The North Pacific & Solar Cycle Change

vukcevic says:
September 6, 2010 at 11:26 am
John Finn
Length of a cycle can be determined at any two corresponding two points along its 360 degree ( 2π ) phase, theoretically minima are no more significant than maxima or any other two points in between. To be certain that result is a meaningful you could slide an imaginary ‘ 2-slot visor’ with 2π separation along all the cycles length.
I can certainly accept that min-> min and max-> max could both be valid in determining SCL. How would you determine SCL from “any other two points in between”. I’m obviously missing something here.

Further to this, vukcevic & tallbloke: the quote that may interest you: Leif Svalgaard: “[…] the more magnetic the Sun is, the more rigid is its rotation.”. See figure 1 in the article referenced here.
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Re: John Finn
As indicated in the
earlier thread, the variable SCL’ is calculated from the following data:
Sunspot Numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
For anyone who understands wavelet methods, I have explained here & here.
Important cautionary note:
Beware that there are all kinds of so-called “accepted” versions of solar cycle length summaries based on eyeball methods that ignore the vast majority of the data. (This is no trivial issue.)
For anyone needing to learn wavelet methods, the simplest intro I’ve been able to find on the net:
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
As previously indicated: I can make it much simpler for a lay audience if & when reliable sustainable funding arises for this purpose. (The project would take months of full-time engagement and require funding in the thousands of dollars. The potential benefits to society if someone [not necessarily me] does a careful & thorough job on such a project: immeasurable.)
In the meantime John, the best I might be able to do is dig out some notes I once drafted. Let me know…
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John Finn wrote: “How would you determine SCL from “any other two points in between”. I’m obviously missing something here.”
That is what the wavelet methods do.
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vukcevic,
You seem to have the general idea of wavelet methods intuitively. I use a complex wavelet (which has both real & imaginary parts). The window-edges are tapered by a gaussian (i.e. bell-shaped envelope). The complex wavelet facilitates the simultaneous extraction of both amplitude & phase [(r,theta) from (x,y)] information. This is standard stuff. It’s actually dead-simple – (i.e. once a beginner is over the initial rise on the learning curve).
The “2pi” in “Morlet 2pi” is a wavelet paramater (which can be adjusted along a continuous spectrum) — i.e. it is not the number of radians in a cycle …but as you may suspect, the choice of “2pi” (instead of the usual “6” that many researchers use & regard as a conventional choice) facilitates interpretation.
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John Finn wrote: “Statements like “Conventional statistical methodology is inapplicable” and “Wavelet methods can be tailored to handle the challenge” aren’t terribly helpful without knowing why. They could be interpreted as “arm waving”.”
As I have explained many times on WUWT, assumptions of randomness, “i.i.d.” (i.i.d. = independent, identically distributed), etc. upon which standard statistical inference is based are untenable for many (if not most) natural time series.
Be aware that statistical inference (not to be confused with exploratory data analysis) can also be performed on wavelet results, but given that inference is based on untenable assumptions, why bother (unless one’s funding, boss, or whatever insists on following misguided norms)?
Important Clarification:
There is a fundamental difference between exploratory data analysis & statistical inference.
I do exploratory data analysis, not statistical inference.
Eventually, with increasing understanding of, for example, the climate system, modelers may arrive at a level of understanding where standard assumptions become at least bearable, but mainstream knowledge of systems like climate is presently nowhere near that point.
Elaboration:
Nonrandom effects are being misrepresented as random in models. This is no trivial matter since they are strong effects, many of them involving conditional switching, aggregation criteria (related to resolution, extent, & measurement scale), spatial phase-relations, etc. – i.e. this is where advanced physical geography needs to meet statistics.
Mainstream statistical inference tools can eventually become applicable. It will require a lot of clever multidisciplinary work. The statisticians appear unable to do it alone. They appear to need the physical geographers. And obviously physicists have a role to play, but they appear to be stuck, largely due to the stuff with which the physical geographers can help. It is physical geographers with advanced intuition in the area of spatiotemporal analysis who appear to potentially be the ones who might play a critical role in breaking the current log-jam, but key insights can arise anywhere folks are taking the time to learn very basic principles of advanced physical geography.
Thank you for your comments & interest John.
Best Regards,
Paul.
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Re: BenAW
There is a role for the moon – (so no need for anyone to erect false dichotomies). How does it all fit together? Another day…
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Agile Aspect wrote: “[…] show us the time-frequency plots of the SLC, PDO and AMO […]”
First of all, be careful not to confuse:
a) SCL’ with SCL.
b) PDO with North Pacific SST.
Next, as indicated in the
earlier thread, I have no plans to publicize such results for free.
Regarding your description of what you think I have done:
1) You are not even remotely close.
2) You have a very narrow image of what can be done with wavelet methods. They are far more than a means of generating spectral power plots to explore stationary frequencies. Nowhere have I suggested that my interest is in stationary waves; on the contrary, I have gone out of my way to emphasize nonstationarity. Terrestrial climate has a strong spatial dimension. The last thing the climate world needs is yet another power spectrum that is not even a function of time.
Agile Aspect wrote: “It was the misguided use of wavelets and data mutilation which triggered the response.”
The validity of the SCL curve has been verified by a well-known solar physicist. There is no controversy there.
And again: I have not made any assumptions or claims about the center of mass of the sun. Such notions are pure fiction.
Your attack is absolutely unfounded.
Have you run the analysis? Do you know how?
Best Regards.

