Guest post by David Archibald
With respect to the month of minimum, it is very likely that Solar Cycle 24 has started simply because Solar Cycle 23 has run out. Most solar cycles stop producing spots at about nineteen years after solar maximum of the previous cycle. Solar Cycle 23 had its genesis with the magnetic reversal at the Solar Cycle 22 maximum. As the graph above shows, Solar Cycle 23 is now 19 years old. Only 9% of the named solar cycles produced spots after this.
The graph also shows the position of Solar Cycle 24 relative to its month of genesis. Solar Cycle 24 is now the second latest of the 24 named solar cycles. January is 105 months after the Solar Cycle 23 maximum. Only Solar Cycle 5, the first half of the Dalton Minimum, is later. This lateness points to Solar Cycle 24 being very weak.
This graph shows the initial ramp ups of six solar cycles that were preceded by a vey low minimum. The ultimate trajectory of Solar Cycle 24 should be apparent by late 2009. If Solar Cycle 24 is going to be as weak as expected, the monthly sunspot number should remain under 10 by the end of 2009.
What’s the other way? Entrails and incantations? What are “dusins”?
Leif Svalgaard (07:50:12) :
to
vukcevic (04:38:16) :
… The idea of clockwork is alluring. Many scientists have been attracted to it. E.g…. Never mind the details, but you can perhaps recognize the general idea.
But the devil is in the detail, it is the final result that counts.
I barely new sunspots existed when I devised my formula (2003); it was the sight of the SSN diagram in my daughters homework. To be usually immodest: my formula is new, simple and elegant, easy to understand, logical and based on real numbers, and most of all, gives best correlation to sunspot cycle for the last 200 years (in either sense). An amateurs achievement to be proud off, I keep telling myself.
Rudolf Wolf’s work was good effort considering he did not have many cycles to work on, but again he stopped too short, should have ignored minnows and gone for the big cheese. (abbreviating vukcevic to Vuk = Wolf, nice, but to early!).
For the other two quoted works not much to learn there, they are guessing what the numbers should be, my numbers were known long before times of Newton and Copernicus, I only put them together in a way that is new and meaningful.
Bracewell describes what formula might be, did he actually produce one ?
Dicke, R. H: It is a guess work again. Too many parameters, and do we do not what they are? Take the Greek alphabet sup, mix with a bit of trigonometry, and you can simulate anything you desire.
Only worthwhile thing in there is:
It is shown that the great solar anomaly of 1760 – 1800 is most likely real and not due to poor data.
I agree with that; there is a good reason why should be a phase change not only at 1800, but every 250 years. I did not extrapolate my formula back beyond 1600, until 2-3 weeks ago, when I put the link on WUWT within hours (4.Jan 2009, Igl was the first to comment). I believe those who see out 2030-40s will have to do change phase again soon after. After looking closely at WSO data (thanks again, I see they have more recent numbers on their website, I’ll keep updating), I am now convinced I know why should be a phase change, and more importantly, it confirms one of my earlier ‘odd’ assumptions.
http://www.vukcevic.co.uk/GrandMinima.gif
Jeff,
ups! Norwegian words don’t work here. Dusin=Dozen
Nature’s way is usually the easy way out. In this case that the planets create a lot of sine waves and the sum of them is reflected in the sun spot curve.
On the other hand, modulation is a fascinating idea. Wonder if it will be a AM if Jupiter is a component of both the 11 y carrier and a much longer cycle.
Then that would also be an easy way out.
Hop I got it all in inglesch this time 🙂
Heh, no worries, my grandfather was Norwegian. 😉
Still, you’re still doing things the “scientist’s way” by even learning that there are sine waves in the first place. Nature doesn’t display them for all to see, they have to be discovered, scientifically.
lgl (10:28:00) :
the planets create a lot of sine waves and the sum of them is reflected in the sun spot curve.
Is this consistent with ~snip~’s ideas? If so, how?
Leif Svalgaard (10:50:16) :
lgl (10:28:00) :
the planets create a lot of sine waves and the sum of them is reflected in the sun spot curve.
