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
Geoff Sharp says:
September 12, 2010 at 8:44 pm
Only the Keller drawings can provide this.
I have Keller’s monthly sunspot numbers since 1996. Comparison with SIDC show good agreement up to ~2001: http://www.leif.org/research/Keller-SIDC.png [a few of the very highest numbers being a bit off].
Thereafter, SIDCs report systematically LOWER numbers, showing the recent undercounting by SIDC. BTW, tomorrow, I’ll be at SIDC http://sidc.oma.be/seminars/index.php so will have opportunity to grill them on this.
Ulric Lyons wrote: “But strange that the dots line up on the vertical but not the horizontal.”
You can’t have the same start & end dates for different length measurements. Changes to lengths require changes to neighboring length(s).
Paul Vaughan says:
September 12, 2010 at 9:47 pm
—————-
The length for cycle 23 [min to min a tad more than 12 years] is now known but not used on your graph [except perhaps the JA value.
Leif Svalgaard says:
September 12, 2010 at 9:11 pm
Geoff Sharp says:
September 12, 2010 at 8:44 pm
Only the Keller drawings can provide this.
I have Keller’s monthly sunspot numbers since 1996. Comparison with SIDC show good agreement up to ~2001: http://www.leif.org/research/Keller-SIDC.png [a few of the very highest numbers being a bit off].
Thereafter, SIDCs report systematically LOWER numbers, showing the recent undercounting by SIDC. BTW, tomorrow, I’ll be at SIDC http://sidc.oma.be/seminars/index.php so will have opportunity to grill them on this.
Great, ask them about the eyepieces…its important. And if the Keller’s drawings are available somewhere. I observe all day currently and take lots of pics, esp when vision is good. Will have today’s best pic available soon
The modern optical adavantages that Wolf did not enjoy:
Superior Glass formulas (affects chromatic aberrations (requires training to overcome)
Superior lens grinding & polishing (more useable clear aperture)
Superior eyepiece design (correction and FOV advantages)
Coatings (increased transmission and less ghosting interference, which clearly plagued the Kellner design)
And 2 things which no amount of good luck in seeing can ever overcome: AO and Image Stacking/reduction from CCD integrations. These hit way below the belt, in my opinion.
For observers earlier to Wolf, they did not have achromatic eyepieces, just the Ramsden and the Huygens. Lots of training.
Anybody who has used these eyepieces with or without coatings knows what overcoming limitations is all about.
I haven’t even mentioned the really superior designs, like Plossls, Orthoscopics and Erfles.
So, my suggestion is that if SIDC really wants to nail it down, make the observers use Wolf’s uncoated scope with his eypeice of the time (Kellner) in parallel with the modern equipment, and do the calibration accordingly.
Remove all doubt.
Leif Svalgaard says:
September 12, 2010 at 8:59 pm
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.
Wolf and Wolfer did not use projection?
That’s a major piece of news. So they actually counted what they saw and transposed that into a diagram from memory? I have wondered along with rbateman how Wolf used his pocket scope which now turns out to be very similar to what I am doing (my filter is probably better). The difference between visual and projected might be interesting to gauge.
Today’s image is close to what Wolf would have seen through his 40x pocket scope. The image is taken through a modern eyepiece, the image is sharper than what is viewed through the Kellner eyepiece which cannot be used for good photographic reproduction due to the small eyepiece aperture. I am going on the eyepiece design dates and guessing Wolf used a Kelllner (1849) but he may have used something inferior like a Ramsden. The “modern” Kellner eyepiece is also coated providing a better lens than Wolf’s day.
Soon I will have 64x images available.
http://www.landscheidt.info/images/1106_sept_13_4.30UTC.png
Geoff Sharp says:
September 12, 2010 at 10:17 pm
Great, ask them about the eyepieces…its important.
As a professional astronomer I tell that for observing sunspots the eyepiece is not important if it is achromatic.
rbateman says:
September 12, 2010 at 11:11 pm
So, my suggestion is that if SIDC really wants to nail it down, make the observers use Wolf’s uncoated scope with his eypeice of the time (Kellner) in parallel with the modern equipment, and do the calibration accordingly.
Remove all doubt.
