Guest post by Paul L. Vaughan, M.Sc.
“Eyeball” methods of measuring solar cycle length (SCL) by looking at successive minima or maxima only take a measurement on average every 11 years. They ignore all of the sunspots occurring during the interim.
In contrast, wavelet methods utilize all sunspots, producing objective estimates of instantaneous solar cycle length at the temporal resolution of the data.
Graph legend notes:
1) measurements based on successive solar:
min = minimum
max = maximum
2) authors:
FCLT = Friis-Christensen, Lassen, & Thejll
http://web.dmi.dk/fsweb/solarterrestrial/sunclimate/SCL.txt
( pv08 = my 2008 “eyeball” adjustments to FCLT )
JA = Jan Alvestad
http://www.solen.info/solar/index.html
3) Wavelet measurements based on all sunspots are denoted SCL[w], where w = Morlet wavenumber. (Large w indicates coarse resolution, while small w indicates fine resolution.)
Here’s a look at the rate of change of solar cycle length (SCL’):
Friis-Christensen, Lassen, & Thejll were completely off my radar when I produced results presented here and here . Comments appearing in the latter thread reminded me of the existence of their work. I had considered their work a few years ago, finding:
1) Their measurement methods were wholly unsatisfying.
2) Leif Svalgaard was steamrolling their claims (and Leif was making substantive points).
Wavelet methods are simple. The Morlet wavelet is nothing more than a sine & cosine wave multiplied by a bell-shaped curve to taper the edges. All a wavelet algorithm does is iteratively calculate correlations (to see what matches the wavelet shape) and perform scaling, coordinate, & units conversions. That’s it.
Most of the confusion which arose in the discussion here was a result of participants not realizing that the spacing of the sine & cosine waves in a wavelet can be adjusted to see at varying resolution (Morlet 2pi being a coarse view).
Important:
Generalizations about SCL do not apply to SCL’.
Just as sine & cosine waves have zero correlation, oscillations of SCL & SCL’ are nearly orthogonal. Consider why data reduction methods like PCA (principal components analysis) have been developed and why differential equations include (rather than omit) terms with neighboring low-order derivatives.
Perhaps Friis-Christensen, Lassen, & Thejll were looking at the right variable, but not thinking about orthogonality & differential equations?
Graph notes:
Raw (not anomaly) ERSSTv3b data are from KNMI Climate Explorer.
[1a] indicates smoothing over the annual cycle.
ERSST = extended reconstructed sea surface temperature
0-90N = northern hemisphere
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Paul Vaughan says:
September 14, 2010 at 3:06 am
Re: John Finn
John, it is possible that there has been some misunderstanding. I suggest that you think very carefully about this. For example, if you want to challenge the notion of orthogonality of SCL & SCL’, here is what you are up against:
Paul
There is no misunderstanding. The orthogonality argument is a red herring. Sine and Cosine are effectively
just ‘out of phase’. The fact there is no mathematical correlation is irrelevant.
I gave you a scenario of 6 solar cycles with SCL= 13,13,13, 10, 10, 10 respectively. You told me that the morlet 2 pi analysis would produce a strtaight line with a short downward spike. I agree. There would be a V-shape just under half along the straight line but the points represented by the 1st and 2nd cycles would be the same as the 5th and 6th cycles , i.e ZERO – implying no change in temperature – apart from the sharp cooling (and rebound).
Do you agree with this?
This runs completely counter to the ‘supposed’ SCL/temperature link. If you asked David Archibald what he expects from the same sequence of cycles (i.e 13,13,13,10,10,10) he would say that the temperatures for the 2nd group of cycles would be ~1.5 deg higher than the first group. The plot would have sort of zig-zag shape.
Paul – It would look nothing like yours. At least, one of you would be wrong – very wrong . I am not trying to challenge the orthogonality of SCL/SCL’ . I am, though, trying to discover whether you or David Archibald (or F-C&L) has come up with anything very meaningful. I’m quite sure that neither of you have managed to explain the surface temerpature trend over the pas century – as your own plot shows.
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
No, Leif, that is not how resolving power, optical quality and seeing work in the real world.
The SSN link with the past is in shambles, because you cannot use abstractions to calibrate correctly.
