Interannual Terrestrial Oscillations

There’s a saying, “timing is everything”. After reading this, I think it is more true than ever. In other news. Paul Vaughn is giving Bob Tisdale serious competition in the contest over who can fit the most graphs into a single blog post. ☺ There is a helpful glossary of symbols and abbreviation at the end of this post that readers would benefit from reading before the essay. A PDF version is also available via link at the end of the article. – Anthony

Guest post by Paul L. Vaughan, M.Sc.

Lack of widespread awareness of the spatiotemporal nature of interannual terrestrial oscillations is perhaps the most paralyzing bottleneck in the climate discussion.

North Pacific Pivot

Elegant factor analyses by Trenberth, Stepaniak, & Smith (2005) concisely chart the limits of linear climate exploration, providing strong clues that the North Pacific is a globally pivotal intersection.

D – T = -SOI (an index of El Nino / La Nina – details below in “Data & Symbols” section)

WUWT readers are well-acquainted with Tsonis, Swanson, & Kravtsov (2007). Recently Wyatt, Kravtsov, & Tsonis (2011b) shared the following on Dr. Pielke Senior’s blog:

“PNA participates in all synchronizations.”

Orientation for ENSO- & PDO-centric readers:

Complex Correlation

Simple linear correlation can do a part-way decent job of summarizing the preceding intrabasin relations, but properties of interbasin & interhemispheric multiscale spatiotemporal relations clarify the need for complex summaries. For example:

Limitations of linear methods are emphasized by Maraun & Kurths (2005). A mainstream audience might not appreciate their beautifully concise section 3 primer, but there’s a simple way to look at interannual spatiotemporal phasing.

The ~2.37 year signal which is so prominent in the equatorial stratosphere is also easily detected in the troposphere, but there’s clearly “something else” contributing to interannual tropospheric variation.

Note that when iNPI’ doesn’t “go with” iAAM & iLOD, it “goes against” them, much like a switch that is either “off” or “on”. Specialists like Maraun & Kurths might speak of coherence and illustrate the nonrandom distribution of phase differences.

Multiscale complex correlation (for example using adjacent derivative based complex empirical wavelet embeddings) can measure complex nonstationary relations where simple linear correlation fails catastrophically. Naive investigators unknowingly encounter Simpson’s Paradox by falsely assuming independence and blindly running linear factor analyses (such as PCA, EOF, & SSA) without performing the right diagnostics.

Northern Hemisphere Inter-Basin Interannual Coherence

Nonrandom phase relations explored by Schwing, Jiang, & Mendelssohn (2003):

Interannual Solar-Terrestrial Phase-Relations

Terrestrial phase relations with interannual [not to be confused with decadal] rates of change of solar variables, including solar wind speed (iV’), are nonrandom:

Inter-Hemispheric Interannual Phase-Relations

For those wondering how AAO & SAM fit in:

Global Synchronicity

Synchronicity’s the norm. Orientation, configuration, amplitude, & extent of globally constrained & coupled jets & gyres are pressured while network monitoring remains stationary. Regional temporal phase summaries are intermittently flipped by the stationary spatial geometry of monitoring networks in the turbulent global context.

Note particularly (in the last 2 graphs) the strong & stable interannual synchronicity of northern annular, southern annular, & global modes for the decade beginning ~1988. The commencement of the pattern coincides with concurrent abrupt changes in Arctic ice flow (e.g. Rigor & Wallace (2004) Figure 3) and European temperature (e.g. Courtillot (2010)).

Local Connection

Here’s how NPI relates to minimum temperatures at my local weather station:

Concluding Speculation

Terrestrial geostrophic balance is affected by the concert of changes in:

a) interannual (not to be confused with decadal) solar variations.

b) decadal amplitude of semi-annual Earth rotation variations – [see Vaughan (2011) & links therein].

c) solar cycle length – [see links in Vaughan (2011)].

Nipping Potential Misunderstandings in the Bud

“So you’re claiming the North Pacific controls global climate?”

No.

Why do I hear the same places mentioned every rush hour on the traffic report? Bottlenecks are easy places to detect changes in pressure & flow (whether global &/or locally intersecting), even using the simplest methods. Methods such as those suggested by Schwing, Jiang, & Mendelssohn (2003); Maraun & Kurths (2005); and Tsonis, Swanson, & Kravtsov (2007) help expand our vision towards the rest of the network. We have a lot of work to do (both exploratory & methodological).

Further Reading

Everything written by Tomas Milanovic at Dr. Judith Curry’s blog Climate Etc.