Paul Vaughan says:
September 6, 2010 at 3:14 pm
………….
Re: John Finn
As indicated in the
earlier thread, the variable SCL’ is calculated from the following data:
Sunspot Numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
For anyone who understands wavelet methods, I have explained here & here.
Your links say this

As indicated previously:
SCL has been measured using a complex Morlet 2pi wavelet. SCL’ is then found by differencing. (Easily reproduced.)

and this

Clarification:
SCL has been measured using a complex Morlet 2pi wavelet. SCL’ is then found by differencing. There is edge-effect (particularly the last few years). I share your appropriately-cautious views on extrapolation.

Fine. You have not used the standard accepted measurements for SCL. However I would not expect your measurements to be markedly different to the ‘discrete’ min->min measurements.
Perhaps if we work backwards it might help. Could you possibly provide a link to a plot of your measurements of SCL (not SCL’).
Another thing, Paul. A number of years ago I managed to convey the concept of Fourier Analysis to a group of lay people using a simple (very) matlab program. It was later used by lecturing staff as a teaching tool. The fact that you are having problems explaining your analysis suggests you don’t really understand what factors are influencing the analysis. It’s as though you just turn a handle and out pops the result. I may be wrong but that is the impression I get.

Ulric, from the website to which you linked:
“Please note that the start dates for each cycle is calculated using the 13-month smoothed monthly mean sunspot number. One advantage of using this statistical (numerical) approach is that the start month of a solar cycle is the same as the month of the solar minimum. It is possible to use other criteria to separate solar minimum and the start of a solar sunspot cycle, however, which criteria to use and how much importance each is given, unfortunately leaves room for individual opinion.”
Clearly the author isn’t claiming to have had the final say on solar cycle lengths.
Here is what some other folks came up with:
http://web.dmi.dk/fsweb/solarterrestrial/sunclimate/SCL.txt
When I first looked at that a few years ago (before my wavelet algorithms were developed), I found myself disagreeing (using the eyeball method) with many of the summaries. I developed my own set of eyeball measurements at that time.
Yet another approach:
http://jpdesm.pagesperso-orange.fr/sunspots/sfaqs8.html
Indeed, one can devise an infinite number of measures of solar cycle length.
One option is a more objective measure. Wavelet methods have the advantage of not discarding all of the data falling in-between either successive maxima or in-between successive minima.
As I’ve indicated above, the choice of wavelet, the wavelet parameters, & edge-effects (near the ends of the time series) affect estimates.
A Morlet 2pi wavelet has 2pi (i.e. a bit more than 6) waves in a window, so it does a bit of smoothing – i.e. it focuses on coarse structure — something like, “What was solar cycle length like during decades centered on this date?”
If one turns the wavenumber down, the smoothing is reduced and one gains finer resolution as a function of date, but it is important to remember that the wavelet sees all of the data (i.e. sunspot number for every month) as it slides, not just successive minima. If one turns the wavenumber down too far, results become unstable – (an “admissibility” issue arises – far too technical for this thread). If one turns the wavenumber up high, one approaches an average value for the whole series.
The Morlet wavelet is a favorite choice of many researchers and Morlet wavenumber=6 is a fairly conventional choice. (I’m a bit higher at 2pi, a choice which eases interpretation.) At a wavenumber of 6 (or nearby 2pi), the wavelet is seeing adjacent cycles. This, along with the use of all of the data, accounts for the discrepancies which you have noted between different estimation methods.
