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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tallbloke says:
September 12, 2010 at 1:44 am
The value I came up with after analysing by this method was 42SSN.
http://tallbloke.wordpress.com/2010/07/21/nailing-the-solar-activity-global-temperature-divergence-lie/
Tallbloke, I’m so glad at least one other person has actually performed that too. I’ve posted that description two or three other times since last November seemingly to deaf ears. That is what got me here to Anthony in the first place, no kidding. That value stated was just a starting point which depends on the slope. Mine were always across the full 300 years and it does float depending on the temps your are correlating to, GISS, HadCRUT, etc, but always near 45-50 so I’m glad you got the same. And that makes sense, your using SST and mine were land or global, and the sea temperatures don’t show as much of a climb, lower slope. It sure is possible to be some real factor in physics, that balance point.
Every person I have shown those not-yet-correct graphs to have become a bona fide skeptic on the spot. They don’t seem to care of the tiny differences either. Show them the solar plot I described since 1700 and show them the global temp plot today, a bit on the seemingly small lag, that’s all it takes. Love those normal logical people!
No wonder, it does seem to make perfect sense (but not to climate scientists I have found). You know, I don’t understand why the general non-scientific public could think that the sun has something to do with the temperatures here on Earth, crazy, but for some reason they just do. ☺
@jorge
I think in 12-24 months time you will find the wiggle match to be much improved.
Has anybody thought about measuring/counting coronal holes instead of sunspots over time? Those coronal holes throw a LOT of stuff out. More so than sunspots!
http://en.wikipedia.org/wiki/Coronal_hole
Synchronized chaos…….
Tsonis’ hypothesis is looking better all the time; several processes struggling for superiority, when they are in sync, that is when large climate shifts take place. Which metrics are now in sync? Is a new climate shift forming?
Coronal holes are especially important matrices when there are no sunspots. My hunch is that sunspots are not representative of what the Sun is doing in terms of its impact on Earth. A quiet (IE no sunspots) Sun is not necessarily a “sleeping” Sun.
Pamela Gray says:
September 12, 2010 at 7:37 am
Has anybody thought about measuring/counting coronal holes instead of sunspots over time? Those coronal holes throw a LOT of stuff out. More so than sunspots!
………………………………………………………..
More often than sunspots, higher speed turbulent solar wind from sunspots around solar maximum can also give intense warming spurts, but warming events around maximums are less frequent due to a lack of coronal holes, hence more cold episodes/winters at, and close to solar maximums.
“Joseph Day says:
September 11, 2010 at 6:09 pm
There is a solar connection evident through cosmogenic isotopes. Interestingly, northern and southern hemisphere isotope concentrations in ice cores don’t exactly match. That suggests either a weather factor, or more likely anisotropy of the cosmic rays themselves. Furthermore, the differences in cosmic ray flux between glacial and interglacial are so large, that it seems difficult to believe the sun is the only factor controlling climate.
…”
I agree there is a major problem with 10Be and ice cores.
Fujidome Antarctica shows a De Vries pattern and extends this to a longer period. This has interesting linkages to other data.
The Greenland data I have looked at is distinctly different.
Why that is so seems kind of obvious. The radiation flux is calculated using assumed precipitation data (annual ice thickness), the flux is not an absolute measurement, proxies involved.
Antarctica is weather isolated by the southern circumpolar ocean current and similar atmospheric patterns. Greenland is not and is linked to at least Atlantic weather.
The problem is that weather may well be linked to radiation flux and therefore precipitation is correlated in some unknown way with flux. Calculating flux from two proxies where there is unknown linkages and in places with differing weather linkage might well explain the mystery.
Could it be uneven flux, eg. from differing external magnetic fields? Yes.
A recent exercise I carried out was investigating latitudinal correlation (including against time) with global gridded data. To my surprise the Antarctic circumpolar current shows clearly as a discontinuity.
The correlation between tropics and poles is zero. The whole thing is all over the place and what I was expecting was not there. Satellite data shows a smooth bell curve, eg. Hadcrut is a mess but ought to be identical. (this is no surprise)
Given better data I expect there are interesting things. Is a to-be-revisted matter.
Tim Channon wrote: “Antarctica is weather isolated by the southern circumpolar ocean current and similar atmospheric patterns. […] A recent exercise I carried out was investigating latitudinal correlation (including against time) with global gridded data. To my surprise the Antarctic circumpolar current shows clearly as a discontinuity.”
