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.
Leif Svalgaard (09:29:56)
I’m not clear as to what your problem here is.
No problem there, I am familiar with the aspects of the annual change of the Earth’s helio-latitude angle. I just wandered what happen to the quote, if it wasn’t for WUWT, I was fearing that Dr. Alzheimer is about to pay a visit.
Vuk, any comments on that?
I blame my daughter’s homework for all this. At first sight looked like a modulated signal with a diode, but since there were no gaps, I decided has to be a generator with a bridge rectifier and a variable load (without the smoothing capacitor). To find what is going on the generator’s side it is necessary to look at waveform before the bridge, which has a period twice the ‘apparent’ one, and as I discovered later this was the Hale cycle. Actually, I’ve never bothered to consider half periods. This explains my phase change comments, for a half cycle as 90 and not 180 degrees. It is becoming apparent to me, that this is of no help to you.
vukcevic (12:03:14) :
I just wondered what happen to the quote, if it wasn’t for WUWT, I was fearing that Dr. Alzheimer is about to pay a visit.
The effect is due to the combined causes: 1) bunching up, and 2) tipping by 7d. Take anyone away and there is no annual modulation.
Leif,
so 2009-2050 will be exactly like 1700-1741
Only if all the waves have a whole number of cycles in 308 years.
Which waves did you use?
lgl (13:55:22) :
so 2009-2050 will be exactly like 1700-1741
Only if all the waves have a whole number of cycles in 308 years.
Which waves did you use?
FFT guaranties that they will be. But here are the numbers anyway, for peaks of decending amplitudes:
308/period 28.00 31.00 3.00 26.00 6.00 38.00 35.00
period 11 9.935 102.667 11.846 51.333 8.1052 8.800
phase (rad) 2.913 -0.464 -2.681 2.884 -2.2435 -1.914 -0.587
amplitude 65.52 47.76 33.84 32.88 25.92 18.24 15.60
[the amplitudes have been multiplied by 2.4 to compensate for the removal of negative values and the subtraction of 30]
lgl (13:55:22) :
so 2009-2050 will be exactly like 1700-1741
Only if all the waves have a whole number of cycles in 308 years.
FFT guaranties that they will be.
Had we had this discussion 6 years ago, I would only have had 302 years of data and the periods would have been:
10.07 yr 30 cycles in 302 years
11.18 yr 27 cycles
12.08 yr 25 cycles, and it would still have been a perfect repetition.
So the very close [to Jupiter’s period: 11.86] 11.85 yr period I got using 308 years is totally spurious, as was expected, of course.
Ain’t numerology wonderful?
Leif Svalgaard (17:31:51) :
“FFT guaranties that they will be.
for 308 years, the periods are so tantalizing [for people with such a bent]:
period 9.94 vs. time between Jupiter and Saturn conjunctions or oppositions: 9.94 yr
period 11.85 vs. Jupiter’s orbital period 11.86
Both periods are used by Vukcevic [multiplied by 2]. However, these periods only come that close for FFT for 1700-2008. Select another interval and the periods are different [as they must make a whole number of turns within the interval].
Leif,
So 308 years is long enough to get it accurate, shorter periods are not 🙂
But still, don’t you agree a new grand minimum now is very likely.
Leif,
It seems you are mostly getting mid centuries (or 60s) too high and end centuries too low, not sure about early centuries. Is there a 60 years component you have not included?
lgl (23:51:25) :
So 308 years is long enough to get it accurate, shorter periods are not
No, because a few years from now [with an even longer interval] the periods won’t fit any more.
But still, don’t you agree a new grand minimum now is very likely.
No, not necessarily:
1) just extrapolating the FFT is not science
2) Even if we get a ‘repeat’ of the Dalton, I don’t consider the Dalton to be a Grand Minimum.
lgl (05:50:38) :
It seems you are mostly getting mid centuries (or 60s) too high and end centuries too low, not sure about early centuries. Is there a 60 years component you have not included?
FFT gave me a 51 yr period:
308/period 28.00 31.00 3.00 26.00 6.00 38.00 35.00
period 11 9.935 102.667 11.846 51.333 8.1052 8.800
There is no other peaks in that neighborhood that is large enough to make a difference. And, don’t forget that all this is just numerology.
“Welcome to the next ice age!