You use 2 pieces of equipment in tandem, and you compare the empirical data, otherwise you are allowing uncertainty to get the better of things.
You may come close, but you can never be sure.
rbateman says:
September 14, 2010 at 10:44 pm
You use 2 pieces of equipment in tandem, and you compare the empirical data, otherwise you are allowing uncertainty to get the better of things.
You may come close, but you can never be sure.
Perhaps read my comment:
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
which is a comparison of empirical data in tandem. I feared in my comment that since the argument had more than two pieces to it, that I would fail to get the message across, and it seems that my prediction about this was correct, sadly enough 🙁
John Finn wrote: “The orthogonality argument is a red herring.”
It’s most certainly not a red herring. Total ignorance of SCL’ is more fundamental than any common sense afterthoughts arising after attention has been drawn to it. Also, there is a dimension beyond the sine & cosine wave analogy – i.e. SCL’ is not simply phase-shifted SCL.
–
John Finn wrote: “You told me that the morlet 2 pi analysis would produce a strtaight line with a short downward spike.”
I made no mention of wavelets (“morlet 2 pi analysis” in your words). One arrives at a string of zeros with a negative spike in the middle by simply differencing (no wavelet analysis necessary).
–
John Finn wrote: “This runs completely counter to the ‘supposed’ SCL/temperature link.”
None of the ocean regions have SST curves that strongly resemble SCL.
–
John Finn wrote: “[…] It would look nothing like yours.”
Of course! SCL is orthogonal to SCL’.
–
John Finn wrote: “At least, one of you would be wrong – very wrong .”
You are crossing a line if you are putting words in my mouth. I am not making claims of causation & predictive capability. I am raising questions. I have been crystal clear that my current interest is in exploring data, not making forecasts.
If someone decides to make forecasts based on SCL’, they will be wise to not ignore things like the southern oscillation, north-south terrestrial asymmetry, land/sea contrasts, polar vortices, the Southern Ocean, and the Humboldt current. ~11 years isn’t the only temporal resolution and the whole globe isn’t the only spatial resolution. Spatiotemporal heterogeneity is relevant.
–
John, thanks for the spirited exchange. I sincerely appreciate your interest in the topic.
Best Regards.
Paul Vaughan says:
September 16, 2010 at 2:06 am
You are crossing a line if you are putting words in my mouth. I am not making claims of causation & predictive capability. I am raising questions.
Questions without a presumed causation are not worth making…
rbateman says:
September 14, 2010 at 10:44 pm
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
No, Leif, that is not how resolving power, optical quality and seeing work in the real world.
The SSN link with the past is in shambles, because you cannot use abstractions to calibrate correctly.
Well if you are correct all data to 1900/40(?) is invalid. This means the whole article is of no consequence!
Hmmmm!
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
The truth is coming out, the original Wolf 64x telescope does not have the same visibility of the modern telescopes (post 1957). Dr. Svalgaard has been very cunning and hidden the devil in the detail and not properly explained the “weighting factor” he mentions below.
2) Keller was Waldmeier’s assistant [and actually made a lot of the observations of the Waldmeier part of the series] so the weighting and selection of what to count is identical to Waldmeier’s [which I take to be the standard rather than SIDC because of SIDC’s undercount]. Lastly, Keller multiplies his sunspot number by 0.6 to bring it on Wolf’s scale [defined for 1849-1861].
6) If I’m correct that optics is not an issues, then 0.6*Rcatania, Rwolf, and Rkeller should be ‘about’ equal. I say ‘about’, because the three numbers are based on a different number of days [because of occasional cloudy weather, etc] so we would expect some second order variation. Rkeller may for times with very large spots [e.g. beginning of May 1998] be slightly larger because of the weighting of spots by size.
This “weighting” factor is a different way of counting spots invented by Waldmeier. It is a 1-5 range from speck to large spot that the observed speck/spot is multiplied by. According to Dr. Svalgaard and his research Waldmeier created a 22% jump in the sunspot record after 1945 which is attributed to the weighting factor.
This weighting factor is used by Keller. When comparing the Keller values observed on the original Wolf 64x telescope with the current Locarno/Catania values, the 22% weighting factor has to be included to match the modern values.
So there is roughly a 22% seeing difference between the Wolf 64x and Locarno. The SIDC in 1981 continued on with the Locarno observatory as its base reference but does not use the Waldmeier weighting factor.