Vaughan, P.L. (2011). Solar, terrestrial, & lunisolar components of rate of change of length of day.

http://wattsupwiththat.com/2011/04/10/solar-terrestrial-lunisolar-components-of-rate-of-change-of-length-of-day/

Referenced Above

Courtillot, V. (Dec. 2010). YouTube Video (~30min): Berlin Conference Presentation.

http://www.youtube.com/watch?v=IG_7zK8ODGA

Maraun, D.; & Kurths, J. (2005). Epochs of phase coherence between El Nino-Southern Oscillation and Indian monsoon. Geophysical Research Letters 32, L15709. doi10.1029-2005GL023225.

http://www.cru.uea.ac.uk/~douglas/papers/maraun05a.pdf

Rigor, I.; & Wallace, J.M. (2004). Variations in the age of Arctic sea-ice and summer sea-ice extent. Geophysical Research Letters 31. doi: 10.1029/2004GL019492.

http://iabp.apl.washington.edu/research_seaiceageextent.html

Schwing, F.B.; Jiang, J.; & Mendelssohn, R. (2003). Coherency of multi-scale abrupt changes between the NAO, NPI, and PDO. Geophysical Research Letters 30(7), 1406. doi:10.1029/2002GL016535.

Trenberth, K.E.; Stepaniak, D.P.; & Smith, L. (2005). Interannual variability of patterns of atmospheric mass distribution. Journal of Climate 18, 2812-2825.

http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/massEteleconnJC.pdf

Tsonis, A.A.; Swanson, K.; & Kravtsov, S. (2007). A new dynamical mechanism for major climate shifts. Geophysical Research Letters 34, L13705.

http://www.nosams.whoi.edu/PDFs/papers/tsonis-grl_newtheoryforclimateshifts.pdf

Wyatt, M.G.; Kravtsov, S.; & Tsonis, A.A. (2011). Atlantic Multidecadal Oscillation and Northern Hemisphere’s climate variability. Climate Dynamics. doi: 10.1007/s00382-011-1071-8.

Since (to my knowledge) there’s not yet a free version, see the conference poster and the guest post at Dr. R.A. Pielke Senior’s blog for the general idea:

a) Wyatt, M.G.; Kravtsov, S.; & Tsonis, A.A. (2011a). Poster: Atlantic Multidecadal Oscillation and Northern Hemisphere’s climate variability.

https://pantherfile.uwm.edu/kravtsov/www/downloads/WKT_poster.pdf

b) Wyatt, M.G.; Kravtsov, S.; & Tsonis, A.A. (2011b). Blog: Atlantic Multidecadal Oscillation and Northern Hemisphere’s climate variability.

http://pielkeclimatesci.wordpress.com/2011/04/21/guest-post-atlantic-multidecadal-oscillation-and-northern-hemisphere%E2%80%99s-climate-variability-by-marcia-glaze-wyatt-sergey-kravtsov-and-anastasios-a-tsonis/

Important Note: While Wyatt, Kravtsov, & Tsonis (2011) are likely to stimulate a lot more discussion once a free version of their paper becomes available, it needs to be pointed out assertively & clearly that the cross-correlation approach, while informative, is patently insufficient for determining the full nature of terrestrial spatiotemporal phase relations.

Appendices

In the appendices that follow, attention is concisely drawn to key items that are consistently underappreciated in climate discussions.

Appendix A: Spatial Influence on Phase – Important

Nonrandom phase relations demand careful focus on the spatial dimension. Temporal evolution isn’t the only thing driving apparent phase.

If features grow, shrink, rotate, change shape, reflect, or move relative to the stationary windows in which they are measured, phase is affected.

The effect on summaries is plain & simple. (Anyone previously puzzled by “integration across spatiotemporal harmonics” might now get the general idea.)

Appendix B: Reversals in Temperature-Precipitation Relations

Blink between winter & summer panels of Figure 6:

Trenberth, K.E. (2011). Changes in precipitation with climate change. Climate Research 47, 123-138. doi: 10.3354/cr00953.

http://www.int-res.com/articles/cr_oa/c047p123.pdf

Temperature-precipitation relations are a function of absolutes, not anomalies. This is fundamentally important.