Is this consistent with ~snip~’s ideas? If so, how?
I guess our moderator didn’t like how nobwainer referred to himself 🙂 but you should get the idea anyway.
Dr. Svalgaard
I’ve tried to read Dicke’s article again, most of his maths is beyond me to properly understand, let alone assimilate. I do not intend to discuss his formula, but reading his chapter “The Great Solar Anomaly” once more, to make sure I did understand what he is talking about. I am not sure if his convection model is in a conflict with currently favoured ‘conveyor belt’, but I am certain that phase change took place, perhaps gradually over period of 2-3 cycles (SC4 being main culprit), rather than what I did introducing an ‘abrupt’ change for calculating expediency.
As I said in my previous post, the phase change for 1810 I introduced in the original article (2003). Dicke’s article (putting aside my other assumptions) directly justifies phase change for this period, rather than “The connection with the planets now seems gone for the expediency of fitting NASA better” as you put it.
For back extrapolation I was prompted by Robert Bateman’s post I think was on the same or previous day, I thought it looked good, then I searched for NASA’s data, they concurred.
As you can see again, my cyclogram of Grand Minima is not, again as in the case of the original formula, the result of some in depth knowledge of the solar processes. The formula just works.
Further support
for justifiable phase change at 1800
Lost sunspot cycle in the beginning of Dalton minimum: New evidence
and consequences
I. G. Usoskin,1 K. Mursula,2 and G. A. Kovaltsov3
GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 24, 2183, doi:10.1029/2002GL015640, 2002
Authors even suggest new numbering (quick access)
http://www.geocities.com/vukcevicu/usoskin.doc
SC3’ min1784.3- max1788.4
SC4’ min1793.1 – max1795
Or for the article
http://spaceweb.oulu.fi/~kalevi/publications/Usoskinetal2002_GRL.pdf
The phase change has its justification in the actual anomalies of sunspot activities during the period in question. The assessment that it was introduced for ‘ the expediency of fitting NASA better” doesn’t stand, since it was in original article published in 2004.
http://xxx.lanl.gov/ftp/astro-ph/papers/0401/0401107.pdf
long before any of my recent charts were constructed.
vukcevic (14:53:17) :
Further support for justifiable phase change at 1800
Lost sunspot cycle in the beginning of Dalton minimum: New evidence and consequences
I. G. Usoskin,1 K. Mursula,2 and G. A. Kovaltsov3
GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 24, 2183, doi:10.1029/2002GL015640, 2002
This is an old paper, long discredited. Three strong arguments against it:
1) cosmic rays do not show it
2) daily variation of declination does not show it.
3) digitization of Staudacher’s observations does not show it.
I have earlier [several times] given links and references.
As you said:
Dicke, R. H: It is a guess work again
Your main problem is that ‘phase change’ introduces two short, small cycles to replace one long, small cycle. BTW, plot for us the two curves [one with the phase shift and one without] for 1750-1850. When I do it, I get a maximum in 1810, the year when no spots at all were observed. I could have gotten your formulae wrong [after the various corrections].
vukcevic (14:53:17) :
FThe assessment that it was introduced for ‘ the expediency of fitting NASA better” doesn’t stand, since it was in original article published in 2004.
http://xxx.lanl.gov/ftp/astro-ph/papers/0401/0401107.pdf
long before any of my recent charts were constructed.
Don’t kid yourself, NASA did not make those numbers just now, Wolf did in the 19th century. The link doesn’t seem to work for me.
1800 sunspot cycle phase change
It appears to me that there is a lot of misunderstanding here, either accidental or deliberate, but I am not surrendering.
Your comment
Don’t kid yourself, NASA did not make those numbers just now, Wolf did in the 19th century.
does not make any sense to me, in the context of what I wrote.
I am not questioning either NASA’s data or Wolf’s discoveries. I was not particularly aware of either when I devised the equation, to me only matters that they confirm my results regardless of chronology.
There are three authoritive articles on the phase amplitude anomaly around 1800.