If one runs the analysis with a lower wavenumber, they will get more localized results. I have run such analyses. I considered addressing wavelet parameter variation in this post, but it was more important at this stage to keep the focus on the differences between PDO & North Pacific SST.
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John Finn, you may find that I have addressed your concerns in my response to Ulric (immediately above).
I have written my algorithms from scratch and played around extensively with settings & diagnostics to see what affects what. In the process, I discovered that wavelet methods are far more flexible than what most authors note. Most practitioners appear unaware of the potential.
My comments here are no substitute for readers’ independent conceptual understanding. I encourage you to carefully study the info at the 2 links which I have provided. If & when I have funding for it, I’ll write up a brief intro course. (My current set of obligations makes it infeasible to volunteer such an effort.)
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vukcevic, I see (from your latest graph) that you’ve found this already, but I’ll reiterate it for the benefit of others.
1854+ PDO series:
ftp://eclipse.ncdc.noaa.gov/pub/ersstv3b/pdo/pdo.1854.latest.situ.v3b.ts
The North Pacific SST I’ve used is ERSSTv3b from KNMI Climate Explorer. It is certainly “interesting” to see how ERSSTv3b differs from HADISST. (Initially I wondered if Bob Tisdale had made a mistake, but it’s just that he used HADISST. [I realize many WUWT readers consider use of anything from Hadley a mistake.])
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Thanks to all who have commented.

Bob, thanks for the notes.
Ulric, I’m organizing some files that compare different SCL & SCL’ measurements. Preliminary results show good agreement with Morlet wavelet results for lower wavenumber. 2pi is capturing higher-timescale patterns. I will consider presenting some graphs when the material is organized. I can’t promise when that will be.

John Finn wrote: “My interpretation is that the wavelet analysis has detected a shortening of the solar cycles as early as ~1895”
Careful. SCL’ remains in positive territory for a few more years beyond that. (You appear to be thinking about the rate of change of the rate of change – i.e. the 2nd derivative, which does appear to have turned negative ~1895.)
Also, bear in mind that lengthening can occur when cycles are short and that shortening can occur when cycles are long. There’s no paradox there.
Friis-Christensen, Lassen, & Thejll were completely off my radar when I came up with the results which I have presented. Comments appearing in this 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).
Perhaps they were looking at the right variable, but not thinking about differential equations? Much physics involves differential equations, so it seems pretty common sense to me that we need to look at integrals & higher derivatives.
John, thanks for your comments. I will take them into consideration as I continuing drafting materials for future presentation.

<tallbloke says:
September 5, 2010 at 11:54 pm

Those of us living on the edge of it appreciate the focus, it affects our weather and our fishing. 😉
[Durn sockeye salmon didn’t read the memo from doomsayers – they are returning to the Fraser River system this year in numbers 15:1 over last year, best in a century.
(Sockeye returns were poor last year but other salmon strong.
I have not looked at stream flow and lake levels inland which must affect survival of young fish and of those returning to spawn – that will depend on precipitation timing including melting of the winter’s snowpack which depends on temperatures.
Sockeye need to get into lakes, other salmon don’t.)
Seems like another subject “scientists” don’t understand adequately. 🙂