Insight from my local (ABC) example:

Appendix C: Global Distribution of Continental-Maritime Contrast

High-amplitude regional variance leverages global summaries, but multidecadal variations often draw misguidedly narrowed focus to the North Atlantic Ocean when it is the global distribution of continental-maritime contrast (in relation to flow patterns) that should be attracting the attention. Noting the position of the relatively small North Atlantic in this broader context, carefully compare:

1. http://icecap.us/images/uploads/AMOTEMPS.jpg

2. Figure 10 here:

Carvalho, L.M.V.; Tsonis, A.A.; Jones, C.; Rocha, H.R.; & Polito, P.S. (2007). Anti-persistence in the global temperature anomaly field. Nonlinear Processes in Geophysics 14, 723-733.

http://www.icess.ucsb.edu/gem/papers/npg-14-723-2007.pdf

Data & Symbols

‘ indicates rate of change

[ ] indicates time-integration

AAM = Atmospheric Angular Momentum

AAO = AntArctic Oscillation

ABC = Agassiz, British Columbia (west coast of Canada near USA border)

AO = Arctic Oscillation

COWL = Cold Ocean, Warm Land index

D-T = -SOI = – Southern Oscillation Index = pressure difference between Darwin & Tahiti (an indicator of El Nino / La Nina cycling)

ENSO = El Nino / Southern Oscillation

i = interannual

LOD = Length Of Day

NAO = North Atlantic Oscillation

NPI = North Pacific Index

PDO = Pacific Decadal Oscillation

PNA = Pacific North America index

PPT = PreciPiTation

QBO = QuasiBiennial Oscillation

SAM = Southern Annular Mode

SOI = Southern Oscillation Index

T = Temperature (°C)

V = solar wind speed

x = extreme

Data links available upon request.

Acknowledgements

Sincere thanks to Anthony Watts, the WUWT Moderation Team, readers, and all those who make valuable contributions towards a deeper understanding of nature.

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PDF Version of this essay available here Vaughan, P.L. (2011). Interannual Terrestrial Oscillations (375KB)

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Lots of graphs in one post is good; lots of colored lines in one graph is not good.
Probably would benefit from some animated blink-o-graphs.

That all the terrestrial relations are correlated in complicated ways simply show that they are not independent, which we would not expect in the first place. Heaping more of these on top of what is already there will make no difference at all because the inter-dependencies are still there.
This: “Multiscale complex correlation (for example using adjacent derivative based complex empirical wavelet embeddings) can measure complex nonstationary relations where simple linear correlation fails catastrophically” is just spatiotemporal mumbo-jumbo with no physical content. I shall not shy away from calling the emperor’s new clothes what they are.
The only part that fall outside that web of interdependencies is the claim: “Terrestrial phase relations with interannual [not to be confused with decadal] rates of change of solar variables, including solar wind speed (iV’), are nonrandom”. Both solar activity and atmospheric variability consist of ‘episodes’ of 1-3 years duration [with no spatial relationships whatsoever]. So any ‘multiscale complex correlations’ will always find some coherence over the limited time span we have data for because the underlying data are themselves not random. This does not mean that the data is related in any way.

I don’t pretend to understand most of the science behind this (I’m just a Mechanical Engineer), but what seems obvious to me is that all the factors involved in climate must be considered and it’s not only more complicated than we know, it’s more complicated than we can know (apologies). But I venture, with as much common sense as I can muster, the local star is the single most important variable in the whole system. Everything else must flow from that. I suppose climate could be modeled (simply and inaccurately) as a “spring-mass-damper” system with the forcing mechanism being total solar energy. Does that make some sort of sense?

Mike McMillan

I agree.

commieBob

Here’s a beautiful illustration of a bunch of cycles synchronized in a non-obvious manner:
link

R. Shearer

Obviously, CO2 aligns these variables to increase global temperature. /sarc off

Dr. John M. Ware

If this article is a joke, it’s a lot of effort for negligible result. If it’s serious, it’s simply incomprehensible; the level of gobbledygook-jargon is intolerable. If there is something to say here, please say it in English!

crosspatch

I don’t pretend to understand most of the science behind this

I don’t even pretend to understand what the article is really getting at. It seems like a lot of “A tracks with B — except for when it doesn’t. And a lot of things all seem to change at about the same time.” Not sure what any of that means, honestly.

oldgamer56

What language is this written in? Overbearingly Smug?
I received this from a student it would have been sent back for rewrite. Structure is wrong (fails to start small and build to a main point in a logical progression), it is aimed at the wrong target audience and assumes way to much base understanding.
Looked more like “Baffle them with BS” than a “Blind them with brilliance”
Suffers from “Look at all the pretty colors” syndrome.
And I am not sure yet what the hell the point was.

Gary Krause

Concluding Speculation
The whole point is:
Terrestrial geostrophic balance is affected by the concert of changes in:
a) interannual (not to be confused with decadal) solar variations.
b) decadal amplitude of semi-annual Earth rotation variations – [see Vaughan (2011) & links therein].
c) solar cycle length – [see links in Vaughan (2011)].
Is that something new? Or a confirmation that their is no CO2 affect?

