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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hareynolds (10:47:44) :
Rhetorical questions, as I wouldn’t believe anyone’s answers anyway.
Then nobody would bother answer, so you can stay happy in your ignorance…
year SORCE PMOD diff
2003 1361.39 1365.83 4.44
correction to 2003.
Here is the complete SORCE and PMOD records:
http://www.leif.org/research/SORCE-PMOD.png
They now agree well [apart from a constant difference of 4.44 W/m2, which I have added to SORCE], and except from erratic behavior of PMOD since September 2008.
I am the editor of a journal that overcomes to certain extent the peer review problem by publishing the full review and back and forth comments and corrections. Maybe they should do the same (maintaining anonymity of course}
FT (11:52:34) :
I am the editor of a journal that overcomes to certain extent the peer review problem by publishing the full review and back and forth comments and corrections. Maybe they should do the same (maintaining anonymity of course}
Which Journal?
This is the way forward, with one small modification: if the reviewer so desires, his name should be on the review. That way, the reviewer could get credit for the [sometimes large amount of] work that went into the review. Also, the readers could be warned that the reviewer did not want to be known [which carries information too].
Leif Svalgaard (11:30:52) :
year SORCE PMOD diff
2003 1361.39 1365.83 4.44
Fair cop, I was eyeballing this graph, which seems to have a generally higher level. I guess the year average got pulled down by the anomalous downspike.
http://lasp.colorado.edu/sorce/total_solar_irradiance_plots/images/tim_level3_tsi_24hour_640x480.png
Doesn’t change the woodfortrees graph though. I hope Paul Clark will put us straight on where he is getting the data from, and how it’s been spliced, because “PMOD” is currently at around 0.25W/m^2 less than the last two minima. Which is a lot.
http://www.woodfortrees.org/plot/pmod
To me, it seems likely that Scafetta’s contention that the ACRIM gap was incorrectly bridged by PMOD is correct. The cycle 22/23 minimum should be higher, thus making the current minimum less anomalous.
We’ll have a better idea when we see where TIM/SORCE bottoms out.
Interesting, but does the science matter any more? Read this and weep.
Carbon captures UK imagination
Paul Kelly, Editor-at-large | August 05, 2009
Article from: The Australian
BRITAIN is a case study in the urgency and agony of climate change politics.
Gordon Brown and David Cameron, the leaders of its main parties, see climate change as the generational imperative, yet there is no guarantee their targets can be met.
At Westminster a revolution in governance is advanced. Leading departments have been allocated a legally binding carbon budget running parallel with financial budgets. Under Foreign Secretary David Miliband, British soft power and its foreign policy are being recast with a diplomatic strategy to market Britain across the world as a climate change leader. Prime Minister Brown argues the essence of being a successful society depends on de-carbonising the economy. The revolution is bipartisan: the Tories, heading for victory in next year’s election, attack Labour for not doing enough more effectively and march behind their banner, “Vote blue, go green”.
Rarely in the history of democracies has a new idea been embraced so passionately without any certainty its goals can be realised or what the consequences involve. With Britain legally pledged to cut emissions from 1990 levels by 80 per cent by 2050, one-third by 2020 and 22 per cent by 2012, such policies can be achieved only with a new political culture and immediate action.
British ministers work to promote this whole-of-government revolution. In Whitehall, many of the civil service advisers are young, enthusiasts and women. Behind the parties are tacticians who argue that climate change credentials are critical to carry the under-40 voters.
There are three big political messages from a week of briefings inside the British system. First, catastrophic Al Gore-type negative warnings, although still essential, must surrender to another narrative: that climate change is about positives and clean energy is an opportunity for new jobs and investment. For Britain, this polemic is essential to prevent the global financial crisis from ruining the momentum on climate change.
Energy and Climate Change Minister Ed Miliband — the Foreign Secretary’s brother — recently said: “We think that the environmental industries in Britain can generate about an extra 400,000 jobs by 2015. What’s happened in the past is that we have been good at generating some of the low-carbon energy but not so good at getting industry to locate here. People want to hear what is the post-recession economy going to look like and where are the jobs going to come from. We know the world is switching to low carbon and Britain needs to be at the forefront of that.”