All of our suspicions have been right all along. Modern technology is a large part of the discrepancy in the sunspot record. The right way to fix it is to remove 22% after 1945 and then come up with a better way of measuring today. The important part is to deal with the speck issue which is not being addressed by Wolfer’s change to the K factor.
This is what we get when we do the comparison:
http://www.leif.org/research/Keller-Catania-Wolf.png
As you can see, within the spread expected from missing data, the three counts are virtually identical, QED.
There are nothing like my knowledge, careful numerical analysis, attention to detail, and understanding of the historical events to better bring this to this definitive conclusion.
A bit over the top Dr. Svalgaard.
Geoff Sharp says:
September 17, 2010 at 9:00 pm
Dr. Svalgaard has been very cunning
This is inappropriate and unworthy of serious consideration.
All of our suspicions have been right all along. Modern technology is a large part of the discrepancy in the sunspot record.
I showed carefully that this is not the case.
Geoff Sharp says:
September 17, 2010 at 9:00 pm
The right way to fix it is to remove 22% after 1945
For practical reasons, one should rather add 22% before 1045, as many operational uses involve the SSNs at their present values. I have done that in slide 13 of http://www.leif.org/research/SIDC-Seminar-14Sept.pdf
Leif Svalgaard says:
September 18, 2010 at 12:24 am
For practical reasons, one should rather add 2o% before 1945…
A simple question for Dr. Svalgaard.
Would the original Wolf 64x telescope record the same sunspot numbers as Lorarno if the Waldmeier “weighting factor” was not applied to the Wolf 64x telescope?
Leif Svalgaard says:
September 18, 2010 at 12:25 am
For practical reasons, one should rather add 2o% before 1945…
It would be more practical to preserve the original record(pre 1945), it has on the whole not been contaminated. But there is a greater challenge, Wolfer changed the system by attempted to equalize back to Wolf by invoking the .6 K factor. This factor was based on the original Wolf 64x telescope and probably was successful during his lifetime . This factor is now irrelevant as the modern telescope will pick up more specks than the Wolf original. The problem also escalates when the speck to spot ratio changes in times of grand minima, very simply the specks need to be eliminated to preserve the record. It would also end the current controversy, the F10.7 values will still wiggle match and will in fact align with the geomagnetic record.
Geoff Sharp says:
September 18, 2010 at 1:45 am
Would the original Wolf 64x telescope record the same sunspot numbers as Lorarno if the Waldmeier “weighting factor” was not applied to the Wolf 64x telescope?
Ill-posed, see below.
Geoff Sharp says:
September 18, 2010 at 2:49 am
It would be more practical to preserve the original record(pre 1945)
You know not where-over you speak. There are many operational programs [military, avionics, etc] that require sunspot numbers with their current calibration, so this CANNOT be changed for practical reasons.
But there is a greater challenge, Wolfer changed the system by attempted to equalize back to Wolf by invoking the .6 K factor.
This was Wolfer’s mistake. He should have multiplied the Wolf numbers by 1.67, like Wolf himself did in 1861 and later in 1874. This is the correct way. But Wolfer was afraid to rock the boat [Wolf didn’t have any qualms].
This factor is now irrelevant as the modern telescope will pick up more specks than the Wolf original.
As I have explained so many times, that is not the problem.
The problem also escalates when the speck to spot ratio changes in times of grand minima, very simply the specks need to be eliminated to preserve the record.
The specks are an important part of the record. Eliminating them would make the disagreement with the F10.7 record even worse.
It would also end the current controversy
There is really no controversy, just you not knowing what you are doing and in addition pushing an agenda.
the F10.7 values will still wiggle match and will in fact align with the geomagnetic record.
As I just pointed out, the F10.7 discrepancy would get worse as it is that too few spots are counted; eliminating the specks would that even fewer and the problem even worse. The geomagnetic record matches the F10.7 perfectly after and 1947, so this will also apply to that record.
Have to run now, but when I come back, I’ll elucidate the history [again] of the sunspot number and how to count it correctly.
Leif Svalgaard says:
September 18, 2010 at 6:01 am
How do you answer that…other than we have a mad scientist in our mist.