KR

No offense, you’ve put a lot of work into this.
But… what are your conclusions? There’s lots of variability on various scales, does that mean anything regarding climate change? Do any of these fairly short term periodic and aperiodic fluctuations add up to anything meaningful, or indicating a long term trend?

KR

commieBob
Great video! I think I need a drink, now, though…

Paul Vaughan

One of the reasons I wanted to post this was to see the reaction. Whatever you’re thinking, please say it.
I’m particularly curious to hear from the Tsonis, Swanson, & Kravtsov (2007) fans […and we know there are a good number of them around].
Thanks sincerely to those who have taken the time to comment. I look forward to carefully reading what others have to say.
I also have a request of the community. There’s a slide in Jasper Kirkby’s recent SFU IRMACS presentation that I need to find in the literature. (I’ll look up the time-index tomorrow…)

Best Regards.

CRS, Dr.P.H.

I’m sorry, but you lost me with “Elegant factor analyses by Trenberth…”
Putting the word “elegant” in the same sentence as “Trenberth” seems contradictory, unless in the context about “Trenbreth’s elegant emails written to cover up climate skullduggery” or some such.
http://wattsupwiththat.com/2011/01/13/trenberths-upcoming-ams-meeting-talk-climategate-thoughts/

savethesharks

Paul,
May I be so bold to say that you are on to something…but, be that as it may, the Newspeak interannual blah blah blah stuff…has got to go.
In science, as you well know….might does not make right,
As a matter of fact…it often creates error.
Just by nomenclature alone, you open yourself up to criticism from the wolves….such as Dr. S.
And actually, besides rigorous tests…their criticism is is well-founded. Nobody knows what the hell you are talking about. You have to define it more clearly.
Your friend,
Chris
Norfolk, VA, USA

Paul Vaughan

Leif Svalgaard wrote (May 15, 2011 at 5:41 pm):
“That all the terrestrial relations are correlated in complicated ways simply show that they are not independent, which we would not expect in the first place. Heaping more of these on top of what is already there will make no difference at all because the inter-dependencies are still there.”

Well put Leif.
Now try to explain that to climate science & statistical science, which insist on drawing so-called “conclusions” based on PATENTLY FALSE assumptions of independence.
You nicely make my PRIMARY point.

Paul Vaughan

Leif Svalgaard wrote (May 15, 2011 at 5:41 pm):
“This: “Multiscale complex correlation (for example using adjacent derivative based complex empirical wavelet embeddings) can measure complex nonstationary relations where simple linear correlation fails catastrophically” is just spatiotemporal mumbo-jumbo with no physical content. I shall not shy away from calling the emperor’s new clothes what they are.”

Can you be more specific about what you find so offensive about Maraun & Kurths (2005) section 3 and related methodologies?

I’m not a scientist either, but I think I got a conclusion from this (accepting that it could have been written more clearly): standard linear analysis fails to recognise correlations between between non-random cyclical events because it cannot take account of the fact that, in a spatio-temporal chaotic system, the changes you are measuring move around. Sometimes therefore, your data will appear to be out of phase when it is in fact in-phase.
Perhaps this is something all other readers of WUWT were aware of, but it wasn’t something I’d thought of before!

jorgekafkazar

CRS, Dr.P.H. says: “Putting the word “elegant” in the same sentence as “Trenberth” seems contradictory…”
Well, I beg to differ. Here are two well-known Trenberthisms:
“I remain somewhat skeptical… It is hard to make data where none exist.” (regarding Steig et al)
“The fact is that we can’t account for the lack of warming at the moment and it is a travesty that we can’t.” (from the Climategate emails)
These quotes are brief, pithy, very much to the point, and accurate. In short, elegant.

gnomish

“absolutes not anomalies”
i love it!

Paul,
Does the variation represented in the vertical axis represent the state of the correlation between the indices. If not, then what?

