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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Try Mortlet (Pi/2) for a more PSF function.
When you find the finest resolution that can be supported without artifacting, then the data can be put through a deconvolution process (at the PSF of the finest resolution) to increase the signal to noise ratio.
Talk to Astronomers about this: They do it all the time to get the most information out of thier work.
I’ve been trying to think of a good way to generate an instantaneous frequency plot of the solar cycle. It always seemed to me as if the solar connection should be through a frequency modulation.
Holy cow! The wiggles match. Except when they don’t, which seems to be the case for the latest wiggle. Up to that point, it’s very interesting. Are there known data smoothing end effects that would make the last (2000-2010) wiggles match better if we had real data beyond 2010?
And why just the northern hemisphere? Then there’s the issue: does selection of the resolution constitute {gasp} cherry-picking, especially given that there are only 5 wiggles? ¿Two pi, or not two pi, that is the question. Is there some physical basis for selection of that number? What solar mechanism or phenomenon exists that should result in any correlation between SCL’ and ERSSTv3b? TSI doesn’t seem to fill the bill. Is a puzzlement.
Solar cycles, pfft.
What about Earth’s cycles? Every year, every spring, I travel like what, about 7000 km closer to the sun and our average temperature goes from 15-20 below to 25-30 above, in degrees C. In just a couple of month’s time really. I have observed this fact every year for pretty much my whole life. It’s also reinforced due to the fact that during high winter where I live we sometime go south about 7000 km during a short vacation and lo and behold in just 6 hours flight time we go from sub zero 20 below to 30 above, 24 above water temperature. To me this seem to infer that our own little star called Sol prolly has a more then a slightly more then a major impact on our climate, and all for a measly tilt or for a few measly thousand kilometers.
But I’m sure me and my family will be very very sad indeed that our average temperature during four month of winter will be about 19-24 below instead of about 20-25 below in 2094. But hey in like 3000 years I’ll be able to go in shorts all year round at a nice 15C, and that’ll be the day.
Give students an equation and they will apply it no matter whether it is appropriate or not … just saying.
The correlation between ERSST and rate of change of SCL is strong. But still not satisfying – why does the final ERSST rise so much more than the SCL’ curve? Suspect data?? changes of instrumentation allowing AGW slides elsewhere to corrupt the calibration?? or not?? or does the correlation depend further on (a) lag (b) cumulative effects??
1DandyTroll says:
September 11, 2010 at 5:07 pm
Aw shucks Dandy, there you go again complicating and overstating everything.
You are well aware that it is not 7000km it is but a mere 4350 miles!
But you folks all enjoy that 1 deg in 2094, fairly sure I won’t be around to take advantage, but I will rest happy knowing my contribution is appreciated.
Regards
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.
It seems reasonable there could be different densities of cosmic rays flowing through the galaxy. If the Earth passes into or out of one of these higher density streams, the solar effect could be dwarfed by the change in the external source. Galactic magnetic fields and nearby nebula densities could be factors affecting the density of cosmic rays reaching Earth. Although we currently see little anisotropy, it is expected that cosmic ray anisotropy, density and energy variability are expected. Medvedev, et al., state, “The magnetic field fluctuations in the Galaxy are of high amplitude…. The effects of [cosmic ray] particle trapping and mirroring are important.” See: http://iopscience.iop.org/0004-637X/664/2/879/70903.text.html
It is very clear that the Greenland ice core 10Be levels contain the Younger Dryas signal, whereas the antarctic data do not. Whatever happened in the northern hemisphere at the end of the Ice Age is different from what happened in the south. Cosmic ray anisotropy and external density fluctuations could explain that difference, whereas solar cycle variations could explain lesser events like the Little Ice Age and Medieval Warm Period which show a much smaller amplitude cosmogenic isotope correlation.
The model is:
Solar wind density (higher), correlated with sunspot number (also higher) ->
Cosmic ray flux at Earth (lower) ->
Cloud formation (less) ->
Temperature (higher)
See: http://www.greatglobalwarmingswindle.com/pdf/Gamma%20Rays%20and%20Climate%20-%20Perry,%20Charles.pdf
And of course, in this model the reverse is true. With fewer sunspots, the temperature on Earth is expected to be cooler.
Naturally, we can add on refinements like the heat capacity of oceans, and the effects of deep ocean currents to begin to address climate. Also, we know there are changes in Earth’s orbit around the Sun that may play a role. Perhaps the best we can do is to adapt to whatever happens. Humans are ordinarily good at adaptation. Unfortunately, governments are getting in the way of individual choice, so we collectively suffer the same fate.
