ½ A sin(2pt) that we are referring to and that Benestad and Schmidt also report in their paragraph 48. It is hard to believe that two prominent scientists such as Benestad and Schmidt do not understand the meaning of a factor ½! So, again, Benestad and Schmidt just needed to think more before writing a study that criticizes ours.
4) Finally, Benestad and Schmidt’s paper is full of misleading claims that they are reproducing our analysis. Indeed, Benestad and Schmidt’s paper is self-contradictory on this crucial issue. In paragraph 85 Benestad and Schmidt claim that they “have repeated the analyses of Scafetta and West, together with a series of sensitivity tests to some of their arbitrary choices.” However, in their paragraph 76 Benestad and Schmidt acknowledge: “In our emulation, we were not able to get exactly the same ratio of amplitudes, due to lack of robustness of the SW06a method and insufficient methods description.” It is quite singular that Benestad and Schmidt claim to have repeated our calculation, at the same time they acknowledge that, indeed, they did not succeed in repeating our calculation and, ironically, they blame us for their failure. It is not easy to find in the scientific literature such kind of tortuous reasoning!
In fact, the reason why Benestad and Schmidt did not succeed in repeating our calculation is because they have misapplied the wavelet decomposition algorithm known as the maximum overlap discrete wavelet transforms (MODWT). This is crystal clear in their figures 4 where it is evident that they applied the MODWT decomposition in a cyclical periodic mode. In other words they are implicitly imposing that the temperature in 2001 is equal to the temperature in 1900, the temperature in 2002 is equal to the temperature in 1901 and so on. This is evident in their figure 4 where the decomposed blue and pink component curves in 2000 just continue in 1900 in an uninterrupted cyclical periodic mode as shown in the figure below which is obtained by plotting their figure 4 side by side with itself:
Any person expert in time series processing can teach Benestad and Schmidt that it is not appropriate to impose a cyclical periodic mode to a non stationary time series such as the temperature or TSI records that present clear upward trends from 1900 to 2000. By applying a cyclical periodic mode Benestad and Schmidt are artificially introducing two large and opposite discontinuities in the records in 1900 and 2000, as the above figure shows in 2000. These large and artificial discontinuities at the two extremes of the time sequence disrupt completely the decomposition and force the algorithm to produce very large cycles in proximity of the two borders, as it is clear in their figure 4. This severe error is responsible for the fact that Benestad and Schmidt find unrealistic values for Z22y and Z11y that significantly differ from ours by a factor of three. In their paragraph 50 they found Z22y = 0.58 K/Wm-2, which is not realistic as they also realize later, while we found Z22y = 0.17 K/Wm-2, which is more realistic.
This same error in data processing also causes the reconstructed solar signature in their figures 5 and 7 to present a descending trend minimum in 2000 while the Sun was approaching one of its largest maxima. Compare their figures 4a (reported above), 5 and 7 with their figure 6 and compare them also with our figure 3 in SW06a and in SW08! See figure below where I compare Benestad and Schmidt’s figures 6 and 7 and show that the results depicted in their Figure 7 are non-physical.
Because of the severe and naïve error in applying the wavelet decomposition, Benestad and Schmidt’s calculations are “robustly” flawed. I cannot but encourage Benestad and Schmidt to carefully study some book about wavelet decomposition such as the excellent work by Percival and Walden [2000] before attempting to use a complex and powerful algorithm such as the Maximum Overlap Discrete Wavelet Transform (MODWT) by just loading a pre-compiled computer R package.
There are several other gratuitous claims and errors in Benestad and Schmidt’s paper. However, the above is sufficient for this fast reply. I just wonder why the referees of that paper did not check Benestad and Schmidt’s numerous misleading statements and errors. It would be sad if the reason is because somebody is mistaking a scientific theory such as the “anthropogenic global warming theory” for an ideology that should be defended at all costs.
Nicola Scafetta, Physics Department, Duke University
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Very interesting.
Usually there is pickup on a new Schwabe cycle before the old has petered out entirely. (But this time, not so much.) The new cycle is said to have begun at the point where the new polarity spots outnumber the old.
It seems entirely plausible that TSI would vary at the minimums, seeing as how the crossover points cannot be at identical levels identical each time.
