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:
Interesting finding. I did a brief excursion into PDO and found a ‘correlation’, which of course does not mean causation.
http://www.vukcevic.talktalk.net/PDO.htm
There is also a tenuous link between GMFz and solar activity.
I’m sure it’s interesting, and it’s certainly succinct, but as a layman [?intelligent ditto?], can I request some reduction in jargon?
Is the PDO confined to 20N to 70N?
And might 260E be 100W in ‘real’ Longitude?
> Some folks, thinking of the PDO, seemed troubled by a misperception that the Atlantic tracks SCL’ much better than the larger Pacific.
[Thanks for making it easy to save the bolding and italics!]
This sentence confuses me – it has the PDO (clear), the Atlantic (SST? AMO?), and the Pacific (SST? PDO?).
Its followed by graphs of the North Pacific SST and PDO. No Atlantic. SST or AMO.
What jumps out to me, is how the sea surface temperature graph completely mirrors the global temperature graph – and how those both, in turn, mirror the rate of change of solar cycle length (SCL’) … Aha, this looks like a much-needed primary correlation to solar activity… Now I just want to know how far, when UHI is reasonably subtracted, the global temperature record really mirrors the records of SST and SCL’ and rate of change of Length of Day (LOD’) up to the present time – because if so, surely this is where we really need to look hard, to find/clarify the driving mechanism for climate.
Can anybody produce that chart comparison? Willis?
Re: Autochthony
Regarding wavelet methods: I left some (down-to-earth) notes here.
For a layman’s overview of climate, I can refer you to Bob Tisdale’s website:
http://bobtisdale.blogspot.com/
If Bob is around, perhaps he can point directly to articles most relevant to this thread. (If so, thank you Bob.)
Best Regards.
Echoing Autochthony’s comment – your last two posts have been very interesting and important clues as to astrophysical climate mechanisms; but they are much too short – just a paragraph.
Why? This is not Twitter – you are allowed more than 128 characters.
Just throwing us bones to tantalise us? Why not some introduction and background, and some conclusions and pointers for future work, to sandwich the facts and figures?
Combining the morsels of stark data given in the last two posts, one could draw the odd conclusion that the AMO drives North Pacific SSTs (or vice versa). Clearly it is more likely that both share an astrophysical forcing driver.
Paging Mr. Tisdale…
Why does it appear that SST is leading SCL, particularly 1905 – 1930? A reasonable leap of logic would suggest that some missing third thing is affecting both SST and SCL. Where are all the outer planets while this is going on?
Fascinating, but two caveats. Maybe three:
(1) “Lump matching” over a short run can show order where none exists over the long run.
(2) Derivatives [dx/dt] entail loss of information.
And I don’t immediately see a physical mechanism that would cause SCL variation rate to affect SSTs.
Re: Autochthony and further to this…
Regarding PDO definition:
Data:
ftp://eclipse.ncdc.noaa.gov/pub/ersstv3b/pdo/pdo.1854.latest.situ.v3b.ts
Alternately:
http://jisao.washington.edu/pdo/PDO.latest
I have used the former in this presentation. From the latter page, note the following:
“[…] the PDO index, derived as the leading PC of monthly SST anomalies in the North Pacific Ocean, poleward of 20N. […]”
PC = Principal Component — a concept from multivariate stats. (I may elaborate more on such techniques later…)
You are correct that 260E = 100W.
“Supplementary graphs may help motivate efforts to overcome misunderstandings:”
Clearly a teacher speaking here. I have 48 years experience with educator speak.
Thanks for the graphs! I am hoping you do not have an issue with my saving them for future reference? Also, I echo Lucy’s reasoned points. As well as the following thoughtful intimations;
“Combining the morsels of stark data given in the last two posts, one could draw the odd conclusion that the AMO drives North Pacific SSTs (or vice versa). Clearly it is more likely that both share an astrophysical forcing driver.”
You have the goods. Put your foot in it! Matt that sucker! Let ‘er rip. Blow our minds!
Cheers!
What Phlogiston said. This is laconic to the point of unintelligibility.
Re: Ric Werme
As indicated, AMO was featured in the earlier article.