The phase variations of the solar cycle
Dicke, R. H., Princeton University
Solar Physics (ISSN 0038-0938), vol. 115, no. 1, 1988, p. 171-181
http://articles.adsabs.harvard.edu/full/1988SoPh..115..171D
Period and phase of the 88-year solar cycle and the maunder minimum: evidence for a chaotic sun
J. Feynman and S. B. Gabriel 1989
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, U.S.A.
http://www.springerlink.com/content/x176761610l512x3/fulltext.pdf
Lost sunspot cycle in the beginning of Dalton minimum: New evidence and consequences
I. G. Usoskin,1 K. Mursula,2 and G. A. Kovaltsov3
Geophysical research letters, vol. 29, no. 24, 2183, doi:10.1029/2002GL015640, 2002
http://spaceweb.oulu.fi/~kalevi/publications/Usoskinetal2002_GRL.pdf
Two waveforms of the equation (with the phase change around 1800), both show coincidental minimum at 1800, so you could have plotted equations wrongly.
For time being I shall concentrate on 1800s, if it is accepted that there is a phase anomaly there, than the extrapolations can be considered.
For detailed assessment of plotting of equations and the phase change, see following link:
http://www.geocities.com/vukcevicu/1800phase.pdf
The link doesn’t seem to work for me.
Try one of these:
http://xxx.lanl.gov/ftp/astro-ph/papers/0401/0401107.pdf
http://arxiv.org/ftp/astro-ph/papers/0401/0401107.pdf
http://xxx.uni-augsburg.de/ftp/astro-ph/papers/0401/0401107.pdf
vukcevic (03:39:54) :
I am not surrendering.
Keep it up Vukcevic….I was wondering, how would your equation stack up over longer periods? We should be able to compare it with the 11000 yr C14 graph.
Additional note for Dr. Svalgaard
For extrapolation from 1000 to 2100 actually there is no need to make phase change (every 250 yrs) , when I think about it only moves wayform sideways for half a cycle, which for the time scale considered is nearly irrelevant.
Just plot:
=100*ABS(COS(2*PI()*(A1-1941)/19.859)+COS(2*PI()/3+2*PI()*(A1-1941)/23.724))
vukcevic (03:39:54) :
There are three authoritive articles on the phase amplitude anomaly around 1800.
Appeal to authority [BTW, I’m also a ‘prominent solar physicist’ 🙂 http://www.stelab.nagoya-u.ac.jp/ste-www1/pub/ste-nl/Newsletter40clr.pdf , page 4] does not change the fact that there was no lost cycle at that time as I have pointed out several times.
Apart from the indirect evidence [ http://www.leif.org/research/Gilpin.png ] the sunspot record also shows no lost cycle:
Digitization of Sunspot Drawings by Staudacher in 1749 – 1796,
Solar Physics, Volume 247, Number 2 / February, 2008
DOI 10.1007/s11207-007-9113-4, Pages 399-410
Abstract Original drawings by J.C. Staudacher made in the period of 1749 – 1796 were digitized. The drawings provide information about the size of the sunspots and are therefore useful for analyses sensitive to sunspot area rather than Wolf numbers. The total sunspot area as a function of time is shown for the observing period. The sunspot areas measured do not support the proposition of a weak, “lost” cycle between cycles 4 and 5. We also evaluate the usefulness of the drawings for the determination of sunspot positions for future studies.
—-
Two waveforms of the equation (with the phase change around 1800), both show coincidental minimum at 1800, so you could have plotted equations wrongly.
No error. You changed the phase change from 1810 to 1800, which changed the calculated maximum from 1810 to 1809. But, it should be obvious from your own Figure [ http://www.geocities.com/vukcevicu/1800phase.pdf ] that you have no fit at all to the actual sunspot data between 1790 and 1813 [apart from the misfit in size of the maxima from 1750 to 1800]. At least, your earlier curve with the 1810-shift got the phase [and size] of cycle 5 correct. I think you should drop back to your original 1810 change and not trying to shoehorn your cycles to fit the [old, discredited, and speculative {Dicke is just guessing… as you said before you discovered that there was ‘support’ in his paper}] papers you dug up.
It is not a question of surrendering, it is simply about getting the science right.