Bravo. Nice work Tim! …except for the “surprised” part. [ :
Re: Lucy Skywalker
The obvious one is the Southern Oscillation.
(Remember that the analysis presented here has focused on the ~11 year timescale.)
Beyond that: other spatiotemporal heterogeneities — e.g. north/south asymmetry, including nonlinearities related to the contrasting heat capacity of land & sea – and the absence of a spinning maritime hub in the north.
Also, don’t forget about the various annual & diurnal cycles and relationships that flip sign regionally during parts of these cycles …only a seeming paradox to the unwary.
MDR wrote: “[…] would it be possible to also provide a brief explanation of the hypothesis you are testing, as well as an interpretation of the conclusion you arrive at?”
I’m not testing a hypothesis; rather, I’m exploring data. I do not arrive at a conclusion; rather, I raise questions for physicists & climate scientists.
The physicists & statisticians on this job need a few lessons from physical geographers – specifically, the ones with advanced understanding of issues arising in data analysis due to spatiotemporal heterogeneity. (In short: The assumptions underpinning conventional mainstream models, including the ones used to test for statistical significance, are untenable.)
I suggest focus on the job rather than on emotions, territoriality, funding politics, etc. The job is multidisciplinary. No field need feel threatened by a lack of internal expertise.
I appreciate your interest MDR.
Best Regards.
M White says:
September 12, 2010 at 2:04 am
Below is the first published picture on the landscheidt website of the sun using their new Wolf pocket scope.
Several comments:
1) Wolf’s scale was not based on his magnification x40 ‘pocket telescope, but on his magn. x64 large telescope
2) which is still in use and produces sunspot count a bit larger than the official SSN
3) an experienced observer is far superior to a photograph, because the seeing varies rapidly and the observer can [and does] take advantage of brief periods of good seeing
4) and experience itself is a large factor. Experiments show that it takes about a year of daily observations to become experienced, during which time the count about doubles
M White says:
September 12, 2010 at 2:04 am
Locarno has counted 13 with Catania at 12, I am struggling to see how they arrived at the extras.
Because there were one or two tiny ‘pores’ next to the spot. Modern counting methods count everything, so the SSN becomes SSN = 10*G + (1 spot + 2 pores) = 13.
G is the number of groups which is clearly 1 in this case. Wolf did not count pores, so his count would have been 10*1+1 spot = 11.
Re: rbateman
Pi/2 would violate admissibility …(way too technical for this forum…)
—
jorgekafkazar wrote: “Are there known data smoothing end effects […]?”
As indicated in the earlier threads: Yes (at the recent end of the graph).
—
JDN wrote: “Paul: What is your y-axis? […] Also, whose sunspot data are you using.”
On the 1st graph: Solar cycle length in years.
2nd & 3rd graphs: Normalized rate of change of solar cycle length, preserving sign (i.e. normalizing relative to maximum absolute deviation) and normalized SST (normalizing based on range since there is no sign issue).
Sunspot numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
—
Re: wayne
Bear in mind that in the current post I’m focused on phase, not amplitude.
If we switch the focus to amplitude and consider the integral of solar wind, then yes we’ll find interesting patterns shared with SAOT (stratospheric aerosol optical thickness) and Southeast Pacific & Southern Ocean SST, but judging from comments appearing in this thread, this audience is not ready for that (at this point in time). Patience & timing wayne. Sequence matters. Cart-before-the-horse sort of thing…
—
Re: vukcevic
You’re raising some interesting questions there vukcevic.
—
Re: M White
The focus in the current post is on phase, not amplitude.
—
Re: John Finn
In your example you’d have a flat zero-line with a negative spike in the middle. However let me be absolutely clear: At this stage I am not interested in making forecasts. My current interest remains exploratory data analysis.
—
Re: Joe Lalonde
The current post is focused on phase. There are, indeed, other factors on which to focus in other studies — for example, see here for an interesting example:
Donner, R.; & Thiel, M. (2007). Scale-resolved phase coherence analysis of hemispheric sunspot activity: a new look at the north-south asymmetry. Astronomy & Astrophysics 475, L33-L36. doi: 10.1051/0004-6361:20078672.
http://www.aanda.org/index.php?option=article&access=standard&Itemid=129&url=/articles/aa/pdf/2007/45/aa8672-07.pdf
Regarding this [ http://funwithgovernment.blogspot.com/2010/09/solar-cycle-and-climate.html ] overview of the earlier thread [ http://wattsupwiththat.com/2010/09/04/the-north-pacific-solar-cycle-change/ ], a few corrections:
1) I’m not a solar scientist. My background is in landscape ecology, physical geography, biology, statistics, engineering, & forestry.