I second the request for a longer article with a bit more explanation. Although many here at WUWT are well acquainted with the subjects that are discussed, there have been many new readers since the Climategate e-mails.
Please explain terms and abbreviations so interested laypeople joining us have a chance of understanding.
A tip to article writers from my technical writer husband. Run your article by a lay person. If he understands it great. If he asks questions you now know where to beef up the article.
the technical writer’s guinea pig
In select response to a few comments (e.g. here & here):
Regarding physical drivers:
As I have indicated many times in the past:
I leave the physics to physicists.
Elaboration:
I am raising questions, not providing answers. Climate investigations are relying far too heavily on untenable modeling assumptions — for example: misapplication of inapplicable assumptions of standard statistical methodology – and to make it worse: with insufficient [& in many cases completely absent] diagnostics. Spatial phase-relations are not irrelevant to global temporal analysis due to “Simpson’s Paradox”. There is no use putting the cart before the horse, so it is back to fundamentals. A multidisciplinary effort appears necessary.
–
Regarding succinctness:
Many people are busy. They need the soundbite and ski (skim & skip) through details. (Details can be discussed in the comments section by those with extra time.)
No less importantly:
Details arising in the last discussion were, in part, responsible for the theme of the current post. Without first clearing up the misunderstandings about what PDO is and what it is not, there seemed to be little hope of having an audience prepared for future posts in this series.
Re: Michael Larkin & Gail Combs
The presentation style is deliberate.
In part, I base the following comments on years of experience running online forums:
There are many voices in the choir and the audience is not solely political. At this point in time an expanded article would undermine the core message. There may come a time when elaboration will be both feasible & strategic — for starters, if sufficient funding becomes reliably sustainable.
—
Re: dp
Important:
That’s not a temporal lag. It’s related to spatial phasing.
Bear in mind that so far we’ve only looked at the North Atlantic & North Pacific in this series. (This is just how the story begins…)
Also dp:
We have not yet even gotten into variation of wavelet parameters.
Suggestion for anyone with the tools:
Run the complex Morlet 3pi/2 analysis and take a look at the results for the interval dp singles out.
(I may include this analysis in a future article addressing the Southern Oscillation, Southern Ocean, Southeast Pacific, &/or Indian Ocean.)
Posted yesterday (Sept. 3, 2010):
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
Convenient timing — thanks Bob.
Readers will note that Bob dispels many of the myths about PDO.
(Due to my investigations of EOP [EOP = Earth Orientation Parameters] I have a few reservations, but at present they are neither worthy of my time nor Bob’s, as I have more work to do before such an exchange can be fruitful.)
Note the comment left by Bill Illis, who often raises highly worthwhile points.
Is the PDO index useless? No. Rather:
Sensible interpretation of multivariate statistics requires (a) an intimate understanding of the impact of abstract mathematical assumptions, including (b) the application of a battery of post-analysis diagnostics.
In the specific case of PDO vs. North Pacific SST:
Don’t be surprised if thorough diagnostics reveal an instance of what statisticians call “Simpson’s Paradox”.
See for example Bob’s illuminating Figure 18:
http://i52.tinypic.com/9lgxlg.jpg
[If this figure is surprising, this may indicate insufficient conceptual understanding of PCA (& factor analysis more generally).]
—
Re: INGSOC
Good instincts! I do have experience teaching stats – (and yes I am restraining the pace at which new material is released…)
Thanks for the supportive comment!
Best Regards.
I don’t understand the graphs or what the point of this posting is.
Could someone please explain for me?
Paul, thanks very much. I have copied your second graph from above into my next climate presentation. You have provided a part of the physical link in Friis-Christensen and Lassen theory.
Your graph has predictive power. 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? I think you’d get a sea surface decline of 1.5 to 2.0 degrees by 2020.
Once again, great stuff and thank you.
Since comments have now moved to this thread I’d better repeat my post from late in the first thread and which might otherwise be missed by someone who might want to attempt a reply:
Interesting stuff and at present somewhat beyond my capability to comment constructively.
However the mechanisms that give rise to oceanic and solar cycles are very important to top and tail my attempt at setting out a coherent climate overview and describing the way the troposphere then deals with (possibly independent) influences from within the oceans and from variable solar activity.
