Guest post by Paul Vaughan, M.Sc.
Awhile back I drew attention to temporal patterns shared by the <i>rate of change</i> of solar cycle length (SCL’) and the Atlantic Multidecadal Oscillation (AMO). (See here.)
Correspondence I received later alerted me to the existence of fairly widespread misunderstandings about fundamental differences between the following:
a) Pacific Decadal Oscillation (PDO).
b) North Pacific SST (SST = Sea Surface Temperature).
Some folks, thinking of the PDO, seemed troubled by a <b>mis</b>perception that the Atlantic tracks SCL’ <i>much</i> better than the larger Pacific.
Supplementary graphs may help motivate efforts to overcome misunderstandings:
The North Pacific & Solar Cycle Change
Paul Vaughan, M.Sc. – Sept. 4, 2010
Awhile back I drew attention to temporal patterns shared by the <i>rate of change</i> of solar cycle length (SCL’) and the Atlantic Multidecadal Oscillation (AMO). (See <a href=”http://wattsupwiththat.com/2010/08/18/solar-terrestrial-coincidence/”>here</a>.)
Correspondence I received later alerted me to the existence of fairly widespread misunderstandings about fundamental differences between the following:
a) Pacific Decadal Oscillation (PDO).
b) North Pacific SST (SST = Sea Surface Temperature).
Some folks, thinking of the PDO, seemed troubled by a <b>mis</b>perception that the Atlantic tracks SCL’ <i>much</i> better than the larger Pacific.
Supplementary graphs may help motivate efforts to overcome misunderstandings:
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Bob Tisdale, Please identify the source of the North Pacific data smoothed in the following graph: http://i56.tinypic.com/t9zhua.jpg . If possible, please link directly to the data. Thank you.
The Morley wavelet is essentially a sine wave times a gaussian when used to represent smooth a 1 dimensional time series.
Typically, the purpose of a Morely wavelet is look at the two dimensional phase plot – or the wavelet power spectrum.
Without knowing how the smooth curve relates to the original data, the frequency content and gaussisan spread of the fitted curve, the wavelet power spectrum of the data, and how the wavelet weights were clipped in order to generate a smooth curve representing the data, it’s art.
And I disagree with the implicit assumption that all physical processes occur on the same time scale as the rotation of the Sun’s center of mass.
How’s about some graphical fun with DMI80N?
Ok.
http://www.robertb.darkhorizons.org/TempGr/meanT_2010vs58-09.jpg
How 2010 80N temps are running compared to the whole spectrum of 1958 – 2009.
Been meaning to do this for some time.
Made a few changes to the 2009 & 2010 DMI 80N images for the composite. They changed thier legend which altered the scale and continued into the next year which stretched the timeline.
Fixed those issues and expanded the image 200%.
http://www.robertb.darkhorizons.org/TempGr/meanT_2010vs58-09.jpg
Highlights how cold it was up there this summer.
I was wondering if Paul had any particular reason for focusing on the north Pacific. How much inflow/outflow does the Bering strait have compared to the Fram Strait? Is that a factor in the better match between SCL’ and North Pacific than SCL’ and North Atlantic?
Paul Vaughan says: “Please identify the source of the North Pacific data smoothed in the following graph: http://i56.tinypic.com/t9zhua.jpg . If possible, please link directly to the data. Thank you.”
The dataset is HADISST and it’s available through the KNMI Climate Explorer.
http://climexp.knmi.nl/selectfield_obs.cgi?someone@somewhere
I used the coordinates 20N-65N, 100E-100W for the North Pacific subset, north of 20N. (The northern limit of 65N is the latitude of the Bering Strait. North of that is the Arctic Ocean.) To detrend the data, I let EXCEL determine the linear trend and I had it list the equation. Then using the slope listed in the equation, I reproduced the linear trend line and subtracted the linear trend from the North Pacific SST anomaly data. The result is the detrended North Pacfic SST anomalies.
tallbloke says: September 5, 2010 at 11:54 pm
……………..
As far as I remember the Bering strait flow is maily into the Arctic and about one Sv, while the Greenland-Scotland ridge is bidirectional with about 8 and 9Sv respectively (?).
I think is just matter of the Pacific’s size and existence of two (on each side of the Equator) large relatively self contained circulation systems. The Pacific’s central areas of the huge water mass are far less affected by the distant continental and more volatile temperatures. In comparison the Atlantic is more chaotic, and mainly affected by the bi-directional Arctic flow.
http://upload.wikimedia.org/wikipedia/commons/6/67/Ocean_currents_1943_(borderless)3.png
Paul Vaughan says:
September 5, 2010 at 6:19 pm
rbateman wrote: “They cross each other, they run parallel with each other in unison or on opposite sides of a gap […]“
One can find such relations for dozens upon dozens of pairs of terrestrial climate variables. The keys are things such as spatiotemporal aggregation criteria, integration over spatiotemporal harmonics, eddies/back-eddies/turbulence at a variety of spatiotemporal scales, etc. – i.e. this is the stuff of advanced physical geography.