John F. Hultquist

The link to Pielke Senior between the first and second charts did not work for me.
~~~~~~~~~~~~~~~~~~
Next, I think this post fits nicely with Donald Rumsfeld’s explanation of knowns and unknowns. Namely . . .
Lack of widespread awareness of the . . .
I am aware of the Pacific Decadal Oscillation (PDO) but I do not understand why it exists, what it is doing, nor why it changes when it does. The same can be said for many of the other oscillations mentioned, and thus this is somewhat of a “paralyzing bottleneck” toward improving my personal know, don’t know, don’t know that I don’t know list of things. The post does inform me that there seem to be a lot of known (by somebody) things that I do not know about “the spatiotemporal nature of interannual terrestrial oscillations” and will never know much about most of them.
That seems to be the general purpose of the exercise and in that sense it has succeeded.

Fergus T. Ambrose

I read it backwards on tape and Bill Clinton said “I did not have sex with that woman”.

Paul Vaughan says:
May 15, 2011 at 10:16 pm
Now try to explain that to climate science & statistical science, which insist on drawing so-called “conclusions” based on PATENTLY FALSE assumptions of independence.
I don’t think they are doing that. It seems to me that they are well aware of the fact that almost all measures of atmospheric variability are strongly correlated with each other and hence not independent.
Paul Vaughan says:
May 15, 2011 at 10:27 pm
Can you be more specific about what you find so offensive about Maraun & Kurths (2005) section 3 and related methodologies?
I don’t find them ‘offensive’. I fail to see [could simply be a failure on my part] what they bring to the table that is not trivial, new, and interesting. What do we learn that we did not already know? Where is the phenomenon that ONLY can be discovered with their methodologies? and that will not yield to standard techniques.
Now, in my field, we deal with the ultimate in spatio-temporal analysis: successful helioseismic exploitation of the integrated effect of millions of standing waves observed simultaneously over the entire solar disk. We don’t have any difficulties with what you call ‘abstract conceptualization’ [although it is not quite clear to me what you mean]. I don’t think people that search for oil with seismic techniques have difficulties either, so I fail to see how the formalisms you are pushing will improve something that works quite well already.

Paul
Your article may be a goldmine for more enthusiastic reader, but I felt overwhelmed by methodology of the presentation.
Inter annual oscillations very often have appearance of random noise. One could consider this to be a case with the Multivariant ENSO or the closely related Southern Oscillation Index (SOI).
My short excursion into analysis of these events has found a close correlation with a non-climate process with power and the means to influence, or even drive ENSO.
http://www.vukcevic.talktalk.net/SOI.htm

jorgekafkazar

Paul: I, too, found the post somewhat impenetrable. I decided not to comment after seeing some of the responses, lest I seem to be piling on. But since you ask:
(1) I’m not a fan of “wiggle matching,” especially of the sort where “it matches except where it doesn’t.” There must be some sort of statistical or mathematical handling of in-phase / 180° out-of-phase periodic data to make such statements meaningful.
(2) I really like graphs and charts that have a full legend: Ordinate and abscissa units, indication of any averaging/smoothing and how it was done, base period for anomalies, labels, all of it, the whole nine yards.
(3) I have a strong preference for authors who eschew sesquipedalian phraseology. I’m not accusing you of being inebriated by the exuberance of your own verbosity, but rather of having missed an opportunity to achieve even greater clarity.
(4) I’d suggest adopting the methods of the award-winning teacher who explained her pupils’ outstanding performance by saying: “First, I tell ’em what I’m gonna tell ’em; an’ then I tell ’em; and then I tell ’em what I told ’em.”
(5) I read the charts carefully and thus was looking for the indicator of derivatives, which I found only because I knew it must be there. Others might have easily missed the little ‘ symbol. It would be easier to read (though more challenging to include) the full dx/dt nomenclature. Legibility helps.
Hope this is helpful. I’m a technical editor, so this sort of paper isn’t as strange to me as it is to some, but I still found it too challenging to translate in the time I had available this weekend.
Jorge Kafkazar, MS

Richard111

Rather beyond my comprehension level. I notice there seems to be at least four time periods. I assume the vertical axis is common to all graphs. No individual trace appears to exceed the +1 -1 levels over the total 110 year period. I have to ask, “What or where is the problem?”

James Sexton

Paul Vaughan says:
May 15, 2011 at 10:16 pm
Leif Svalgaard wrote (May 15, 2011 at 5:41 pm):
“That all the terrestrial relations are correlated in complicated ways simply show that they are not independent, which we would not expect in the first place. Heaping more of these on top of what is already there will make no difference at all because the inter-dependencies are still there.”
Well put Leif.
Now try to explain that to climate science & statistical science, which insist on drawing so-called “conclusions” based on PATENTLY FALSE assumptions of independence.
You nicely make my PRIMARY point.
==========================================