2) Although I sincerely appreciate his interest, Mr. Oplas has seriously misunderstood my point about the fundamental difference between PDO & North Pacific SST. In particular: PDO matches neither North Pacific SST nor SCL’.
I again encourage people to make an effort to clear up any misunderstandings about what PDO is and what it is not. Bob Tisdale gives help at an accessible level:
Tisdale, Bob (2010). An Introduction To ENSO, AMO, and PDO – Part 3.
http://bobtisdale.blogspot.com/2010/09/introduction-to-enso-amo-and-pdo-part-3.html
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.
There are good physical reasons for this. Sunspots ~11 year apart are independent in the sense that the Sun has no way [we know of] of preserving the memory of short-lived spot-complexes. Having said that, it is also true that there is high autocorrelation because the solar cycle has a time scale of many years. The high auto-correlation means that a cycle only has about 20 degrees of freedom. The polar fields is sort of a crude ‘memory’ in the sense that they result from the decay and migration of sunspot fields [only 1/1000 of the latter makes it to the poles], and a ‘physical’ definition of the length of the cycle might be from polar field reversal to the next reversal, which is roughly from maximum to maximum of the sunspot cycle. But it is doubtful that the SLC or its derivative, as such, can have any effect on the climate, that we cannot see by simply looking at the direct correlations [such as they are] between solar activity and climate. This is IMHO the main flaw of Friis-Christensen/Lassen the ‘findings’ [apart from the sloppy and inadmissible ‘analysis’]
The independence bit is like measuring the difference in altitude between Death Valley and Mt. Whitney, it doesn’t matter what the terrain between them looks like.
Ulric Lyons,
Good links you provide. I see, for example, mention of emergent properties in the very last line of the latter link.
Further reading:
Allen, T.F.H.; & Hoekstra, T. W. (1992). Toward a unified ecology. New
York: Columbia University Press.
Pattern is a function of scale.
There are endless of examples of what statisticians call “Simpson’s Paradox” (which goes by different names in different fields).
There is nothing paradoxical for those who take the time to realize that even if fine resolution is available, aggregation criteria affect spatial patterns.
Fotheringham & Rogerson (1993) assert that scale-dependency “[…] presents us with the challenge of reporting on the reliability of parameter estimates in the light of changes in scale […]”
Fotheringham, A.S.; & Rogerson, P.A. (1993). GIS and Spatial Analytical Problems. International Journal of Geographic Information Systems 7(1), 3-19.
This point is relevant to a concern raised by jorgekafkazar about “cherry-picking”. In short: Look at all scales – i.e. roll the focus, noting the scale of pattern transitions and whether transitions are abrupt or diffuse, etc., bearing in mind the concept of emergence.
Re: Leif Svalgaard
Let’s just be mindful of confounding. For example SCL’ is confounded with solar cycle phase acceleration …and with what else? As always, I’m leaving physics to physicists…
…and have they convinced me there is no possible reason for a connection (whether direct or via confounded variables): Absolutely not.
Paul Vaughan says:
September 12, 2010 at 3:31 pm
Ulric Lyons, Good links you provide.
_________________________________________
I though you might find some tips there, though my question did not get an answer, but I do like the way Lief puts it; “it doesn’t matter what the terrain between them looks like.”
In your SCL graph http://wattsupwiththat.files.wordpress.com/2010/09/scl_morlet_fclt_pv_ja1.png with the red dots on the minimums and the blue dots on the maximums, there does not seem to be any significant disagreement in SCL. But strange that the dots line up on the vertical but not the horizontal.
Leif Svalgaard says:
September 12, 2010 at 12:38 pm
1) Wolf’s scale was not based on his magnification x40 ‘pocket telescope, but on his magn. x64 large telescope
But he used the pocket telescope a hell of a lot. It is nice to know what he saw and I think the smaller scope may have relevance to his x64 threshold.
2) which is still in use and produces sunspot count a bit larger than the official SSN
I am investigating this area and will do a report soon, do we have daily drawings from Keller so we can compare properly? The difference between the modern telescope and Wolf’s at x64 is substantial.
Geoff Sharp says:
September 12, 2010 at 5:53 pm
But he used the pocket telescope a hell of a lot. It is nice to know what he saw and I think the smaller scope may have relevance to his x64 threshold.