Conventional statistical methodology is inapplicable. The assumptions are violated.
Wavelet methods can be tailored to handle the challenge. The stuff I’ve been doing is not even so much as a speck on the tip of the iceberg of what will be done with wavelets in the future.
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”. In an earlier post you said
Important:
“Eyeballing” methods based on ~11 year steps between either maxima or minima ignore the vast majority of the data. Wavelet methods utilize all of the data
The data used in your analysis is, as far as I am aware, SCL (or SCL’) and North Pacific SST. What data does the wavelet analysis utilise that “conventional statistical analysis” does not.
Re: Agile Aspect says:
September 5, 2010 at 9:58 pm
Your post is more helpful and seems to make sense.
Paul Vaughan says:
September 5, 2010 at 5:05 pm
Bear in mind that the wavelet is operating on monthly data and that it is a complex wavelet (i.e. it has both a real & imaginary part – [this is how phase information is extracted]).
………………………………………………..
Maybe someone else would like to plot the rate of change in solar cycle length;
SC23 9.66yrs
SC22 11.58
Sc21 10.25
SC20 11.66
SC19 10.42
SC18 10.17
SC17 10.42
SC16 10.08
SC15 10
SC14 11.5
SC13 11.92
SC12 11.25
SC11 11.75
SC10 11.25
Why is the graph curve rising from SC15 to SC17 while the cycles are getting longer?, why is there not a bigger drop from SC22 to SC23 ? there is a greater difference in length between 22 and 23, than 14 and 15.
David Archibald says: September 4, 2010 at 8:43 pm
What would it look like if you extended the solar cycle length line for Solar Cycles 24 and 25, making them each 12 years long as per Solar Cycles 5 and 6 of the Dalton Minimum.
No idea what Paul can come up with, (my) geomagnetic algorithm gives an indication of the PDO’s future movement, which is not particularly exciting or different to what might be expected, but here it is anyway for the record.
http://www.vukcevic.talktalk.net/PDOa.htm
vukcevic says:
September 6, 2010 at 4:54 am
Extreme range seasonal forecasts will pick up on the large year to year differences, and show exactly which way the trend will wiggle next.
See what yearly PDO is like in comparison with winter CET, and then using a 179yr and 1 month look back, estimate what the string of cold N.H. winters from 2014 to 2020, will be doing to the PDO.
Ulric Lyons & John Finn,
Here are the links you need:
1) Wavelets:
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
2) Sunspot Numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
Best Regards.
Agile Aspect,
Wavelets do more than what you suggest.
Suggested: Run the analysis.
See here for info on time/timescale trade-off:
http://web.archive.org/web/20080603223427/http:/www.clecom.co.uk/science/autosignal/help/Continuous_Wavelet_Transfor.htm
(I suspect you may already know this, but others might appreciate the link.)
You will find that the results are robust against variation of wavelets & wavelet parameters.
Thank you for joining the discussion. I encourage you to present some of your own results, especially any which you have developed using wavelet methods.
Best Regards.
vukcevic,
Please clarify what lagging you have done for curves labeled “ETHZ” & “NOAA” on your plots here http://www.vukcevic.talktalk.net/PDOa.htm . If you can link to the data &/or succinctly describe the data, that will also be appreciated. Thank you.
tallbloke, it’s just avoiding the cart-before-the-horse thing – i.e. if this PDO vs. North Pacific SST confusion is not cleared up, folks aren’t going to understand when I start presenting more results on this theme.
—
Bob Tisdale, as often happens, your notes & graphs have led to a key insight. Thank you.
Elaboration for anyone trying to follow along:
Compare North Atlantic & North Pacific HADISST & ERSSTv3b. Data are available via KNMI Climate Explorer.
For preliminary visualization I recommend using annually-smoothed raw data rather than anomalies, but generally speaking this isn’t a huge deal (and often context will dictate what is most appropriate – e.g. when using wavelets, use raw unsmoothed data, not anomalies).
Bob, I would be interested in hearing your general impressions of HADISST data quality versus that of ERSSTv3b.
Regards.
Paul Vaughan says: September 6, 2010 at 8:41 am
If you can link to the data &/or succinctly describe the data, that will also be appreciated. Thank you.
I intend to write a short paper on lines of :
http://www.vukcevic.talktalk.net/NATA.htm
with all necessary details.
When posting this I should have addressed the following:
Agile Aspect wrote: “And I disagree with the implicit assumption that all physical processes occur on the same time scale as the rotation of the Sun’s center of mass.”