Trends? Why not? Almost everything involved here is part of some sort of trend. Even if there were no underlying trend, there could be a trend in terms of the point of crossover.
evanmjones (21:49:14) :
Even if there were no underlying trend, there could be a trend in terms of the point of crossover.
I don’t see how. Can you construct an example?
evanmjones (21:49:14) :
It seems entirely plausible that TSI would vary at the minimums, seeing as how the crossover points cannot be at identical levels identical each time.
Yeah… Amplitude is what fluctuates. It seems that, for larger amplitudes, larger effects on Earth’s climate.
Benestad and Schmidt use of constants tend to lessen solar forcing
eg
Albedo *
30 239.26 w/m^2 Benested and Schmidt
28.9 255.9 w/m^2 Kim and Ramanthan
28.6 256.1 w/m^2 CERES
29.6 255.2 w/m^2 Erbes
* Energy at the earths surface in a non absorbing atmosphere
I already had written about increases of amplitude of solar irradiance:
http://www.biocab.org/Amplitude_SI_Svalgaard_s_Database.jpg
The amplitude of the solar irradiance is what has fluctuated and increased since 1610 AD; the intensity of solar irradiance has increased, in consequence.
In concluding his comments above, Nicola Scafetta :
I just wonder why the referees of that paper did not check Benestad and Schmidt’s numerous misleading statements and errors. It would be sad if the reason is because somebody is mistaking a scientific theory such as the “anthropogenic global warming theory” for an ideology that should be defended at all costs.
It is one more proof that the famous “peer review” method of journals depends on the integrity and willingness to work hard in evaluating a paper of the reviewers. It is an “honor system”. Honor systems are as strong as the weakest link in the chain, and it seems to me that in climatology there are many week links.
I’m not a scientist but I spent many months trying to learn as much as I could about Global Warming (and I was COMPLETELY neutral when I started) and there was one thing that was very obvious to me. Almost all of the the “skeptics” of AGW kept making some very, very thoroughly debunked arguments over and over again even though they were obviously false. To me, that’s a SURE sign that they are biased or lying. It doesn’t take a scientific genius to know when people are scamming you. It just takes a good bullshit detector (and I DO have that!). Maybe some of you skeptics are unbiased and telling the truth, but you’ve been so completely overwhelmed by the liers and scammers that your voice is lost in the crap.
Angel (22:55:50) :
“It just takes a good bullshit detector (and I DO have that!).”
I think it’s faulty.
Nasif Nahle (17:08:17) :
We could add also another effect provided by the interplanetary medium due to the mentioned photonic excitation and deexcitation which definitively modifies the temperature of the stratosphere and of the troposphere.
Thanks for that Nasif. I’m a graph junkie at the moment. Got any good ones which illustrate the effect?
Leif Svalgaard (17:36:40) :
They also use a TSI reconstruction with a secular trend, so have the same problem. See their Figure 1A in http://www.acrim.com/Reference%20Files/Sun%20&%20Global%20Warming_GRL_2006.pdf
The other [and more significant] departure is the lack of evidence of a secular trend in TSI at sunspot minima
Yes, but they have explained why they think Frohlich’s ‘Adjustment’ of the TSI data is wrong and why they bridge the ACRIM gap differently, producing the trend in TSI at minima which supports their argument. Personally, I can see some merit in what they have produced, though as I said earlier, I regard their reconstruction and yours/Frohlich’s as the boundaries between which the truth is lurking.
Paul Vaughan (20:08:53) :
You might want to check out…
Thanks Paul, I will. We need to find a place for ongoing discussion, perhaps a thread on solarcyle24.com?
“they applied the MODWT decomposition in a cyclical periodic mode […] it is not appropriate to impose a cyclical periodic mode to a non stationary time series […] This severe error […]”
This is still funny hours later.
Re: Nicola Scafetta (21:30:21)
Thank you for your insightful comments Dr. Seeing more than one side of a story helps cut through the usual BiaS.
Re: Angel (22:55:50)
Welcome to the discussion Angel. Please feel welcome to be very specific. Regards, Paul.
Show me, Angel. What ‘thoroughly debunked’ arguments?