The good news is, Nature is always teaching us a lesson. The latest one is in progress. Government plans may furiously be rewritten in the next few years as they try desperately to remain credible.
This one leaves me totally confused, what are you trying to say.
Paul: What is your y-axis? Surely not sunspots, they’re at a low right now.
Also, whose sunspot data are you using. I don’t like the counting of every little speck as a sunspot that has recently taken place. It’s sort of like counting every tropical depression as an actual storm; it destroys the value of the historical record just to increase your current numbers to fit your theory.
Use the measured Sunspot Area, and recompute.
Additionally, use the measured Faculae Area data 1874-1974.
Paul,
I would like to provide some (hopefully constructive) criticism regarding the format of this post. Presumably you are making a scientific measurement (or measurements) of SCL, but unfortunately for me this post reads like a list of research notes rather than an explanation of anything.
You seem to have generally listed and explained your methodology here (applying wavelet analysis to what I glean is a proxy for the Wolf sunspot number), but 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?
Thanks.
You have assumed your readers have same level of understanding on this topic that you do. I don’t. The relevance of those charts is lost without a dumbed down summary.
I agree with Tom and the other posts requesting clarification.
This is not a report suitable for the general public.
It is also not suitable as a paper in a scientific journal where at least the abstract is vaugely understandable.
I see that some readers could understand it and have commented, unfortunately in terms that I also cannot understand.
Surely this is not such a difficult subject that nobody can put it all into plain English?
Help please!
Paul, ( and tom September 11, 2010 at 8:07 pm )
I agree with rbateman, try the area instead of merely width. Sometimes height also seems to matter. Could get you even tighter of a match. The only thing you might have problems with is that area is an ever increasing function (across time). The area always grows of course.
You might already know every thing I’m about to say just by the mention of the word area, so, maybe this is just for others interested in this topic and, as tom, just want some words to help explain this better. Here’s my limited understanding.
If you try it, by the area, first, you are assuming that solar activity has something to do with the Earth’s temperature. Right? The LIA was cooler and activity was way down, same as the times around 1810 and 1910. The 1990’s were warmer and solar activity was way up. And I tend to agree there seems something here. Set that in stone so the next variable is real and necessary.
Second, you need to pick a value that represents a certain “balance” level of activity where if every solar cycle was at that level, the temperature would not change at all. Cycle areas under the curve above this value would cause warming, cycle areas below, cooling. I found the number is around 45-50 if using SSN yearly as a proxy to the activity for starters. Other activity proxies would have their own value of course. Your analysis should coerce out that balance level value. Now, offset downward this value from each year’s value as you integrate by merely adding each year to the previous sum and subtracting the balance value. You now have a sinusoidal function of the cycle areas. Above zero warming, below cooling. From this you can get the aerial change (i.e. differentiate).
BTW, I have tried very simple analysis but lacked some of the finer tool such as your Morlet wave function, that was over my head. Great job. I however DID notice across this “area” view of solar activity that you can see the ringing across many cycles that dies out gradually as the decades go by and on multiple scales, then along comes another big pulse. After reading about the Morlet function that’s so close to what it does, the ringing. Hope this helps getting you even a closer correlation, though, yours above is so very close to begin with. You’ve got something there. Interesting.
Paul
Many of us sense you are on to something interesting but don’t understand your writing. This is exactly the trouble, increasingly, with scientific papers that are incomprehensible to the ever-smaller in-crowd, and WE KNOW WHERE THAT HAS LED US with the Team as Steve McIntyre calls it.
If citizens’ science is to provide the needed counterweight to deadly orthodox papers (deadly because they are apocalyptic, cannot be understood, and cannot be reproduced and verified), as Open Source does to Bill Gates, the work needs to be explained accessibly, always starting from the human interest and ending with human conclusions, going back to basics frequently, to catch each new boatload of interest, and to reinforce all our understanding.
It is to PNAS’ credit that they’ve just published a work challenging a study that “correlates” climate change and civil wars, and that the whole Abstract of that study tells a very human story and uses commonsense.
Paul is doing good analytical exercise, but to be convincing relationship it has to be simple and direct . Think of all great relationships from F=ma and V=RI to e=mc2 etc., climate relationships are convoluted and simplicity here may be impossible.
Direct influence of either the cycle intensity or SCL is likely to be small to make large enough impact . Also correlation is required during whole of SC historical record, or at least from 1700.
On the other hand global temperature averaging does not make great deal of sense since there is a definite time lag between the Atlantic and Pacific, the regional changes with a good long term record may be preferable.