lol, well why didn’t you say so in the first place!
Seriously though, Paul I thank you for all of this information. Its going to take me a while to sift through much of this. I can appreciate all the effort you went through to make these statements. While, like others here, the presentation style was a bit much for me, I acknowledge that we all respond to visuals in a different manner. But what seems lost on many here, is that the concluding statement is often the most poignant.
We have a lot of work to do (both exploratory & methodological).
Yes, and it is seemingly much more complex than any one can grasp.
Thanks much,
James

steveta_uk

At night I can hear my watch ticking, very close to my ear on the side table. I can also hear my wife’s clock ticking on the other side of the bed.
Lots of the time, they tick together, making a nice rhythm. Then after a while, the patterns breaks down, with apparently random gaps between ticks. Then shortly after, they seem to re-sync and tick along together for a while.
So how do you explain this strange phase shift, when they appear to by in sync for substantial periods, then the odd random periods before they re-sync?
Or perhaps they are simply both ticking happily along in their own way, and I’m imposing a correlation where none exists?

Bloke down the pub

Addition to Data and Symbols
AMP = Above My Paygrade

John Marshall

I need to go and lie down.

Maybe this is what Leif was getting at, but I’m not sure….
I have to wonder what these plots would look like for a variety of time series of low-pass filtered random numbers. Given only a certain number of climate events/quasi-cycles in various regions in the last 100 years, there can be apparent associations that have no physical connection. For example, you can do spectral analysis of time series of random numbers and get spectral peaks that have no physical significance.

wayne Job

Multi-variable perambulations of non-interconnected newspeak in a close formation of unintelligible graphic representations of a somewhat dubious usefulness with no apparent conclusion. This post may excite perhaps a dozen people in the entire world , until it is rendered into the laymans dialect it will be an abstract of non-sense.

P. Solar

Paul, I was about to post but Jorge Kafkazar sums up my main complaints about this presentation:
(2) I really like graphs and charts that have a full legend: Ordinate and abscissa units, indication of any averaging/smoothing and how it was done, base period for anomalies, labels, all of it, the whole nine yards.
This is a scientific subject, posting sociologist style graphs is really of little help. I’m very surprised that someone with a M.Sc would present anything in that way. I can’t see what most (any) of these graphs are supposed to be showing and I don’t have the time play guessing games. If you have something interesting, please state exactly what your point is and correctly and fully label your graphs.
“data available on request”.
Why not just post a link with each graph? You spent the time plotting and writing all this , what is so hard about providing a link?
Also any discussion is near impossible if you don’t label each graph , figure 1. etc.
Almost any semi random data starts to look like it has cyclic components once you smooth it. Any climate data will have interannual variations. If the go in and out of phase it means they have different frequencies. There is nothing interesting in that.
I can only guess that you have failed to get across what you were hoping to show.
best regards.

Gary Pearse

A thesis superviser 50 years ago told me that the best way to hammer in a nail is to hold it, give it a few taps, then drive it in with 2 or three strong blows, after I had given him everything, including the kitchen sink in support of an idea. The enthusiasts who spend any time at WUWT include climate scientists, other scientists and engineers, but also, the whole gambit of laypersons – I’ve read pithy comments from farmers, politicians, military pilots, journalists … and so on. They all seem to find the subjects here interesting so it is a generally bright lot. If you have a legitimate thesis, it can be put forward intelligibly to all. You can of course put in a few highly technical asides and links for the expert, but even the expert wants clear exposition.

Paul Vaughan

Leif Svalgaard wrote (May 15, 2011 at 11:39 pm):
“It seems to me that they are well aware of the fact that almost all measures of atmospheric variability are strongly correlated with each other and hence not independent.”

So why the culturally dominant adamant insistence on statistical inference based on the FALSE assumption of independence?

Paul Vaughan

Anthony said “timing is everything”.
Actually:
Timing & spacing.
Timing AND spacing.
This one comment makes the whole exercise worthwhile:
John Syfret wrote (May 15, 2011 at 11:00 pm):
“I’m not a scientist either, but I think I got a conclusion from this (accepting that it could have been written more clearly): standard linear analysis fails to recognise correlations between between non-random cyclical events because it cannot take account of the fact that, in a spatio-temporal chaotic system, the changes you are measuring move around. Sometimes therefore, your data will appear to be out of phase when it is in fact in-phase.
Perhaps this is something all other readers of WUWT were aware of, but it wasn’t something I’d thought of before!”

Appreciated – Thanks John.

Paul Vaughan

Roy Spencer wrote (May 16, 2011 at 4:57 am):
“Maybe this is what Leif was getting at, but I’m not sure….