The British road map is laid out in last month’s Low Carbon Transition Plan. By 2020, renewable electricity will rise to 30 per cent, with wind power pivotal to this target; nuclear is seen as vital, with government looking to new nuclear power stations; and the assumption is that Britain stays a fossil fuel nation. Britain’s plans assume no alternative to fossil fuels in coming decades and this drives a huge campaign to make carbon capture and storage viable in technological and commercial terms. For Britain, its entire strategy hinges on bringing CCS to fruition.
Second, the road map is plagued by doubt, uncertainty and technologies not yet commercially applied. Pricing carbon via relying on the European emissions trading system is not sufficient. British policy says that the ETS alone “will not be enough to enable the rapid development and use of low-carbon technologies”. This opens the door to far-reaching winner-picking, government interventions, subsidies and renewable energy targets. The policy calls for financial support for renewables worth pound stg. 30 billion between now and 2020. There is a huge drive within the Whitehall bureaucracy to identify and support such projects.
As the policy concedes, such targets are “very challenging”. They mean a “more active and strategic role for government” by encouraging businesses to invest and “mobilising individuals and communities across the country”. Britain is completely unapologetic in its constant argument that “market forces on their own” cannot do the job. The carbon price won’t be high enough to force the new investment needed.
But it will be a hit-and-miss affair. A Danish company has just closed its wind turbine manufacturing operation on the Isle of Wight. In response, Ed Miliband admitted there were planning problems and that “people have significant concerns about wind turbines being put up in different areas”.
Meanwhile, ScottishPower at its Longannet power station on the Firth of Forth is testing a small prototype unit that captures carbon for the first time in any British coal-fired station, the aim being full application by 2014.
The problem is not technology but cost. So, huge government financial support for CCS is unavoidable. The British intent is to kick-start a new CCS industry. Frankly, it has no choice, as Britain’s emission targets cannot be reached without CCS as onesolution.
There remains, however, a reluctance to confront the economic downside of this overall structural transformation of Britain’s economy. How many jobs will be lost? Who will bear the higher energy costs? When these questions were pressed in Whitehall, there was always one resort: the Stern bible. Indeed, it is tempting to think the embrace of Nicholas Stern’s report is the greatest intellectual movement in Whitehall since the embrace of John Maynard Keynes last century. Stern is the constant reference point: the message is that a low-cost, high-carbon option does not exist and Stern has shown “that the costs of action will be far less than the costs of inaction”. It would be nice to think the politics will end here, but that would be a false conclusion.
Third, Brown in his recent “Road map to Copenhagen” speech spelled out one essential condition for a global compact: a decision by the rich nations to help finance emission reductions by the developing nations. Brown proposed a $US100bn ($119bn) global fund (bribe is more accurate) in an effort to bring the big emitters from the developing world into the tent. Sounds good, you think?
Just consider the politics. The big developing emitter is China, a net creditor power with the largest foreign currency reserves in world history. It invests these reserves in the US, funding America’s current account deficit. The idea of the rich nations (led by the big debtor power the US) generously financing China’s emission cuts despite China’s huge surplus will sound to the man in the street like an act of madness.
In Whitehall, private views about Copenhagen recall those of Kevin Rudd: it is difficult to discern how a meaningful, comprehensive agreement can be reached. A visitor leaves Whitehall seeing no need to change his perception that China’s national interest means that it will not meet the size and type of emission action demanded by the developed nations. As for India, forget it.
There is, however, no gainsaying that a revolution has occurred in Britain with climate change policy entrenched in its laws, civil administration, political culture and foreign policy.
The consensus is even collapsing in Germany
http://www.climatedepot.com/
peer review:
would have Joseph Louis Gay-Lussac’s
ideal gas law survived peer review at his time?
would have Catalan’s conjecture made it through peer review?
would have Pierre de Fermat’s conjecture made it through peer review?
was Alfred Wegener’s theory of plate tectonics accepted by peers?
was Einstein’s general relativity accepted by his peers?
was Galileo Galilei view accepted?
was Giordano Bruno’s view accepted? It was burned, together with him.