Leif,
When I split into 1700-1907, 1800-2007 (and 1700-2007) I find the 10 and 11 very stable, but your modulation signal is all over, 65, 85, 128. Is there something wrong with my FFT tool? Using yearly avg.
lgl (13:13:26) :
When I split into 1700-1907, 1800-2007 (and 1700-2007) I find the 10 and 11 very stable, but your modulation signal is all over, 65, 85, 128. Is there something wrong with my FFT tool? Using yearly avg.
FFT or power spectra in general can be tricky, because we are trying to fit real data into strict cycles it most of the time doesn’t have. There are two ways of calculating FFT:
1) best fit, where the data is repeated indefinitely on both sides, and
2) zero fill after the data up to a power of two [this is the fastest method and is often preferred – although I prefer the first method].
In both methods the periods you find with most power are the ones that fit exactly a whole number of turns inside the data window. Let me illustrate that by the 1700-1907 data.
1) 10.947 yr, fits exactly 19 times into 208 years
8.32 yr, fits exactly 25 times into 208 years
2) 11.1304 yr, fits exactly 23 times into 256 years [the next higher power of two up from 208]
10.240 yr, fits exactly 25 times into 256 years
8.5333 yr, fits exactly 30 times into 256 years
What is happening is that different cycles have different lengths from 8 to 13 years [or so]. The true power spectrum should therefore have many closely spaced peaks between these two limits. Because the waves that just fit are deemed [by FFT] to be ‘better’ than the ones that don’t make a whole number of turns, those peaks will have more power and stand out, perhaps misleading you into believing that there are only a small number of ‘true’ peaks [e.g. 2 or 3]. The precise periods [and even number] of peaks depend on the data interval taken. Using a different interval, e.g. 1700-1902, will give you a different set of peaks. None of this is physically significant, of course. And all of this is most noticeable for the longer periods that only make a very small number of turns.
Leif,
It’s not misleading. “those peaks will have more power and stand out” because there really are more cycles of lengths close to those peaks.
You have a strong belief in coincidences, I don’t.
lgl (11:47:31) :
It’s not misleading. “those peaks will have more power and stand out” because there really are more cycles of lengths close to those peaks.
You have a strong belief in coincidences, I don’t.
I see a coincidence for what it is when I see it, apparently you don’t. The peaks stand out because the waves make a whole number of turns within the data window [number of years analyzed]. Change the window and you get different peaks. There is, of course, no doubt that there is real power in the band from 8 to13 years, that’s called the Schwabe cycle.
One way of dealing with the problem of window size is to vary the window and compute FFTs for each, then average these together. A result is here http://www.leif.org/research/FFT-Power-Spectrum-SSN-1700-2008.png where I calculated for 308, 307, 306, …, 288 years, deleting one year at a time , alternating from the beginning and the end.
And now for the coincidences:
The triple peak near 11 years has these sub-peaks:
9.935 yr, fits exactly 31 times in 308 years
11.000 yr, fits exactly 28 times in 308 years, and
11.846 yr, fits exactly 26 times in 308 years
There are 2nd harmonics at precisely half these periods, and significant power at 8.324 yr, which fits exactly 37 times in 308 years.
The peak at 102.6667 years fits exactly 3 times in 308 years.
And has a 2nd harmonic at precisely half that [fitting 6 times].
The lesson is that FFT is voodoo if over-interpreted. The SSN series is too short to attach much significance to the minor peaks.
Leif
9.935 yr, fits exactly 31 times in 308 years
11.000 yr, fits exactly 28 times in 308 years, and
11.846 yr, fits exactly 26 times in 308 years
Why not
10.267 yr, fits exactly 30 times in 308 years
11.000 yr, fits exactly 28 times in 308 years, and
12.320 yr, fits exactly 25 times in 308 years
Because 10.267 and 12.320 yr are not ‘preferred’ cycle lengths of course, 9.935 and 11.846 yr are closer to the, for some reason, preferred length the last 300 yrs.
You think it’s a coincidence, I don’t, no voodoo.
Dr. Svalgaard,
I have been searching for N-S excess (asymmetry) SSN data prior to 1995, but without success (re: http://www.vukcevic.co.uk/MaunderN-S-excess.gif ) .
Any ideas?
lgl (08:37:33) :
Because 10.267 and 12.320 yr are not ‘preferred’ cycle lengths of course, 9.935 and 11.846 yr are closer to the, for some reason, preferred length the last 300 yrs.
You think it’s a coincidence, I don’t, no voodoo.
There are two ways of dealing with this:
1) divide the data into two halves and see what periods you get
2) append to the data a little bit more and see what you get.