The initial question remains unanswered.
oops dropped the d in midst.
But, when you come back perhaps you can explain how the overall record will not align with a 22% cut after 1945. Wolf used the geomagnetic record to verify his reconstruction prior to his record. That is now set in stone according to your opinion.
Waldmeier then decided to change the rules, and introduced a false step that would be completely apparent if we had F10.7 records going back over the same period. This step has to be dealt with.
Geoff Sharp says:
September 18, 2010 at 8:23 am
How do you answer that…other than we have a mad scientist in our mist.
oops dropped the d in midst.
Your ‘mist’ sounds eminently more plausible.
This step has to be dealt with.
It can be dealt with simply by increasing all pre-1945 numbers by 22%.
Here is the whole story:
Before 1861 Wolf used the superb Fraunhofer x64 refractor to set the standard. For several years after 1860 Wolf was engaged in the Geodetic Survey of all Switzerland and was often away. In order not to disrupt the sunspot series by prolonged absences, Wolf took to use a smaller, portable x40 ‘pocket’ telescope which he eventually used exclusively, letting this assistant Wolfer from ~1877 observe with the x64. Wolf was well aware that the x40 did not show all the spots that he would count [plus the many even smaller ones that he wouldn’t count anyway] with the x64, so Wolf increased all x40 counts by 50% [In particular this means that the x40 did not set the ‘threshold’ for what should be counted with the standard x64]. Also in 1861 Wolf summarily doubled all values before ~1800 that he had derived using Staudacher’s drawings because that would bring the count into better agreement with the magnetic needle]. Using the same argument, Wolf in 1874 increased all values before his own observations started in 1849 by 25% based on new magnetic data from Milan since 1835.
Wolfer realized that Wolf’s criterion for what to count was too subjective and proposed to [and did for his own measurements] count everything that could be seen with a given scope. Based on 17 years of simultaneous measurements, Wolfer [after Wolf’s death in 1893] found that multiplying his all-inclusive counts by 0.6 would bring them into agreement [on a statistical basis – not on a day-by-day basis] with Wolf’s values. This was a mistake. Rather than lowing the numbers, they should have been increased by a factor of 1/0.6=1.67, just as Wolf increased the numbers in 1861 and 1874. Had he done that, we might not now have all the discussion about the 0.6, because that factor would have been quietly forgotten, just like nobody today worries [and most don’t even know] about the factors 2.0 and 1.25 that Wolf applied to the early data. But perhaps there was by 1893 a ‘user base’ that might object to such correction.
Wolfer’s successor Brunner carried on Wolfer’s count faithfully using the x64, so no discontinuity was introduced. Waldmeier who took over in 1945 was inexperienced with the x64 and wrongly [as far as I can discover from reading all the thousands of pages of the Astronomische Mitteilungen from Zurich] believed that Wolfer [since 1882] had used a weighting scheme counting the smallest specks once, pores twice, ordinary spots thrice, and larger spots 5 times. The weighting schema that was applied to x64 counts [which was always used for the sunspot number, even as Waldmeier used larger telescopes in his studies of filaments and faculae].
The weighting schema introduces an [artificial] upward jump of some 20% of the sunspot number. It would be best to compensate for that by increasing the earlier numbers by that factor [following Wolf’s procedure of adjusting earlier data] to maintain the current calibration of the sunspot number [which is used by operational programs – military, avionics, satellites, etc].
At the end of 1978 Waldmeier retired and the custody of the sunspot series was transferred to SIDC in Brussels. Waldmeier’s assistant, Hans-Uwe Keller continued observing [to the present] with the original x64 using Waldmeier’s weighting scheme [as far as I know – the sources just say that he ‘continued the series the same way’]. SIDC used various methods [including Keller’s overlapping data] and observations from Locarno to harmonize their calibration with Waldmeier’s. They were partly successful in achieving this, although comparison with F10.7 may indicate a small [5%] change. Later, about 2001, there has been a downward jump of 12-15% in the SIDC calibration, which are now undercounting the spots compared to NOAA and all the other dozen organizations counting spots [including Keller]. The reason for this is under investigation, but there is no doubt that the SIDC count is now too low [even SIDC as per my recent visit, does not dispute that].