===================================
Leif Svalgaard (20:54:40) :
From 10Be cosmic ray fluxes Steinhilber et al. reports:
http://www.leif.org/EOS/Holocene-TSI.pdf
that
“The entire record of TSI covering the past 9300 years is shown in Figure 3. Throughout this period TSI has varied by approximately 2Wm−2″
This extreme variation was reached only rarely and most of the time TSI stays within +/-0.5 w/m2 of average. A variation much lower than normally assumed in climate studies.
A lot of the reason it’s a much lower variation is because it’s calculated from a TSI slope which has been ‘adjusted’ to keep the minima value level between cycles 21/22 and 22/23. This is what the argument over the ACRIM gap bridging is all about and why it is important.
The much lower TSI at 23/24 minimum is the chicken coming home to roost.
I await a reply from the currently holidaying Paul Clark of woodfortrees.org on the provenance of his TSI ‘PMOD’ data and the splicing method employed, and who it was employed by…
Regardless of all that, the document is a great piece of work whichever vertical scale people prefer to calibrate against it and I congratulate all those involved in it’s production, both cited authors and behind the scenes collaborators.
Leif Svalgaard (21:48:21) :
My claim is that there is no other long-term, secular trends over and above the open flux, e.g. as given by the Heliospheric Magnetic Field. The HMF can be reliably determined back to 1882 and with somewhat greater uncertainty back to 1835 and shows no secular trend, specifically HMF in 1901-1902 is just what it is right now, thus TSI should be the same then as now.
Your graph:
http://www.leif.org/research/Heliospheric-Magnetic-Field-Since-1900.png
shows an increasing trend from 1900 to 1993, just before the cycle 22/23 minimum. In fact, as an absolute quantity, ignoring the cyclicity it increases on average right up to 2005, just around the time cooling becomes evident.
This would seem to be not inconsistent with the global temperature changes observed since 1900. Especially if the raised SST’s around the war years are seen to be problematic in the light of information about the bias of cooling water intake sensors in military vessels.
Angel (22:55:50) :
“I’m not a scientist but I spent many months trying to learn as much as I could about Global Warming (and I was COMPLETELY neutral when I started) and there was one thing that was very obvious to me. Almost all of the the “skeptics” of AGW kept making some very, very thoroughly debunked arguments over and over again even though they were obviously false. To me, that’s a SURE sign that they are biased or lying. It doesn’t take a scientific genius to know when people are scamming you. It just takes a good bullshit detector (and I DO have that!). Maybe some of you skeptics are unbiased and telling the truth, but you’ve been so completely overwhelmed by the liers and scammers that your voice is lost in the crap.”
Woaht? And you used to be neutral?! Meh!
And now you look on science skeptics as lairs and scammers and debunked?
You are absolutely right, you are NOT a scientist.
Angel. Don’t bother reading anything not written by scientists or engineers.
Leif Svalgaard (18:56:20) :
Now, let me go the next step: with a TSI reconstruction [such as mine] with NO secular variability, their (Scafetta and West’s) logical conclusion would be that the climate secular feedback to TSI change is extremely much [in the limit infinitely] stronger.
I think this argument is known in the trade as a ‘reductio ad absurdum’.
This was my original reason to comment on blogs [started out at Tamino’s – and was banned; then ClimateAudit where the discussion ran to 4000 posts without any progress; and now here, still without any real resolution of the problem], because I was asking the ‘climate people’ [I thought] if they could help me understand such hypersensitivity, which would likely lead to runaway [yet the long-term climate is stable within narrow bounds].
I would recommend you read James Lovelock’s original Gaia hypothesis for how it is that the earth has such a strong tendency to homeostasis (stable life benefiting climate). Although he has been lumped in with the ‘mother earth worshiping green leftist pinko communist enviro-whackos’ his analysis is cogent, measured and informative. Back then he was nobody’s fool.
What you come away with is a better understanding of how the earth can be sensitive to small external changes, yet resilient in it’s internal systems myriad methods for achieving equitable balance.
“I completely beleive in Global warming! ”
But not spelling I see. Still without rational thought I suppose accuracy is irrelevant.