Peer review is to create consent.
The soul of science is neverending doubt and – very often – plain dissent.
I haven’t read the entire thread so please forgive if this question has already been answered.
Nicola Scafetta is most likely an XY. (Nicola Tesla is another dude with the same first name)
AlanG (12:22:09) : So…”GREEN-GO” to nowhere?. After all, all will rest in peace under a mile of ice. But, what if well informed politicians have conveniently bought houses in the bahamas?
tallbloke (12:15:54) :
Fair cop, I was eyeballing this graph, which seems to have a generally higher level. I guess the year average got pulled down by the anomalous downspike.
Yes, but only by 1/10 W/m2, but it is always questionable to omit what doesn’t ‘fit’
To me, it seems likely that Scafetta’s contention that the ACRIM gap was incorrectly bridged by PMOD is correct. The cycle 22/23 minimum should be higher, thus making the current minimum less anomalous.
This would make the difference between 22/23 and 23/24 even larger, so I don’t understand that statement. Solar activity during 21/22 minimum and 22/23 minimum were close, it is the 23/24 that is the odd man. One would expect 21/22 to be high too, then.
We’ll have a better idea when we see where TIM/SORCE bottoms out.
It has already.
“they applied the MODWT decomposition in a cyclical periodic mode”
LMAO when I read this
“it is not appropriate to impose a cyclical periodic mode to a non stationary time series […] This severe error […]”
True – & TRUE.
tallbloke (12:15:54) :
We’ll have a better idea when we see where TIM/SORCE bottoms out.
There is some evidence that the solar magnetic flux is related to TSI. Scafetta even subscribes to that [indirectly by using data by Krivova and Solanki]. Here are the directly measured HMF for the past five minima:
year IMF B magnitude nT
1965.5 5.06
1976.5 5.45
1986.5 5.74
1996.5 5.11
2009.3 4.12
It is possible to deduce IMF [or heliospheric magnetic field at Earth] since about 1835. Here is a plot back to 1900: http://www.leif.org/research/Heliospheric-Magnetic-Field-Since-1900.png
It shows that HMF now is just what it was 1901-1902, so on that note TSI now should be what it was back then, and temps too [if one believes that temp has anything to do with TSI]. The green curve is B derived by our ‘competitors’ [Lockwood et al.] who have finally come around to do it [almost – they still got cycle 14 slightly wrong] right. Also shows that if anything 21/22 should be higher than 22/23.
That TSI should be related to the solar magnetic field makes good sense physically as it is the magnetic features that are responsible for the faculae and spots. the 0.25 W/m2 lower TSI [if you believe we have that so well in hand – I don’t, but we don’t know, really] is not inconsistent with the HMF the past 30 years.
Of interest is that the HMF graph [and by extension the TSI graph] show very little correspondance with any of the temperature graphs out there. This seems to be true even if you hide some heat in the oceans for a decade. If you want to store it for longer [say 100 years] then we can’t say much either way.
Paul Vaughan (13:27:07) :
“they applied the MODWT decomposition in a cyclical periodic mode”
This doesn’t matter if the data is faulty to begin with [which it is]. So discussing what is wrongly done to garbage is just silly.
“an ideology that should be defended at all costs”
I began suspecting it had escalated to the extremist level of “at all costs” a few years ago. Recent events have convinced me beyond doubt that this is what is happening.
My perspective is that of an ecologist with grave concerns about what this is doing to the reputation of both science & the environmental movement.
My understanding of “Peer Review” was that your paper was reviewed by selected “peers” looking for inconsistencies, errors in calculation and unsupported departures from orthodoxy on the given subject. I have never understood it to mean that this meant the paper to be unassailable, only that it should be free of error. It would also be usual in my circles for the names of the Peer Reviewers to be published together with a precis of their critique.