Feynman argues for a strong 88-year modulation of the cycle [her paper was written prior to the strong cycle 22, which effectively demolished the 88-year cycle, already suffering from a strong cycle 21]. This is at variance with your very clear ~120-year modulation. You can’t have it both ways. BTW, two 88-year cycles is 176 years [as she also points out]. She argues that there was a phase change of 35 years of the 88-year cycle upon emerging from the Maunder minimum. Nothing at all like what you are wishing for. You cannot just take every paper you find with the words ‘phase change’ in them as support for your ideas.
vukcevic (03:39:54) :
“that there was no lost cycle at that time as I have pointed out several times.
Arlt [who digitized the Staudacher drawings] has a very nice discussion here:
http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.2233v1.pdf
In particular, the butterfly diagram on page 10 is very telling. This is good stuff. No sign of a cycle 4′ with a maximum in 1795. One persistent problem is the difficulty of getting people to stop quoting old obsolete papers [the internet and Google is partly to blame :-)] and to ignore later data that shows otherwise. A typical example [apart from you] is the climate modelers use of the obsolete Hoyt-Schatten TSI reconstruction [because it fits their ideas better – thus in their view ‘validating’ the data].
Leif Svalgaard (08:55:28) :
I think you should drop back to your original 1810 change and not trying to shoehorn your cycles to fit the old, discredited, and speculative….
Small phase difference between this and previous chart is factor 2pi/3 (old chart) or 2pi/4 (pi/2) which produces better fit (recently suggested anonymously to me from a US scientific establishment). I used old factor since it is in my original article (2004).
I do not know who is discredited and who is not, I just look at their credentials. If J. Feynman suggests there is a phase change in the 84 year cycle, which she on number of occasions states, is derived from 11 and 22 year cycle, so it would be physically impossible for 88 to change phase and 22 or 11 do not.
Ok, lets put that one aside for time being.
What about the
http://www.vukcevic.co.uk/GrandMinima.gif
where this argument started.
For extrapolation from 1000 to 2100 actually there is no need to make phase change (every 250 yrs) , when I think about it, only moves waveform sideways for half a cycle, which for the time scale considered is nearly irrelevant.
Just plot:
=100*ABS(COS(2*PI()*(A1-1941)/19.859)+COS(2*PI()/3+2*PI()*(A1-1941)/23.724))
for 1000-2050 (no phase changes). I hope you will process it through your system, I would be interested to see what you come up with.
I can assure you, I may be ignorant of many things, may make mistake in assessment or calculation, my knowledge is very limited (slow learner), etc. that all I am happy to accept, but I do not shoehorn, mislead or deceive.
vukcevic (10:00:55) :
I do not know who is discredited and who is not, I just look at their credentials.
Look at the data instead.
If J. Feynman suggests there is a phase change in the 88 year cycle, which she on number of occasions states, is derived from 11 and 22 year cycle, so it would be physically impossible for 88 to change phase and 22 or 11 do not.
When you deal with wild ideas, nothing seems to be physically impossible. The phase change she is talking about is 35 years.
What about the http://www.vukcevic.co.uk/GrandMinima.gif
where this argument started.
For extrapolation from 1000 to 2100 actually there is no need to make phase change (every 250 yrs)
Then why do you argue that there should be one?
but I do not shoehorn, mislead or deceive.
self-deception. We all fall into that trap from time to time. that is why peer-review is so important [even with all its flaws] to protect one from oneself.
vukcevic (10:00:55) :
For extrapolation from 1000 to 2100 actually there is no need to make phase change (every 250 yrs) , when I think about it, only moves waveform sideways for half a cycle, which for the time scale considered is nearly irrelevant.
Just plot:
=100*ABS(COS(2*PI()*(A1-1941)/19.859)+COS(2*PI()/3+2*PI()*(A1-1941)/23.724))
for 1000-2050 (no phase changes). I hope you will process it through your system, I would be interested to see what you come up with.
http://www.leif.org/research/Vuk-Curve-vs-Rz-1700-2010.png
shows that the fit is very poor before ~1820 [especially around 1790-1813] so it seems a regression to fall back to the curve without phase shifts. A formal colleration plot:
http://www.leif.org/research/Vuk-Curve-vs-Rz-1700-2010-correl.png
shows no correlation between your curve and the data.