Leif,
I get what’s going on now. The variometer data does indeed seem easy to calibrate and is likely trustworthy. I assume there are multiple datasets with good quality match to each other?
Now I’m left wondering how the corrections to sunspot numbers were calculated. Are the corrections simply the magnetic data through Wolf’s equation?
I wonder if you would mind emailing the data and calcs for the corrections to me. It seems like an interesting thing to do a post on.
Also, I see that in your discussion with Dr. Scafetta he claims a contradiction with recent sat data due to a shift in the minimum, I assume from your certainty there are ground based variogram equivalent measures which also demonstrate this slight shift in minimum values. It seems to me that, that would conclude any disagreement between you.
The same question again: Is Angel a man or a woman?
The Earth is a big system and it doesn’t respond greatly to small variations. That’s more a job for some of its subsystems by indirect means. Maybe Leif is right and there is 0 secular trend in TSI coming from the Sun and reaching the Earth’s orbit. Approximately 30% of that of that highly stable TSI is being reflected away in albedo which is tremendously variable in comparison. 80% of that albedo is cloud cover (and atmosphere) and cloud cover varies from moment to moment on the small local level and it is evidently significantly variable at the global level over time. Clouds and cloud formation are subject to about everything as well. Differences in TSI content, cosmic rays, air pollution, natural particulates, downwelling insolation – you name it- it probably has some bit of an effect in the creation and nature of clouds. And when that cloud fraction (or type of cloud makeup) changes – the effective TSI impacting the Earth has changed and it varies in the multiple W/m^2 arena – which is enough to have some impact without having super sensitivity to TSI or CO2 or anything else directly from W/m^2 power density variations.
BTW, I’m enjoying these presentations by the heavy hitter solar guys like Leif & Nicola. However, I think I’ve got to side with Leif on the simple concept that fusion in the solar furnace is an incredibly low power generation per m^3 volume or mass of material and that energy is superheavily averaged over area and filtered by long time constant filters so it’s got to be low variation over the longer time frames. That leaves the magnetic field and its effects to vary which are rather miniscule relative to total power for the Sun. Maybe it’s a bit simplistic to think in just those terms but it seems to make some sense.
Leif Svalgaard (22:06:44) :
evanmjones (21:49:14) :
Even if there were no underlying trend, there could be a trend in terms of the point of crossover.
I don’t see how. Can you construct an example?
Suppose the sunspot series consists of two cycles of opposite polarity. Suppose that for whatever reason, there is a run of cycles more active than previously, or one of the two cycles gets slightly out of kilter with the other either in terms of phase angle or longevity.
Any of these three possibilities will affect the value of the ‘crossing’ between cycles.
Given that the Hale cycle of sunspot polarity would indicate that something like this is actually going on in the sun, it seems like a reasonable bet.
[REPLY – Yes, that’s what I meant. ~ Evan]
Mark – You can add financial analysis to the list where wavelet analysis is used. It has been used there for over 15 years. In addition, it is used in 2D spatial filtering, along with Spectral analysis.
Mark T. (17:30:11):
Usually it takes a few decades for an analytic technique developed in one field to become fully cross-disciplinary. “Climate science” has not even adequately grasped ordinary power spectrum estimation, what with raw FFT periodograms being presented (usually as functions of period, no less) as “power spectra,” in blithe ignorance of the fundamental Wiener-Khintchine Theorem, which is pre-WWII. Less-venerable decimation-in-frequency (or time) algorithms remain largely terra incognita. And the subtleties of the difference between circular autocovariance of a record (similar to the cyclical repetition implicitly used by BS here) and the true sample autocovariance sometimes escapes even some signal processing engineers bent on doing things efficiently. Yet unwarranted resort to wavelet transforms and SSA is made ever more frequently in fashion-conscious “climate science.” Go figure!
tallbloke (01:00:38) :
Yes, but they have explained why they think Frohlich’s ‘Adjustment’ of the TSI data is wrong and why they bridge the ACRIM gap differently, producing the trend in TSI at minima which supports their argument.