However I do have some questions.
How significant are all these potential mechanisms compared to the variability that the sun and oceans would be quite capable of setting up on their own within the climate system from just changing the global albedo via latitudinal shifts in all the main cloud bands and thus introducing variability of solar shortwave input into the oceans ? Then the internal structure of the oceans and density/ salinity/ temperature driven cycling movement within them would do the rest.
Couldn’t the sun and oceans pretty much do it all on their own ?
Wouldn’t all those potential mechanisms just provide a modulating effect possibly a whole order of magnitude weaker ?
David Archibald says: September 4, 2010 at 8:43 pm “…Your graph has predictive power. What would it look like if you extended the solar cycle length line for Solar Cycles 24 and 25…”
Since the SCL function variable is based on solar cycle shape (apparently as smoothed by some time-average algorithm), based on what I see here, the “predictive” period is no greater than the past solar cycle, less a residual portion of whatever averaging period was used to smooth the raw solar data, at least sufficient to avoid taking the slope at a discontinuity. Using putative SC24/25 curves would be employing extrapolations to perform an extrapolation. Without a cited physical mechanism, the predictive power would therefore seem to be close to zero.
Fascinating curve matching exercise, though, and there may be something useful here. I’m just not sure what it is yet.
Re: Orkneygal
Since not long after I began climate investigations in late 2007, I have believed that something terribly simple has been right under the noses of physicists & climate scientists – but overlooked — for example due to inappropriate analysis, such as reliance on untenable assumptions, masking due to spatiotemporal aggregation criteria, failure to appreciate derivatives & integrals, or whatever – i.e. due to lack of attention to fundamentals. To explore what might have been overlooked, I spent much of the last 2.75 years auditing the work of others [including calculations], while also pursuing ideas arising during audits.
There have been several attempts to explain “60 year” natural climate “cycles”. The thing is: Empirical data reveal the cycles to be nonstationary – i.e. they don’t “stay” 60 years long.
I leave the physics to physicists. (My background is in landscape ecology, physical geography, statistics, engineering, & forestry.) However, I have left an empirically-motivated suggestion:
http://wattsupwiththat.com/2010/08/18/solar-terrestrial-coincidence/#comment-475401
Further elaboration at this point in time would be both burdensome & premature. The practical points [from a layperson’s perspective] might be that (a) an alternative line of inquiry into natural terrestrial oscillations is under development and (b) it does not rely on notions of stationary “60 year cycles”.
–
Re: David Archibald
I will reiterate that the shared pattern involves rate of change of solar cycle length. Thus, anyone using the shared pattern as a basis for prediction based on 2 consecutive 12 year cycles would predict no change (since 12 – 12 = 0).
Personally: I will leave forecasting to forecasters for now. My interest remains in studying recorded patterns.
Thank you sincerely for your kind & encouraging comments David – much appreciated.
I thought I had some idea of movements in temperature and even in the various ocean patterns (PDO etc). I also thought that I had some training and understanding of ststistics (most CA posts for example are at least basically understandable to me).
But Paul Vaughan, you are far too criptic for me, with blizzards of initials and references soe where else, instead of sentences. I understand that you are a scientist, used to writing for fellow scientists, who share a common understanding. I also realise that you cannot, or will not, change your preferred writing style to suit those of us with different training and experience.
I believe that there are a few people reading this thread who DO understand quite clearly. I sense that it contains very interesting information and is pointing towards an important hypothesis, whic may be, or may not be, both valid and earth shaking.
Can somebody please help out, by rewriting this post in language which is more understandable, not necessarliy to the general public, but at least to the large number of people at WUWT who are knowledgeable about climate matters, but who are not experts in Paul’s field.
We would be very grateful.
David Archibald says:
September 4, 2010 at 8:43 pm
Paul, thanks very much. I have copied your second graph from above into my next climate presentation. You have provided a part of the physical link in Friis-Christensen and Lassen theory.
How?
Your graph has predictive power. 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? I think you’d get a sea surface decline of 1.5 to 2.0 degrees by 2020.
No you wouldn’t. The graph might even predict a rise because SC 23 was ~12.5 years long, i.e. the rate of change would be positive (I’m assuming shorter is positive and longer is negative).