I don’t think I’m getting across. There is no doubt [only jinki’s]. Keller observes [as he has done the past 50+ years] with THE ORIGINAL WOLF TELESCOPE [EYEPIECE AND ALL] AT CLOSE TO THE ORIGINAL LOCATION.
Leif Svalgaard wrote: “The length for cycle 23 [min to min a tad more than 12 years] is now known but not used on your graph [except perhaps the JA value.”
You’ll have to take it up with FCLT:
http://web.dmi.dk/fsweb/solarterrestrial/sunclimate/SCL.txt
Ulric Lyons wrote: “Can you explain what “all of the sunspots occurring during the interim” has to do with the time passed from a given minimum, to the following maximum, and to the next minimum.”
It is possible to devise any number of metrics. The one that makes sense will depend on the phenomenon under study. For example, if one is studying a phenomenon that occurs only during maxima…
And there is nothing particularly special about sunspots, except that the series goes back to 1749. Other series could have been used to extract solar cycle phase (but records don’t go back to 1855 when ERSST starts).
Despite the amount of detail appearing in the exchange about sunspot measurement issues, the issue has only a tiny influence on phase measurements.
Paul Vaughan says:
September 13, 2010 at 1:30 am
Leif Svalgaard wrote: “The length for cycle 23 [min to min a tad more than 12 years] is now known but not used on your graph [except perhaps the JA value.”
You’ll have to take it up with FCLT:
No, with you. It is the user of data that is responsible for checking the data quality.
Your link to FCLT states:
1996.8 10.0 10.2 1991.80
2007.3 2 10.5 2002.05 <==== should be 2008.9
Solar cycle data for maxima
2000.3 2 10.7 10.5 1994.95
2011.2 2 10.9 2005.75 <==== new estimate 2013.5
Notes:
2 Estimated in Thejll&Lassen (2001)
Thus they used estimates from 2001, which we now know are wrong.
Paul Vaughan says:
September 12, 2010 at 9:47 pm
You can’t have the same start & end dates for different length measurements. Changes to lengths require changes to neighboring length(s).
……………………………………………………….
Exactly, maybe its just the scale makes it hard to see the difference in date for each point.
Re: Leif Svalgaard
I’m not “using” FCLT’s summaries. I plotted their summaries to quell the confusion of a number of commenters who don’t understand wavelet methods. As indicated, I am using the following (not FCLT): ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
Although my estimates (black, grey, & light grey) run through to 2010, they are affected by edge effect for recent years, as I have indicated.
I appreciate the alert which you have volunteered — and I should point out (for the benefit of anyone trying to follow along) that you have your arrows pointing at the wrong column.
I thought the reception for this was a bit odd. People seemed to be complaining that the author hadn’t told them what conclusions to draw. Surely, it’s perfectly valid to present data or some other finding and let people draw their own conclusions.
However, there is a pretty important – and obvious – conclusion to be drawn. Providing the data and methods described are valid, then the conclusion is fairly explosive. It appears to show a remarkable correlation between solar activity and the climate over the last 100 years.
Over long time periods it is easy to demonstrate a dramatic correlation between solar activity and climate. But it has been claimed that the correlation failed in more recent decades, and so the correlation is probably false. In particular, Lockwood published an important paper a few years ago which apparently showed that the correlation has broken down in recent decades. Ironically, in a more recent paper he demonstrates a strong correlation between falling solar activity and falling temperatures. A logical conclusion would be that, if they correlate when activity is falling, there would almost certainly have to be a similar correlation when activity is rising. But of course, that would contradict the whole basis of AGW.
It would be interesting to compare the graph with CRUTEMP. It seems to correspond pretty well. It shows the three major climate legs: warming 1900 – 1945, cooling 1945-1975 and warming again 1975-2000. The graph also predicts slight cooling post-2000. Of course, this is precisely what has happened, although the cooling – so far – is quite small.
Here’s a small thought experiment. Compare this graph showing correlation with sea temp or CRUTEMP with a graph showing carbon dioxide and CRUTEMP. Which shows the greater and more dramatic correlation?
Sadly, if this correlation is true and has predictive ability, then the world is headed for an extended period of global cooling, unless the sun perks up and gets back to work. It’s global cooling we should fear, not global warming.