We do 1) first. Here http://www.leif.org/research/FFT-SSN-two-halves.png is the FFT. The two purple curves are for the two halves. Between freq 0.03 and 0.2 they agree pretty well. Outside the noise takes over. The green curve is the average power spectrum. The main peak is at 11.000 years [fits 14 times]. The side-peaks are at 8.5556 [fits 18 times] and 15.4000 [fits 10 times] years for both halves, so the Sun has forgotten its ‘preferred peaks’.
2) My prediction of the next cycle is Rmax = 75 in 2013. Usign that I can construct SSNs for the years until then. These will be close to the truth if I’m right. If I’m wrong we can try another Rmax [perhaps 40]. We now have 314 years of data in the window. Here http://www.leif.org/research/FFT-SSN-1700-2013.png is the FFT. The main peak is at 10.4667 years [fits 30 times in 314 years]. The two side peaks are at 12.07692 years [fits 26 times] and at 8.486486 years [fits 37 times]. Every single peak to the right of 12 years [up to 31 years] fits a whole number of turns [26, 24, 21, 19, 17, 15, 13, 11]. Similarly with most of the peaks to the left. In general most of the peaks will be at whole turns. In the end, it is the magnitude and the reproducibility of the peak [does it show up in subsets or supersets of the data] that determine if the peak is real.
Now, you are, of course, free to believe as you seem to do that your preferred peaks only show up for a data window of 308 years. Perhaps you’ll find it significant that 308 years is just twice the ‘Jose Period’ of 179 years or some such coincidence.
iillnoopps
vukcevic (12:07:41) :
I have been searching for N-S excess (asymmetry) SSN data prior to 1995, but without success
There is no ‘official’ data sets on this. The best you can do is to take the Greenwich sunspot area data [e.g. at http://solarscience.msfc.nasa.gov/greenwch.shtml ] and calculate a Group sunspot number from that back to 1874 or so. There is sporadic data for the 1860s and the 1790s that can be used too, but it will be a large amount of work.
Leif, I think if you could try to upsample the FFT. While this will not increase information content, it will make it visually easier to find the exact position of the peaks.
BTW: How many points are using? And what kind of window?
To clarify: You could try to upsample the resulting FFT-spectrum.
I think you might know this, yet I say it anyway:
And if you can’t increase the number of FFT-points to get a better resolution at the low frequencies (long period): Downsample the time-signal. (make sure a proper low-pass filter is used!)
Dr. S.
Thanks for the link. They also provide files containing the monthly averages of the daily sunspot areas ( in units of millionths of a hemisphere) for the full sun, the northern hemisphere, and the southern hemisphere. I think as a measure, these values are probably more meaningful than actual SSN.
TonyS (14:54:32) :
BTW: How many points are using? And what kind of window?
one point per year for a total of 308 years. The window is the whole 308 years.
To clarify: You could try to upsample the resulting FFT-spectrum. And if you can’t increase the number of FFT-points to get a better resolution at the low frequencies (long period): Downsample the time-signal. (make sure a proper low-pass filter is used!)
Upsampling [either by interpolation or – btter – by using actual data, since we do have monthly data, i.e. 12 times as much as the yearly data points I was using] does not make much difference as the sunspot number series has a high autocorrelation [a sunspot cycle only contains about 20 independent points], and downsampling can’t really help on periods of a hundred years if the total time span is only three periods. People have played with this for decades with no real success [in the sense of finding stable periods].
Ok, you have 308 points in the time-domain and compute a FFT to get 308 points in the spectral-domain. Now I understand (I think).
You use a rectangular window. Usually you need to apply a different window (Hann, Hamming, etc.) to create different shapes of the created peaks in the FFT. Try using the Hamming or Gauss window, it should create finer peaks (weaker side lobes). Windowing will lose information, of course…
I fear that the shortness and resolution of the signal will be a problem, I am used to much longer signals. So forget my remarks about downsampling. 🙂
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Still, what you should try: Take the 308 point FFT-spectrum and do upsample it:
1. Pad in zeros, for example in a rate 3 to 1 (e.g. take 1 2 3 4, and create 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0)
2. Now you have 1232 points. Filter them with a 1/4f low-pass filter. You may need to append zeros before and after, which you can cut away later.
(Maybe your math-software has some upsampling-package that does these steps)
Now you have 1232 points smoothed. It has the same information content as the 308 points, but you can localize the peaks better. You can of course try other upsampling ratios (1to8 or 1to16)…