Once again, great stuff and thank you.
It doesn’t support your work, David.
dp says:
September 4, 2010 at 4:12 pm
Where are all the outer planets while this is going on?
The Green curve in the graph at the link below shows the combined effect of the motion of (predominantly) the gas giants on the up-down motion of the sun’s equatorial plane relative to the centre of mass of the solar system smoothed over two Jupiter orbits. The blue curve is changes in Earth’s length of day. http://tallbloke.wordpress.com/2009/11/29/planetary-solar-climate-connection-found/
It does seem to bear some relation to Paul’s plot of rate of change of solar cycle length. Thanks for an interesting post Paul.
Re: jorgekafkazar
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.
Hi Paul
Differentiating could be a useful tool. Prompted by your SCL-SST graph, I applied it to the North Pacific GMFz (Δt=12years) and by delaying the result by 12 years, I got reasonable match for the PDO.
http://www.vukcevic.talktalk.net/PDOz.htm
p.s. for PDO I normally use the washington.edu data (1900 – ), do you have link for 1855 – ?
Has the influence of the moon been ruled out in climatestudies?
Seeing the effect the moon has daily on the oceans (and thus the atmosphere),
and seeing the change in its orbit, combined with the gravitational pull of the sun this should have at least some effect?
The following link has a study into the moon cycles and how they could influence climate:
http://globalweatheroscillations.com/GWGCNCF/index.htm
I would like to see some discussion on the merits of this study.
Paul Vaughan, M.Sc.
Thank you for responding to my pitful cry for help.
Your response was basically lost upon my tiny mind, since your explanation didn’t resonante with me.
Now, I think I understand what the graphs show
scl 2pi does not track with PDO1a.
That means the graphs provide no insight into the real world, right?
Your charts are a send up of, right?
Is the point you are tying to make that we need to understand more about the relationship between SST and Atmospheric Pressure?
Or is that too simplistic?
Paul Vaughan says: “Since not long after I began climate investigations in late 2007, I have believed that something terribly simple has been right under the noses of physicists & climate scientists – but overlooked…”
I get the same feeling, Paul. The more “climatologists” dance widdershins around the hockey stick, defending the indefensible, the more I suspect we’re being diverted from something even shakier and more fundamental.
@ AusieDan says:
September 5, 2010 at 12:25 am
“Can somebody please help out, by rewriting this post in language which is more understandable,”
Paul is just trying to relate the length of solar cycles to see surface temperatures and temperature differences across large ocean areas, known as oscillators.
Meanwhile, I would not trust his orange line representing solar cycle length, here is the data on solar cycle length, see what you think, I reckon he is up to a bit of rather fishy wiggle matching; http://www.solen.info/solar/index.html
Ulric Lyons says:
September 5, 2010 at 4:41 am
Meanwhile, I would not trust his orange line representing solar cycle length, here is the data on solar cycle length,…
I agree. There is something odd about the SCL’ line. The change (in years) in SCL over SC10-14 is as follows.
sc10 -> sc11 +0.5
sc11 -> sc12 -0.5
sc12 -> sc13 +0.6
sc13 -> sc14 -0.4
SC14 ended in August 1913 so I can’t quite understand where the huge dip in Paul’s graph comes from which starts in ~1895 and ends in ~1913. There is a SCL change of -1.5 years from sc14 -> sc15 but my understanding of “solar length theory” is that shorter cycles cause warming ; longer ones cooling. I suppose the SCL’ for SC14/15 could have produced the post 1913 warming – but that still leaves no explanation for the earlier dip.
It is just possible that you could get some kind of fit using post-1913 data only – but it’s a stretch as there would then be no explanation why a -1.5 year change in SCL in 1913 produced a sharp rise in SST but a 1.2 year change in SCL in 1964 didn’t produce a fall of similar magnitude (I am using start/end dates consistently).
I think it would be helpful if Paul explained exactly what he’s done – or has he already done this in previous thread. Apologies to him if he has.
chart 2 is definitely a beauty, i haven’t seen something this nice that suggests the celestial climate driver is the primary driver since Landscheidt plotted AP index to global temperature trends. Somebody should run some stats on chart 2 and publish it.