Chris
Paul Vaughan says:
September 13, 2010 at 3:06 am
I’m not “using” FCLT’s summaries.
That is not what your post says. To remind you:
“2) authors:
FCLT = Friis-Christensen, Lassen, & Thejll
( pv08 = my 2008 “eyeball” adjustments to FCLT )”
Precision in quoting is paramount. If you don’t have that, your credibility suffers.
When ‘caught’ the best damage control is to fess up immediately…
Leif Svalgaard says:
September 12, 2010 at 8:59 pm
Wolf and Wolfer did not use projection?
Kind of tough to do with the handheld pocket telescope 🙂
So they actually counted what they saw and transposed that into a diagram from memory?
No diagrams. Just counted by eye.
Modern observers are at pains not to use equipment better than Wolf’s. This is deliberate.
Leif Svalgaard says:
September 13, 2010 at 4:07 am
Modern observers are at pains not to use equipment better than Wolf’s. This is deliberate.
I can’t believe you are still holding this line. The comparison of specs has been laid out for you. The links below speak for themselves, only the magnification is the same.
http://www.ct.astro.it/sun/instrument.htm
http://www.leif.org/research/Wolf-Telescope.png
Have a good look how the Catania scope is set up. Notice there is no tube to heat up that distorts the image. The front lens is nearly twice the size of Wolf’s, this lets in more light which enables more detail. The length of the modern scope is over twice that of Wolf’s, this enables a much larger opening in the eyepiece. The Catania eyepiece focal length would be around 35mm, the Wolf scope would be around 8mm. When projecting a 250 mm solar disk this means the paper is closer to the eyepiece. The closer it is the more detail is seen.
I think a lot of people would also disagree with you regarding your statements on lens quality.
Chris Wright says:
September 13, 2010 at 3:10 am
I thought the reception for this was a bit odd. People seemed to be complaining that the author hadn’t told them what conclusions to draw. Surely, it’s perfectly valid to present data or some other finding and let people draw their own conclusions.
However, there is a pretty important – and obvious – conclusion to be drawn. Providing the data and methods described are valid, then the conclusion is fairly explosive. It appears to show a remarkable correlation between solar activity and the climate over the last 100 years.
You need to be careful here. The correlation is not simply one of solar activity and temperature. For example, if the next 2 slar cycles were of the same length as SC23 then any prediction from Paul’s analysis would show NO Change in temperatures, i.e. there would be no cooling. If future cycles were longer (which normally means weaker) than SC23 then a rise in temperatures would be predicted. To be fair to Paul he is not claiming any predictive skill, but I’ve noted that a number of posters are failing to understand the SCL’ plots. He needs to provide more detail in his main post.
Sadly, if this correlation is true and has predictive ability, then the world is headed for an extended period of global cooling, unless the sun perks up and gets back to work. It’s global cooling we should fear, not global warming.
Chris
If this correlation has predictive ability then we could end up with quite the opposite of global cooling.
Paul Vaughan says:
September 12, 2010 at 1:26 pm
……
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.
It’s ok, Paul, I understand what you’re doing – but I’m not sure others do. Regarding my example: Supporters of the ‘conventional’ SCL/temperature hypothesis (e.g. F-C&L, David Archibald etc) would expect temperatures during the second group of cycles to be much higher than during the first group.
In the other thread you stated there was no paradox. I’m not so sure. According to your analysis a lengthening cycle results in rising temperatures and vice versa. I would suggest this is at odds with the findings of F-C&L, Butler&Johnson, David Archibald and possibly Svensmark – in an indirect way. I’m not sure your SCL/SCL’ orthogonality argument is valid. My example illustrates this.
Geoff Sharp says:
September 13, 2010 at 6:25 am
I think a lot of people would also disagree with you regarding your statements on lens quality.
The quality once it is high enough doesn’t matter compared with the effect of seeing and observer experience [because there is a minimum size of about 1.5″ to a spot or pore. Perhaps the best way to demonstrate this is simply compare the counts of the observers and instruments in question. Now, many people have difficulties following a reasoned arguments that has more the two pieces, so you will have to pay attention [I’ll predict that I’ll fail to get the point across, but lemme give it a try].