The ACRIM gap is a red herring. The HMF is the same now as 108 years ago at the minimum between cycles 13 and 14. Solar activity now is as low as it was then. TSI should then be that same then as now under the assumption that the Sun’s magnetic field is the underlying cause for variations in TSI. This is independent of ACRIM contortions.
tallbloke (01:35:29) :
This is what the argument over the ACRIM gap bridging is all about and why it is important.
See above.
Your graph shows an increasing trend from 1900 to 1993, just before the cycle 22/23 minimum. In fact, as an absolute quantity, ignoring the cyclicity it increases on average right up to 2005, just around the time cooling becomes evident.
No, it does not. The average B for cycles 17-18-19 is 6.892 nT, and for 20-21-22-23 it is 6.518. There is no upward trend. The central fact is still that HMF and TSI right now are back to 1901-1902 values. Cycle 23 was very much like cycle 13, and cycle 24 looks [so far] to be much like cycle 14. If solar activity and TSI is the main driver of our climate we would expect 1890-1910 temperatures to be similar to 2000-2020 temps. I don’t think this is [or will be] the case. You could argue that all the heat [or cold] is hidden somewhere and will materialize shortly, but the same argument could then be made for cycle 13/14 as SC10-11 were on par with SC21-22 http://www.leif.org/research/Heliospheric-Magnetic-Field-Since-1835.png
tallbloke (02:26:07) :
“their (Scafetta and West’s) logical conclusion would be that the climate secular feedback to TSI change is extremely much [in the limit infinitely] stronger.”
I think this argument is known in the trade as a ‘reductio ad absurdum’.
The question here is where the absurdity lies.
I would recommend you read James Lovelock’s original Gaia hypothesis
I’m no fan of Mother Earth hypothesis. There is nothing that says that Nature ‘strives’ to achieve ‘equitable’ balance. Rather it has to live with the hand it is dealt, and it apparently does that by NOT being sensitive to small external changes.
Jeff Id (05:48:46) :
I assume there are multiple datasets with good quality match to each other?
Yes, many stations, and all show the same.
Now I’m left wondering how the corrections to sunspot numbers were calculated. Are the corrections simply the magnetic data through Wolf’s equation?
Almost, except done with modern data. This http://www.leif.org/research/CAWSES%20-%20Sunspots.pdf describes the process.
I wonder if you would mind emailing the data and calcs for the corrections to me. It seems like an interesting thing to do a post on.
I would gladly do so, except that it is not in a polished form [yet – the usual excuse] to let you wander over it without a guide nearby, But I’ll send you something, then you can give it a look.
Also, I see that in your discussion with Dr. Scafetta he claims a contradiction with recent sat data due to a shift in the minimum, I assume from your certainty there are ground based variogram equivalent measures which also demonstrate this slight shift in minimum values. It seems to me that, that would conclude any disagreement between you.
Yes there is a similar change as is clear from the Figures. The important issue though is not that particular problem but the whole 170-year record.
cba (06:35:56) :
That leaves the magnetic field and its effects to vary which are rather minuscule relative to total power for the Sun.
Very careful measurements by Bill Livingston over the past 30+ years of the temperature of the Sun in non-magnetic regions show no detectable variation. This from an earlier posting:
Some spectral lines are VERY sensitive to even minute changes in temperature. Livingston et al. have very carefully measured the line depth of such temperature-sensitive lines over more than 30 years spanning three solar cycles [Sun-as-a-Star Spectrum Variations 1974-2006, W. Livingston, L. Wallace, O. R. White, M. S. Giampapa, The Astrophysical Journal, Volume 657, Issue 2, pp. 1137-1149, 2007, DOI; 10.1086/511127]. They report [and I apologize for the somewhat technical turn my argument is taking, but if you really want to know, there is no avoiding this], ‘that both Ca II K and C I 5380A intensities are constant, indicating that the basal quiet atmosphere is unaffected by cycle magnetism within our observational error. A lower limit to the Ca II K central intensity atmosphere is 0.040. This possibly represents conditions as they were during the Maunder Minimum [their words, remember]. Within our capability to measure it using the C I 5380A line the global (Full Disk) and basal (Center Disk) photospheric temperature is constant over the activity cycles 21, 22, and 23′”.
I have known Bill Livingston [and White] for over 35 years and he is a very careful and competent observer using the best and biggest solar telescopes in existence.