Ulric Lyons says: September 5, 2010 at 4:41 am
John Finn says: September 5, 2010 at 5:55 am
……………………
You can always try PDO vs magnetic field instead using 11 or 12 year difference (for one solar cycle).
Here is GMFz data file:
http://www.vukcevic.talktalk.net/GMFzNP.txt
Subtract GMFz for year 1800 from 1812 for the12 year delay (or 1811 for 11 y diff.) , enter the difference at 1800, and so on until 1998 ( 2010-12), plot and compare to the PDO graph.
http://www.vukcevic.talktalk.net/PDOz.htm
Phlogiston, INGSOC: Regarding, “Combining the morsels of stark data given in the last two posts, one could draw the odd conclusion that the AMO drives North Pacific SSTs (or vice versa).”
Always best to compare the two SST datasets directly, because they do not correlate. The data has been smoothed with a 121-month filter in the following graph. I detrended the North Pacific SST anomalies (north of 20N) to help the comparison (since the AMO is detrended North Atlantic SST anomalies). And I threw in NINO3.4 SST anomalies just in case you were interested (it has very little trend so it wasn’t worthwhile detrending it).
http://i56.tinypic.com/t9zhua.jpg
There are parts of the North Pacific that do correlate with the AMO according to NOAA:
http://i38.tinypic.com/10f3yg3.jpg
The map is included in this post:
http://bobtisdale.blogspot.com/2010/08/introduction-to-enso-amo-and-pdo-part-2.html
vukcevic says:
September 5, 2010 at 7:47 am
Ulric Lyons says: September 5, 2010 at 4:41 am
John Finn says: September 5, 2010 at 5:55 am
……………………
You can always try PDO vs magnetic field instead using 11 or 12 year difference
… and eventually we might come up with something that fits. Isn’t this the problem. Try enough combinations and you’re bound to get one that looks convincing.
@ vukcevic says:
September 5, 2010 at 7:47 am
I see from the graph that the PDO and N.Pacific have been moving in opposition for a couple of decades every 45yrs; http://wattsupwiththat.files.wordpress.com/2010/09/northpacificsst_pdo.png
John Finn
There is a good reason for it. The AMO has 70% correlation with the Arctic GMF
http://www.vukcevic.talktalk.net/NFC1.htm
It would not be odd if the PDO, which arises in the north Pacific, is correlated to its GMF too.
Ulric Lyons
I would not be surprised if it is something to do with the circulation ‘loop time’ of the N.Pacific currents.
http://upload.wikimedia.org/wikipedia/commons/6/67/Ocean_currents_1943_(borderless)3.png
Ulric and John Finn: Paul isn’t plotting solar cycle length in fig2. He is plotting rate of change of solar cycle length.
Paul Vaughan says:
September 4, 2010 at 6:42 pm
“The presentation style is deliberate.”
Colour me gobsmacked.
@ tallbloke says:
September 5, 2010 at 12:45 pm
Ulric and John Finn: Paul isn’t plotting solar cycle length in fig2. He is plotting rate of change of solar cycle length.
………………………………………………
Yes, realized already, so why the big drop at 1895 as John said, there is not that much difference between C13 and C14, the change from C19 to C20 has not been treated so generously, and where is the nearly 2yr difference between C22 and C23 gone then ??
@ tallbloke says:
September 5, 2010 at 12:45 pm
And why does the orange line rise from C15 through to C17, while the cycles are getting longer ?
@ John Finn says:
September 5, 2010 at 11:05 am
… and eventually we might come up with something that fits. Isn’t this the problem. Try enough combinations and you’re bound to get one that looks convincing.
………………………………………..
The sunspot cycle is not the solar variable driving this anyway. Most land surface temperatures move in unison with the solar wind speed, but regional SST`s move in opposition to the solar signal around the solstices, moderating land temperature extremes towards polar regions, and at the equatorial regions.
As indicated previously:
SCL has been measured using a complex Morlet 2pi wavelet. SCL’ is then found by differencing. (Easily reproduced.)
As also indicated above, the wavelet parameter (2pi) can be varied. There are also other wavelets (besides Morlet).
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]).