His x64 threshold was established a dozen years before he began to use the x40, and therefore the x40 is not relevant. To compensate for the weaker performance of the x40, Wolf multiplied all counts using the x40 by 1.5 [i.e. increased the SSN by 50%] in order to approximate his standard at x64. This multiplication does not work when the sunspot number is close to zero, that is, there could be small well observed at x64, but not at x40. This skews the SSN at low activity and thus damages the homogeneity of the series.
I am investigating this area and will do a report soon, do we have daily drawings from Keller so we can compare properly?
Yes, I have tried to locate them [no luck yet]. We must assume that Keller reports correctly [he counts everything he can see] and that we cannot improve on what he reports.
The difference between the modern telescope and Wolf’s at x64 is substantial.
I assume that you are talking about your own scope. Keller uses the original Wolf scope built by Fraunhofer in the late 1830s or early 1840s, so no difference there. If you are talking about your own scope there will be a large difference, which makes one wonder why you don’t do as Wolf and use a standard Wolf-telescope at x64, with which the Wolf standard is defined. The x40 has nothing to do with the Wolf standard or with determining what Wolf would count using his standard telescope. He already knew that he would see a lot less and therefore needed to increase his sunspot number determined from the x49 by 50% to match his standard. You can see the damage done using the x49 if you look at the lowest daily sunspot number that he reported during 1862-1877 [omitting a few days where the count was not done by him – that info is available]. You’ll find that instead of the SSN=11 as we would expect for a single spot, he invariably reports 11*1.5 = 16.
Geoff Sharp says:
September 12, 2010 at 5:53 pm
The difference between the modern telescope and Wolf’s at x64 is substantial.
If you are talking about Catania, Locarno, Uccle, etc [which your use of singular may indicate that you do not], then the determining factor is the magnification x64 which is the same. Waldmeier repeatedly found that Locarno and Catania see the same spots as Wolf’s standard telescope in Zurich.
Leif Svalgaard says:
September 12, 2010 at 7:36 pm
determined from the x49 by 50% to match his standard. You can see the damage done using the x49
both should be x40, of course.
Paul Vaughan says:
September 12, 2010 at 3:43 pm
…and have they convinced me there is no possible reason for a connection (whether direct or via confounded variables): Absolutely not.
so why are you doing this?
Leif Svalgaard says:
September 12, 2010 at 7:42 pm
If you are talking about Catania, Locarno, Uccle, etc [which your use of singular may indicate that you do not], then the determining factor is the magnification x64 which is the same. Waldmeier repeatedly found that Locarno and Catania see the same spots as Wolf’s standard telescope in Zurich.
We need further proof of this. Only the Keller drawings can provide this. The Locarno/Catania scope has a 150mm front lens compared with Wolf’s 80mm, this on its own makes a big difference when projecting the solar image. The focal length is also very different being 2300mm vs 1100mm. We also do not know what eyepiece design is used on the modern scopes which is another large determining factor. I use a vintage eyepiece in my 40x Wolf pocket replica.
I agree the 40x scope does damage to the sunspot record but it has still been interesting to get an idea of what he could see. I am currently sourcing a vintage 64x eyepiece that is of solid design that can withstand solar projection (no plastic parts). If anyone has 1.25 inch kellner design eyepiece with a focal length of around 8mm for sale please contact me through my website (click on my name)
Geoff Sharp says:
September 12, 2010 at 8:44 pm
We need further proof of this.
Nonsense, Waldmeier reported year after year that Locarno/Catania multiplied by 0.6 matched Zurich multiplied by 0.6.
We also do not know what eyepiece design is used on the modern scopes which is another large determining factor. I use a vintage eyepiece in my 40x Wolf pocket replica.
The only thing that matters is the magnification [and the seeing]. The design is not important as long at the eyepiece is good enough, and they made superb eyepieces in the 19th century.
I agree the 40x scope does damage to the sunspot record but it has still been interesting to get an idea of what he could see.
Of course, although we already know this from Wolfer’s careful and authoritative comparisons over 17 years. Schaefer reports that a very important ingredient is the experience of the observer. The same observer using the same scope will observe twice as many spots after a year of experience [further years do not improve that number]. Also, don’t use photographs as they do not exploit the rare moments of better seeing [unless you take thousands each day and pick the best]. BTW, Wolf [and Wolfer, etc] did not use projection, but a polarizer to cut down on the glare.