Good for Dr Scafetta in his robust rebuttal, this entire debate is now about keeping the politicans onside for the “Global Warming is all Human” debate so the research funbding keeps flowing in their direction. As Alan G points out in a foregoing comment, Whitehall and the UK politicians are now committed to CO2 reductions that are not only unattainable, but pretty pointless considering that the UK’s CO2 output is a drop in the ocean compared top India or China, neither of whom seem worried.
Leif Svalgaard (13:05:07) :
tallbloke (12:15:54) :
To me, it seems likely that Scafetta’s contention that the ACRIM gap was incorrectly bridged by PMOD is correct. The cycle 22/23 minimum should be higher, thus making the current minimum less anomalous.
This would make the difference between 22/23 and 23/24 even larger, so I don’t understand that statement. Solar activity during 21/22 minimum and 22/23 minimum were close, it is the 23/24 that is the odd man. One would expect 21/22 to be high too, then.
I think the difference would remain the same, but 23/24 would still drop below 22/23 and slightly below 21/22 rather than massively below both of them.
But it doesn’t much matter. Those sufficiently interested can download the data and splice away to whatever fit they think is right, within the uncertainties pointed up by the properly open debate engendered by you, Nicola and others.
AlanG (12:22:09) :
At Westminster a revolution in governance is advanced. Leading departments have been allocated a legally binding carbon budget running parallel with financial budgets.
To which I can only respond with a derisory “yeah, right!” Every year at budget time the government has proudly announced financial targets for the economy. Every year, Mr “No More Boom and Bust” Brown has heavily amended those targets (sometimes several times over) when they are missed. So why does anyone think it will be different this time? What good is making a “carbon budget” legally binding? What are the sanctions when it’s missed? Who are they going to sue?
Let’s face it, the British economy is effectively bankrupt so there is no money to spend on any of these insane schemes. In 2 or 3 years time we will be spending as much on debt interest as we do on Defence, Justice and Security COMBINED.
Some people play Fantasy Football. Over here we seem to be playing Fantasy Government.
AlanG invited us to read and weep. Me, I read and roared with laughter.
Leif:
Is the raw data available for this plot? Heliospheric-Magnetic-Field-Since-1900.png
Bob Tisdale, Thanks for the emphasis on Trenberth & Stepaniak on your blog. Science appears to be about one millimeter from a major breakthrough on ENSO. Once this happens, the solar-terrestrial controversy will be left an inch from resolution. The only thing blocking progress is conventional interference.
“There is, however, no gainsaying that a revolution has occurred in Britain with climate change policy entrenched in its laws, civil administration, political culture and foreign policy.”
Yes, this is exactly the point. The whole movement is a top down movement, not bottom up as some people eg David Cameron seem to think. It makes me laugh (in a tragi-comedy sense) that you can see a poster in your local library proclaiming enthusiastically that “everyone’s talking about climate change and what they can do to help” followed by a list of planet saving actions like not leaving your tv on standby. Well I’ve got news for these people that inhabit planet zod – nobody, but nobody is talking about climate change in my circles. And whenever I mention global warming to people they seem to think it’s a load of rubbish.
However, that said, the future looks bleak indeed. One only hopes that there are still enough old school conservatives in Camerons party who will put the brakes on some of the more outrageous initiatives. But I’m not holding my breath.
Jeff Id (07:43:09) “I’m glad you picked this one up Anthony. Just so people understand, this is a very simplistic error […] The level of embarrassment on this will not be typical”
Agreed …and of course we see the usual parade of strawman counter-points being dished out liberally upthread to nurse the injured faithful (…eat up! I hear the mushrooms are hallucinogenic)
Leif Svalgaard (13:48:16) :
Paul Vaughan (13:27:07) :
“they applied the MODWT decomposition in a cyclical periodic mode”
This doesn’t matter if the data is faulty to begin with [which it is]. So discussing what is wrongly done to garbage is just silly.
Actually, it makes Benestad and Schmidt doubly wrong. Which is itself informative.