I have to wonder what these plots would look like for a variety of time series of low-pass filtered random numbers. Given only a certain number of climate events/quasi-cycles in various regions in the last 100 years, there can be apparent associations that have no physical connection. For example, you can do spectral analysis of time series of random numbers and get spectral peaks that have no physical significance.”

Unwindowed spectral analysis is of limited utility in part for the reason’s Roy explains, but I assure Roy that randomly generated numbers (even smoothed ones, contrary to popular misconception) do NOT routinely fool methods such as those suggested in Maraun & Kurth’s (2005) section 3 …nor do they routinely produce plots like these
http://wattsupwiththat.files.wordpress.com/2011/05/vaughn_npp_image6.png
http://wattsupwiththat.files.wordpress.com/2011/05/vaughn_npp_image5.png .
Leif is saying the variables are NOT independent because they ARE physically connected. My question is: Why do climate scientists pretend the variables are independent when conducting statistical inference?
For readers lacking background but trying to follow along:
Fundamentally unlike data exploration, statistical inference is based on ASSUMPTIONS — assumptions which are far too often made unconsciously. Worse than that, the establishment INSISTS upon them, even when they are patently untenable. This is unacceptable.

Paul Vaughan

oldgamer56 wrote (May 15, 2011 at 8:18 pm):
“it is aimed at the wrong target audience”

Astute observation.
Addressing the “wrong” audience was sure to draw misunderstanding & vicious collateral attack. Isn’t it better to let climate scientists know that some of us know that their uncertainty estimates are based on patently untenable assumptions? Isn’t that worth risking having one single neck turned into a red sprinkler by the “wolves” (as Chris calls them)?

Paul Vaughan says:
May 16, 2011 at 7:20 am
Leif is saying the variables are NOT independent because they ARE physically connected. My question is: Why do climate scientists pretend the variables are independent when conducting statistical inference?
I don’t think they pretend that. Do you have some papers or statements by climate scientists where they say that they pretend the variables are independent? In most cases that I know of, they are trying to show that there is some dependency, e.g. that temperature depends on CO2, or that rainfall in some region depends on ENSO or some such.

Paul Vaughan

In Jasper Kirkby’s SFU IRMACS video from time-index 35:45 to 35:50 he’s drawing attention to a Southern Ocean wind/NaCl pattern (right panel).
Can anyone point to the journal article?
This appears to be the “missing link” between Appendix C (above) and Trenberth, Stepaniak, & Smith’s (2005) powerful Table 3 & Figure 3.
The role of north-south terrestrial asymmetry has been underappreciated. Some of you may recall this:
http://wattsupwiththat.files.wordpress.com/2010/08/vaughn_lod_amo_sc.png
http://wattsupwiththat.files.wordpress.com/2010/09/scl_northpacificsst.png
http://wattsupwiththat.files.wordpress.com/2010/09/scl_0-90n.png
SCL’ = rate of change of solar cycle length = solar cycle deceleration
This detour into “interannual terrestrial oscillations” is just a side trip to help those blinded by interannual spatiotemporal chaos to patterns illustrated by Wyatt, Kravtsov, & Tsonis (2011) https://pantherfile.uwm.edu/kravtsov/www/downloads/WKT_poster.pdf .
John F. Hultquist wrote (May 15, 2011 at 11:35 pm):
“The link to Pielke Senior between the first and second charts did not work for me.”

Some issue with the apostrophe ‘ in the title. Try this approach:
http://pielkeclimatesci.wordpress.com/?s=Atlantic+Multidecadal+Oscillation+and+Northern+Hemisphere+Wyatt
Interesting that the article hasn’t attracted more attention from WUWT commenters, given how excited many are about “60 year cycles”.

George E. Smith

“”””” Elegant factor analyses by Trenberth, Stepaniak, & Smith (2005) concisely chart the limits of linear climate exploration, providing strong clues that the North Pacific is a globally pivotal intersection. “””””
I nominate the above on behalf of its self referencing authors, for entry into this year’s Bulwer-Lytton prize competition; aka the Bloviating BS prize.

George E. Smith

“”””” commieBob says:
May 15, 2011 at 6:27 pm
Here’s a beautiful illustration of a bunch of cycles synchronized in a non-obvious manner:
link “””””
Well commie, I watched the video several times, and I saw no evidence of any synchronisation. As imple demonstartion that the period of a simple pendulum varties with its length, and a camera gimmic to show it off.
Now it would have been far more illuminating, if they had included some sort of energy coupling between the several pendula to show how they exchange energy among themselves. Coupled penula are much more interesting than length varied ones.

Paul Vaughan

erlhapp wrote (May 15, 2011 at 11:35 pm):
Paul,
Does the variation represented in the vertical axis represent the state of the correlation between the indices. If not, then what?”

No. The interannual filter used simply contrasts years with immediately-adjacent years for each variable. Amplitude is normalized to facilitate visualization.
Erl, I’m wondering if you are seeing some connection between this [ http://wattsupwiththat.files.wordpress.com/2011/05/vaughn_npp_image8.png ] and your work on polar voritices & geomagnetic Dst index?
Btw, there’s a whole decade where local precipitation in my area perfectly tracks geomagnetic indices. I want to know why and I’m not buying this nonsense that it’s just random chance.