I’ll take year of low but steady solar activity a couple of years after minimum – like we have now – I don’t have Keller’s data for 2010 so I’ll use 2007 for which I have good coverage.
Here is the situation:
1) Keller is using Wolf’s old, standard [and superb] telescope with the original optics that Wolf used to set his standard with in 1849-1861.
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].
3) Catania reports both spot and pores in each group and the Catania Relative Sunspot Number is then Rcatania = 10*Gc {at least one pore or spot} + {spots + pores}.
4) Waldmeier has always reported that Rzurich = 0.6 * Rcatania. So we can multiply Rcatania by 0.6 to bring it on the Wolf scale.
5) I surmise that Wolf simply did not count the pores, that is that a group was not counted if there were only pores in it. This means that Wolf’s group count Gw will usually be smaller than Catania’s, Gc. Now, Rwolf =k*[10*Gw +{spots}] with k=1
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 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.
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
P.S. the three numbers 9.9, 9.2, and 9.3 are the yearly average sunspot numbers for 2007 for the three ‘observers’. Again, not significantly different. BTW, SIDC has 7.5 for 2007 because of the undercount, i.e. SIDC is too low. I may find out tomorrow why. I’ll post a link to my talk later.
Leif Svalgaard says:
September 13, 2010 at 1:17 pm
e.g. beginning of May 1998
P.P.S. should be 2007, not 1998. I also did it for 1998, but is was too active to compare with 2010. The typo slipped by my ‘attention to detail’, but at least I caught it.
Re: Leif Svalgaard
Note the verb tenses.
I’m not using FCLT (present tense).
I have indicated that I looked at it (past tense) in 2008 and found the metrics “wholly unsatisfying”.
Currently (present tense), I am using wavelet-derived measures of SCL & SCL’, which is pretty clear.
The reason why FCLT & “pv08” were graphed has also been indicated:
There was too much confusion in the last thread from people who don’t understand wavelet methods.
I dug into my archived files to address confusion which arose in the last thread.
I can add that I also had it in mind (not explicitly stated) to illustrate some of the hazards of “eyeball” methods. I can clarify that, beyond FCLT, I was also not satisfied with what I’ve called “pv08”. Hence the switch to wavelets.
Personally, I was done with FCLT (and adjustments to it, such as the “pv08” example) two years ago (i.e. shortly after I first looked at it [past tense]).
To re-emphasize:
Inclusion of FCLT & “pv08” on the above graphs was strictly to get through to the waveletless crowd.
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:
Over the interval 1749-2010:
Morlet 2pi:
0.0021113% of the variance in SCL’ is explained by SCL.
99.9978887% of the variance in SCL’ is NOT explained by SCL.
Morlet 3pi/2:
0.0087877% of the variance in SCL’ is explained by SCL.
99.9912123% of the variance in SCL’ is NOT explained by SCL.
Morlet pi:
0.0445296% of the variance in SCL’ is explained by SCL.
99.9554704% of the variance in SCL’ is NOT explained by SCL.
Who on Earth is going to buy into a challenge against the notion of orthogonality in the face of such stats? Certainly no one sensible.
However, you may be pondering some kind of detrending & temporal lagging. If so, bear in mind that that’s another matter that does not impact upon the definition of orthogonal.
SCL’ is essentially 100% bulletproof against attacks which have incinerated claims about SCL.
Half of the time when a sine wave is positive, a cosine wave is also positive. The other half of the time when a sine wave is positive, a cosine wave is negative. Although there is a 100% systematic relationship between the 2 waves, the correlation is zero.
A note that should have been included in my response to Lucy:
Also consider that the Antarctic vortex runs year-round, while Arctic vortex activity spikes annually (in northern hemisphere winter).
The note also relates to comments made by Tim.
Given there is a context of Antarctic circumpolar I have an incomplete unpublished note which contains a plot and mentions this in UAH data. Ignore the rest of it.
RSS will be the same but does not provide data to +-90 degrees. The only major difference between RSS and UAH is the degree of low pass filtering, RSS is arguably showing artefacts which are not there and UAH perhaps filters excessively. Both contain similar errors originating from the mish-mash of satellites used (and Nyquist problems).
This was an incidental finding which I did not expect in the dataset.
Made it available here
http://www.gpsl.net/climate/data/heat-flow.pdf