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.
vukcevic, rather than resorting to lags, I would recommend differentiation (not necessarily just once) &/or integration. Also bear in mind the spatial dimension. For example sometimes spatial anti-phase is mistaken for a temporal lag. …But I think you already get the idea. (And clarification: I am speaking in general, not about any specific example.) The challenge with the spatial dimension is the aggregation criteria, which can be varied to detect pattern thresholds. (Physical geographers use the term MAUP [modifiable areal unit problem].)
Ulric Lyons says:
September 5, 2010 at 11:20 am
The convergence/sypathetic/divergence of N. Pacific SST and PDO should remind one of the Arctic/Antarctic Sea Ice doing exactly the same sort of thing. They cross each other, they run parallel with each other in unison or on opposite sides of a gap, and they are doing it with noise attached. A fractalized DNA strand. You might say there is a Climate DNA sequence that needs decoding.
Paul Vaughan says:
September 5, 2010 at 5:05 pm
As indicated previously:
SCL has been measured using a complex Morlet 2pi wavelet. SCL’ is then found by differencing. (Easily reproduced.)
Ok – I’ve see you have mentioned the “complex 2pi wavelet” in an earlier post. Could you now tell us why this is an appropriate method of measuring SCL.
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.
I would like to see more detail on this. SCL refers to the Solar Cycle Length. The SCL is, by definition, a step of ~11 years. What “vast majority of data is being ignored”? What part of the wavelet analysis produces the 1895-1913 dip in SCL’ ?
I apologise for my lack of understanding.
tallbloke says:
September 5, 2010 at 12:45 pm
Ulric and John Finn: Paul isn’t plotting solar cycle length in fig2. He is plotting rate of change of solar cycle length.
Yes I know – that’s why I posted a list of SCL differences between successive cycles. I think Ulric knows it as well.
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.
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.)
@ 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.
Paul Vaughan says:
September 6, 2010 at 11:25 am
With a mastery of link#1, your questions will dissolve.
………………………………………………………………
The questions are still there, why does your line go upwards through cycles 15 to 17 when the cycles are getting longer ?
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.
Bob Tisdale says:
September 5, 2010 at 9:10 am
Thanks, very helpful and interesting – I’ll try to find time to go through the AMO / PDO posts. The color-coded correlation map is thought-provoking.
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.
—
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…
—
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.
—
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.
—
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.
—
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…
—
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.
Ulric, you’re going to have to explore the answer to your own question by varying the wavelet parameters (and, of course, by using all of the data instead of just minima/maxima).
Best Regards,
Paul.
John Finn
All cycles have to be of a similar duration (which is case for the SS anyway). For a sine wave difference between two values = 0, regardless of location. Formula (which I do not have at hand) converts R-L difference to 2π + – θ, in essence it is a comparison (at any point in time) of a given waveform to a sine wave of a particular frequency.
Paul Vaughan says:
September 6, 2010 at 3:14 pm
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.)
………………………………………………….
Solar cycle lengths are here: http://www.solen.info/solar/
(ie the solar cycle is min to min [measured and accepted])
John and I were just eyeballing the rate of change, not the lengths.
I guess my question won`t get a direct answer then……
Paul Vaughan says:
September 6, 2010 at 3:29 pm
you’re going to have to explore the answer to your own question by varying the wavelet parameters (and, of course, by using all of the data instead of just minima/maxima).
…………………………………………….
Solar cycle length is min to min, that is all the data.
vukcevic says:
September 6, 2010 at 3:55 pm
John Finn
All cycles have to be of a similar duration (which is case for the SS anyway). For a sine wave difference between two values = 0, regardless of location. Formula (which I do not have at hand) converts R-L difference to 2π + – θ, in essence it is a comparison (at any point in time) of a given waveform to a sine wave of a particular frequency.
OK – I was going to post to tell you not to bother as I’d thought about it again. Thanks anyway but I feel we are drifitng away from the main point.
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
and this
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.
John Finn says: September 7, 2010 at 1:14 am
…….
You made a good point . If there is a solid physic’s law behind a particular process, even a simple measurement should be able to identify the link. I, as probably many others, resort to more and more complex devices to identify something we think it should or should not be there, which may be true but not necessarily so.