Leif Svalgaard (11:05:14) :
formal colleration plot
spelling was unintentional 🙂
Anthony,
This (the exchange above) is why your site deserves to win the weblog award – there is nowhere else on the web that I could learn so much
Jeff,
Thank you. Leif will call what I’m doing anything but science.
Vukcevic,
Just to repeat myself. The FFT shows a 11 y component, so if you don’t include one either directly or through a function like modulation you will never succeed.
You may dislike it, but a FFT spectrum does not lie (neither does Leif I believe) so it is there.
Leif,
Is this consistent with ~snip~’s ideas? If so, how?
I don’t think so. I think my ideas are plain good’ol gravity, not momentum.
I don’t see any ‘arm’ that can transfer the momentum to the Sun.
I assume the Sun’s acceleration we have discussed earlier is pure gravity.
(11*100)+10+22 is quite interesting. With correct amplitudes you will see variation in cycle length and the weak cycles shorter than the strong cycles, like you pointed out. Then of course you have to add some longer cycles to get it complete.
lgl (13:29:49) :
With correct amplitudes you will see variation in cycle length and the weak cycles shorter than the strong cycles,
Available observational data generally suggest the opposite: weaker longer.
Leif Svalgaard (11:07:43) :
Leif Svalgaard (11:05:14) :
formal colleration plot
spelling was unintentional 🙂
Thanks for the note.
The waveform is meant to track phase (periodicity) not the amplitude (I think I did mention before). If you insists on calculating correlation than, since there is a conflict prior to 1800, it should be done from 1812 giving a reasonable correlation of 0.654628 and for a meaningful scatter plot the nominal amplitude factor of 67, 100 is for non-smoothed monthly number with much higher individual peaks.
That should at least have some value even in your book.
Leif
Sorry I misread you last time. Thank you for arguing for my first proposal, simply adding them all. http://virakkraft.com/10-11-11,8.jpg There is no general rule in this like you said last time. Several of the periods show weaker longer, and there’s not a rule in the observed either. It just depends where on the timeline we are. The exact pattern repeats every 10*11*11.8=1300 years (if not including the longer cycles) and we only have a much shorter record.
vukcevic (14:39:56) :
The waveform is meant to track phase (periodicity) not the amplitude (I think I did mention before).
If so, then it would seem necessary to include the phase shifts so that the phases would track the real sunspot cycle phase.
it should be done from 1812 giving a reasonable correlation of 0.654628
And if you do it from 1964 the correlation jumps to 0.8.
When calculating [and assessing significance of] correlation coefficients one has to be careful taking into account autocorrelation or [the older term] ‘conservation’ to get the correct number of freedoms. A solar cycle only has about 20 degrees of freedom, so correlation with a smooth curve must be done on that number of data points [or to be a bit cautious, on yearly non-smoothed values].
Anyway, it only makes sense to look at a formula that at least reasonably well mimics what is actually observed, so we shall continue with your ‘best’ formula with phase changes in 1160, 1300, 1560, 1810, and 2060 (? it is not clear when to use 240, 250 or 260 years, maybe 1310 is better than 1300, in which case it is always 250 years). One can also play with your constant ‘100’ [which is arbitrary, of course, just chosen to yield numbers in the neighborhood of the sunspot numbers]. I have decided to use 50 instead of a 100 to ‘improve’ the visual impact [all tricks of the trade] in my work with your stuff.
The result is
http://www.leif.org/research/Vuk-Curve-vs-Rz-1700-2010.png
http://www.leif.org/research/Vuk-Curve-vs-Rz-1700-2010-correl.png
We further make the reasonable assumption that at a phase change [e.g. in 1810] the sunspot number is ill-defined so we are allowed to ignore the fact that your mini-cycle peaking in 1810 doesn’t fit and simply can be summarily ignored.
I’ll report on my investigation of this series.