Now to your question:
“Would the original Wolf 64x telescope record the same sunspot numbers as Locarno if the Waldmeier “weighting factor” was not applied to the Wolf 64x telescope?”
According to Waldmeier, Locarno shows the same number of spots and pores as the x64. To get from those counts to a Sunspot number, they both have to be treated the same way, weighted and scaled by 0.6. One must assume that Waldmeier did this. But the question doesn’t matter as Locarno was [and in isolation is] not used to derive the SSN.
Leif Svalgaard says:
September 19, 2010 at 2:28 am
More “war & peace”
Man up Dr. Svalgaard, the modern record is greatly influenced by the increased seeing power of superior telescope advancement. Your reluctance to admit the truth says a lot about your scientific credential.
Geoff Sharp says:
September 19, 2010 at 7:20 am
the modern record is greatly influenced by the increased seeing power of superior telescope advancement.
There is no evidence of that. On the contrary, observers strive for using instruments comparable to Wolf’s. Furthermore, the geomagnetic record shows that [apart from Waldmeier’s discontinuity] there is no ‘inflation’ of the modern record. On the contrary, the modern numbers are too low. Both of these statements I have substantiated several times. End of discussion.
Geoff Sharp says:
September 18, 2010 at 1:45 am
Would the original Wolf 64x telescope record the same sunspot numbers as Lorarno if the Waldmeier “weighting factor” was not applied to the Wolf 64x telescope?
BTW, it is obvious from this recent drawing that Locarno applies the Waldmeier weighting:
http://www.specola.ch/drawings/2010/loc-d20100918.JPG
Leif Svalgaard says:
September 19, 2010 at 12:32 pm
Geoff Sharp says:
September 18, 2010 at 1:45 am
Would the original Wolf 64x telescope record the same sunspot numbers as Lorarno if the Waldmeier “weighting factor” was not applied to the Wolf 64x telescope?
BTW, it is obvious from this recent drawing that Locarno applies the Waldmeier weighting:
http://www.specola.ch/drawings/2010/loc-d20100918.JPG
Yes, and you have only just found that out. But you are jumping too quick, I would wait for my report as it seems it’s a partial use of the Waldmeier system. The top and bottom end are being discounted. Here is a sneak preview.
http://www.landscheidt.info/images/Loc-d20100917_detail.png
http://www.landscheidt.info/images/OAC_D_20100917_062000_detail.png
Geoff Sharp says:
September 20, 2010 at 7:11 pm
as it seems it’s a partial use of the Waldmeier system. The top and bottom end are being discounted.
No, it is exactly the same system. Sergio ensures that.
Geoff Sharp says:
September 20, 2010 at 7:11 pm
http://www.landscheidt.info/images/Loc-d20100917_detail.png
As I have pointed out, it takes years of training to count sunspots. Cagnuti is an observer ‘in training’ and his counts should not be taken as representative. “who works on it every day needs years to learn how to understand the images and to count the sunspots” http://www.leif.org/EOS/Sunspot-Counting.pdf
So, eliminate Cagnuti and concentrate on the main observer who has kept the record over the past half-century.
Geoff Sharp says:
September 20, 2010 at 7:11 pm
it seems it’s a partial use of the Waldmeier system. The top and bottom end are being discounted.
Marco Cagnotti is an observer ‘in training’. Don’t use his counts for anything. If you do anyway, you show your colors. As I have told you repeatedly, it takes years to learn how to do this. E.g. from http://www.leif.org/EOS/Sunspot-Counting.pdf “since who works on it every day needs years to learn how to understand the images and to count the sunspots.”
Since Locarno was founded and owned by Zurich it was implicit that they use Waldmeier’s system.
Leif Svalgaard says:
I am not only looking at Marco Cagnotti’s counts, but it does raise the question. He has been counting in a professional manner since about January this year. If you think his methods are not following the standard, is the standard itself in question?
I have emailed Sergio asking him how the the method may have changed since the Waldmeier days as he has stated in his yearly updates.
Geoff Sharp says:
September 21, 2010 at 3:42 am
If you think his methods are not following the standard, is the standard itself in question?
Of course not. It simply means he hasn’t gotten it yet. Remember it takes years to learn. At this point my info from Locarno says that Marco simply draws what he sees and provides a raw count [i.e. not weighted].