Clarification:
I am making no such assumption.
When I search in-page for “center of mass”, I see that no one other than Agile Aspect has used this phrase. “Rotation” also shows up only once – i.e. in Agile Aspect’s post.
Agile Aspect, can you clarify? Was your comment motivated by a general sense you have developed from reading research articles & blogs? Or was it motivated by something specific to this thread?
Thanks if you can clarify.
vukcevic, thank you for your reply. I want to suggest that you indicate very clearly any temporal lags on your graphs. (My concern is about spatial phasing vs. temporal phasing.)
@ur momisugly Paul Vaughan says:
September 6, 2010 at 8:22 am
Ulric Lyons & John Finn,
Here are the links you need:
1) Wavelets:
…………………………………………………………
That does not address my points;
Why is the graph curve rising from SC15 to SC17 while the cycles are getting longer?, why is there not a bigger drop from SC22 to SC23 ? there is a greater difference in length between 22 and 23, than 14 and 15. And why does the line not go up at SC`s 13/14 ? as SC14 is shorter than SC13.
Paul Vaughan says:
September 6, 2010 at 8:22 am
Ulric Lyons & John Finn,
Here are the links you need:
1) Wavelets:
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
2) Sunspot Numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
Best Regards.
Paul
Why have you provided a link of sunspot numbers. I realise there is a relationship between SSN and Solar Cycle Length (SCL) but the SCL is well documented. Are you calculating a SCL which is different in some way to the accepted cycle lengths.
I’m still not clear what data you’ve used .
Paul Vaughan says: September 6, 2010 at 10:21 am
(My concern is about spatial phasing vs. temporal phasing.)
I suspect the second is consequence of the first, resulting from the circular flow of the N.P.’s currents.
Ulric Lyons,
Here are the links you need:
1) Wavelets:
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
2) Sunspot Numbers:
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/INTERNATIONAL/monthly/
With a mastery of link#1, your questions will dissolve.
Best Regards.
—
AusieDan & Orkneygal,
As indicated: If/when I secure sufficient reliable funding, elaboration & catering (for audience segments) may become more feasible.
Until then: It will be whatever balances with indispensable competing obligations. The choice is between sharing nothing and sharing strategically at a reduced pace. I choose the latter.
—
Stephen Wilde, I addressed your original comments here. I will offer a bit more: Of course clouds, pressure, wind, temperature, etc. are interrelated. I would advise (1) against underestimating the role of the atmosphere and (2) considering the alignment, acceleration, & integration of recurring phenomena with respect to annual terrestrial cycles (keeping in mind that there are many). [Relationships involving the hydrologic cycle, for example, reverse seasonally for large portions of the globe, so phase-acceleration (which switches relations as seasonal thresholds are passed) is not irrelevant to integrals.] Variables to look at: earth orientation parameters, geomagnetic aa index, solar wind. [The SCL’ pattern is buried in all of the preceding. Also, I have recently posted this request (which may interest participants like vukcevic & tallbloke in particular). Elaboration will have to wait.]
I wish you efficiency in your synthesizing efforts Stephen. Thank you for your comments.
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.
http://www.vukcevic.talktalk.net/2pi.gif
This may give you unexpected result. I have no idea if Paul is doing this, but I have used it in past for processing of electronic signals.
When posting this I should have addressed the following:
Agile Aspect wrote: “And I disagree with the implicit assumption that all physical processes occur on the same time scale as the rotation of the Sun’s center of mass.”
Clarification:
I am making no such assumption.
Then show us the time-frequency plots of the SLC, PDO and AMO and then comment.
When I search in-page for “center of mass”, I see that no one other than Agile Aspect has used this phrase. “Rotation” also shows up only once – i.e. in Agile Aspect’s post.
The Hale cycle is 22 years – roughly the time it takes the Sun’s center of mass to rotate.
Agile Aspect, can you clarify? Was your comment motivated by a general sense you have developed from reading research articles & blogs? Or was it motivated by something specific to this thread?
It was the misguided use of wavelets and data mutilation which triggered the response.
Using the FFT as an analogy for the wavelet transform, essentially you FFT’d the signal, clipped the frequency spectrum in order to produce a smoothed cure, and then performed an inverse FFT transform back to amplitude-time curve.
That is, you threw away the frequency content – the primary reason for the calculation – which, incidentally, didn’t stop you from making frequency generalizations.
In the wavelet transform, you clipped the wavelet coefficients before you performed the inverse transform. Otherwise you should have gotten the exact same signal back that you fed into transform. This clipping of the coefficients typically requires a separate paper detailing the statistics.
Note, my comments never show up in comments – which is what I read. Today my web browser happened to be parked on the original article so if I don’t respond it’s flawed blogging software.
Paul,
Thanks for the extra information. It helped.