In my own investigation I found events which correlates both the solar cycles and temperature, while not obvious consequence of either.
Atlantic :
http://www.vukcevic.talktalk.net/STP.htm
Pacific:
http://www.vukcevic.talktalk.net/PDOa.htm
There also the odd (Earth’s) magnetic field correlations
http://www.vukcevic.talktalk.net/NFC1.htm
and updated
http://www.vukcevic.talktalk.net/LFC20.htm
Suffice to say, the explanations for none of the above are within easy reach.
wayne says:
September 12, 2010 at 12:13 am
you need to pick a value that represents a certain “balance” level of activity where if every solar cycle was at that level, the temperature would not change at all. Cycle areas under the curve above this value would cause warming, cycle areas below, cooling. I found the number is around 45-50 if using SSN yearly as a proxy to the activity
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/
“In contrast, wavelet methods utilize all sunspots”
Problem, I and many others have asked would the likes of Johann Rudolf Wolf born in 1816 seen some of the specs that are being counted today. Below is the first published picture on the landscheidt website of the sun using their new Wolf pocket scope.
http://www.landscheidt.info/images/Sept_7_2010.png
Compare to the Spaceweather image (Sunspot number: 24)
http://spaceweather.com/images2010/07sep10/hmi1024_blank.jpg?PHPSESSID=as78r0i0063edt17r7ed0jfqk3&PHPSESSID=h05kcakr9c1tdf2g9vi5br2kk1
2010/09/11 08:00 Today is technically the forth spotless day as the new region measures just under the threshold at 300 pixels. Locarno has counted 13 with Catania at 12, I am struggling to see how they arrived at the extras. The Wolfcam has been observing all day and barely makes out this new region through the solar filter. An attempt at projecting delivered zero.
http://www.landscheidt.info/?q=node/50
Compare to Spaceweather
http://spaceweather.com/
I’ve been following blogs on global warming for years: WUWT, CA, BH, etc. And this post is special, because I have no clue as to what it is saying. Why was this posted?
Please can we have a update that puts this into terms regular readers can understand?
As others have noted it is badly written and needs standard stuff like intro and conclusion.
I did conclude that it was explaining the discovery of a correlation between NH sea surface temperatures and the derivative of the solar cycle length. But this observation is left hanging in mud air.
The irony is that the temperature record is often represented as fraudulent and here we have evidence that it us not. Unless of course someone wants to try and fly a conspiracy in which the temperature record was synthesized by using a wavelet analysis of the sunspot cycle. That would take an expert lead balloon aeronaut indeed.
I fixed some formatting issues, which might clear up some confusion.
Paul
I don’t want to comment too much as this stage. Could I, though, just ask a hypothetical question.
Consider 6 solar cycles of the following lengths: 13, 13, 13, 10, 10, 10. Assuming a SCL’ /ERSST link could you tell us what the this sequence of cycles would imply for NH SST. In particular, how would the temperatures during the 5th/6th cycles compare with those during the 1st/2nd cycles.
Please don’t say that the Morlet analysis looks at more than just the min -> min measurements. I know this, but you may recall, on the previous thread, I asked you to plot SCL (not SCL’). You have now done so (first graph) and as I suspected SCL (2pi) is essentially a smoothed version of the ‘discrete’ cycle length values.
Note that the purpose of the question is to clarify the issue – not to show that anyone is right or wrong.
“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.
……………………………………………………………………
Like an ecosystem boundary?
http://el.erdc.usace.army.mil/emrrp/emris/emrishelp/spatial_boundaries_ecosystem_management.htm
http://el.erdc.usace.army.mil/emrrp/emris/emrishelp/what_is_scale_.htm
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.
Paul,
I have a couple of problems with this science.
One, since the sun is massive in size and the sunspots occur at different lattitudes on the sun, how are we getting true readings when the waves would be different in dispersement?
Second, what proxies are being used to calculate back when the measuring technology was not invented going back in time?
The theory on sunspots I find to be incorrect as it does not take into account of the speed of our solar system and rotation. Actual speed of the solar system is impossible to accurately calculate as every other system in space is moving. So, to get a triangulation is impossible.
Next, I believe the estimate is 300km/sec is the speed of the milkyway system.
Now any object to hit the sun would not have time to melt or burn up but to impact the surface of the sun. This would create the sunspot by blocking gases at that impact area.
How accurate are the readings when our planet is moving at 18.5 miles a second and the planet is rotating at 1669.8km an hour when these satellites are being pulled with us?