Leif has to prove that A, B, & C swirl iV’ while X, Y, & Z (independent from A, B, C, & iV’) swirl iNPI’ to satisfy me that he is correct in ruling out a link between iV’ and tropospheric variability. I will welcome a convincing argument, but I’m skeptical that one can be produced.
Thanks for joining the discussion Erl.

Paul Vaughan

Leif Svalgaard wrote (May 16, 2011 at 7:43 am):
“I don’t think they pretend that. Do you have some papers or statements by climate scientists where they say that they pretend the variables are independent?”

They’re a dime a dozen. It’s standard widespread practice – even forced upon subordinates – to assume independence. It’s often done unconsciously in statistical inference; most don’t diligently retain cognizance of the model assumptions (for example when interpreting).
I’m not speaking just of climate science. This is a widespread systemic problem in our society that produces LINEAR p-values to nonsensically dismiss correlations of the following (complex) variety as “insignificant”: http://wattsupwiththat.files.wordpress.com/2011/05/vaughn_npp_image3.png
This is fundamentally unacceptable practice.

George E. Smith

“”””” Roy Spencer says:
May 16, 2011 at 4:57 am
Maybe this is what Leif was getting at, but I’m not sure….
I have to wonder what these plots would look like for a variety of time series of low-pass filtered random numbers. Given only a certain number of climate events/quasi-cycles in various regions in the last 100 years, there can be apparent associations that have no physical connection. For example, you can do spectral analysis of time series of random numbers and get spectral peaks that have no physical significance. “””””
Right on Roy; apply random white noise to any filter input, and it will output that part of the sepctrum which elicits a response, leading to the eroneaous conclusion that it is a signal.
Which begs the question.
In talking about correlation which Dr Svalgaard alluded to; do climatists distinguish or differentiate between the simple correlation of the numbers (mathematics) that represent the observations of climate phenomena; and the physical correlation of the pehenomena themselves.
To me, the statement that experimental observation (A) and experimental observation (B) are “correlated”, implies (or if you prefer; I “infer” from that), that there is some underlying cause and effect relationship between (A) and (B) or alternatively between (A and B) and some other (C) (which might be the cause of both (A and B) ).
That the numbers used to represent each phenomenon (A,B, C….) show some non-zero mathematical cross-correlation coefficient, is not of itself evidence that the phenomena are related let alone correlated. Absent a cause and effect connection; we merely have demonstration of the non-zero bandwidth of the analysing filter; that lets several unrelated signals through.

Paul Vaughan says:
May 16, 2011 at 9:00 am
Leif has to prove that A, B, & C swirl iV’ while X, Y, & Z (independent from A, B, C, & iV’) swirl iNPI’ to satisfy me that he is correct in ruling out a link between iV’ and tropospheric variability. I will welcome a convincing argument, but I’m skeptical that one can be produced.
The shoe is on the other foot. The one claiming a link has to produce the proof. The null-hypothesis is no link. The main arguments [which are not by themselves ‘proofs’] against a link are the weakness of correlations, the lack of mechanism, and insufficient energy input.

Paul Vaughan says:
May 16, 2011 at 9:11 am
“I don’t think they pretend that. Do you have some papers or statements by climate scientists where they say that they pretend the variables are independent?”
They’re a dime a dozen.

I’ll be content if you show me just one. As I said, most people are assuming that the variables are dependent, otherwise why investigate relationships between variables that do not depend on each other. And in the natural sciences, statistics never proves anything, just serves as an indication of a possible line of investigation into the physics and mechanisms involved.

RC Saumarez

Two points:
The first is that many statistical signal processing techniques require an ensemble approach,, i.e.: the behaviour of the means of some parameter. We only have one climate record and therefore we cannot use an esemble approach without segmentation of the data and thus limit the minimum observable frequency. I agree with Spencer’s point about the specrum of a low pass filtered random variable. This is easy to show as random provided one has enough data. With a single observation, statistical methods to eliminate the effect of apparant non-randomness is not robust.
The second is that any interaction between systems of different frequencies will inevitably be non-linear, common examples are entrainment in which a non-linear oscillator is ” captured” by an entraining signal or modulation. I would agree that the assumptions of statistical independence and linearity coherence/phase are probably incorrect in the climate as, I presume, the various measures discussed are physically connected. If this is done on a routine basis, I suggest that some remedial mathematics for the perpetrators.
I may have missed the point but, as a signal processer, I found this paper fairly opaque. I feel an expanded version of the methods and axis labelling would lead to greater “coherence” in the presentation.

Kelvin Vaughan

You don’t have to know how the electrons are flowing through the chips to know what a computer can do!