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.
—
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.)
—
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.])
—
Thanks to all who have commented.
Paul, thanks for the link, v3b base has only fractionally higher peak values.
Paul Vaughan says:
September 7, 2010 at 3:43 am
http://web.dmi.dk/fsweb/solarterrestrial/sunclimate/SCL.txt
pretty much the same picture as regards the larger cycle by cycle length difference.
Paul Vaughan wrote: “Bob, I would be interested in hearing your general impressions of HADISST data quality versus that of ERSSTv3b.”
I use HADISST for posts. I don’t use ERSST.v3b.
Both datasets are reconstructions and both try to reproduce past SST patterns in areas of poor sampling by using known patterns from the satellite era. HADISST has the readings reinserted, but I have found nothing in the ERSST.v3b papers that mention that step. NCDC notes that they reinsert surface station data into the interpolated Land Surface data, but, again, they don’t mention a similar step for SST. Is that why ERSST has a more significant dip and rebound in the late 1800s to mid-1900s? Dunno.
You wrote, “(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.])”
Refer to above.
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.
Paul Vaughan says:
September 7, 2010 at 3:43 am
John Finn, you may find that I have addressed your concerns in my response to Ulric (immediately above).
[snip]
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.)
Paul
A simple interpetation of the SCL’ plot would have been sufficient for starters. We can worry about the algorithms used when we have a basic concept of what the analysis has produced.
My interpretation is that the wavelet analysis has detected a shortening of the solar cycles as early as ~1895 – even though the shorter cycle using the min-to-min measurement doesn’t show up until ~1913. This presumably is because you are analysing all the monthly data at all points within the cycle(s).
From this, though, I now assume that you are plotting SCL’ – not minus SCL’. In other words, the generally accepted relationship between SCL and temperature (i.e. shorter=warmer; longer=colder) doesn’t hold. In your plot, a shortening cycle coincides with falling SST.
If this is the case, then it might have been worth mentioning it in your post. Is David Archibald aware of this since he is intending to use your graphic in his presentations. David is very much of the view that longer cycles lead to colder conditions, though he is referring to the absolute length (SCL) rather than SCL’.
Of course, it’s possible that between you, David and Friis Christensen & Lassen you have discovered a link between SCL (or SCL’) and a change in certain weather patterns.
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.
From one of vukcevic’s comments: “[…] resort to more and more complex devices […]”
Not that vukcevic was necessarily referring to wavelets, but I’ll take this opportunity anyway:
One thing I would like to clear up is any notion that wavelet methods are not 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.
Most of the confusion which arose in this discussion was a simple result of participants not realizing that the spacing of the sine & cosine waves can be adjusted to see at varying resolution (Morlet 2pi being a coarse view). As indicated, this is something I was planning to address in the future, opting to initially concentrate focus on the difference between PDO & North Pacific SST. Each of the misunderstandings will fall – and at a manageable pace.
John Finn says:
September 8, 2010 at 2:06 am
Of course, it’s possible that between you, David and Friis Christensen & Lassen you have discovered a link between SCL (or SCL’) and a change in certain weather patterns.
…………………………………………………..
I doubt it, the last longer cycle, SC20, had a very warm 3yrs at the end (1974/5/6) as did the previous longer cycle, SC14 (1911/12/13). The shorter SC 21 had many cold winters, 1977, 1978, 1979, 1982, 19885, 1986.
The short SC15 had more cold episodes than the longer SC14.
Ulric, don’t forget that SCL & SCL’ are nearly orthogonal. You cannot generalize from one to the other. (Do you know what is the correlation between a sine wave & a cosine wave? You might want to consider why differential equations include terms with neighboring derivatives.)
Paul Vaughan says:
September 8, 2010 at 1:47 pm
don’t forget that SCL & SCL’ are nearly orthogonal
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One could easily think so looking at your graph.
Knowing *only that a sine wave is in positive territory does not tell you what a cosine wave is doing. Half of the time it will be positive and half of the time it will be negative. You cannot generalize from one to the other.
<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. 🙂
Thread continued here:
http://wattsupwiththat.com/2010/09/11/solar-cycle-length-its-rate-of-change-the-northern-hemisphere/