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.
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.
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)
Paul Vaughan says:
May 19, 2011 at 7:30 am
I get the clear impression that you are lax about performing diagnostics to assess “standard” statistical model assumptions.
Explain what diagnostics [if any] you have performed on your iV’ and iNPI’ correlation.
Paul Vaughan says:
May 19, 2011 at 8:31 am
No matter how many times I have to explain it, it won’t get any more complicated:
“i” is a SIMPLE contrast of years with immediately-adjacent years.
You said: “There are 2 immediately-adjacent years (the one before & the one after).”. So take a year, e.g. 1942. the year before is 1941 and the year after is 1943, so you say you calculate the difference between 1943 and 1941 [careful reading]. Now, I don’t think you do this, but that is what you say.
You appear to have used a slightly different smoothing strategy on iV’ (perhaps one not based on the dominant temporal modes in the series?…),
I do not smooth. I’m trying to ferret out what you do. And you are totally non-responsive, so perhaps it is futile [I recall earlier threads where it was also impossible to get any explanations out of you] to keep asking.
“There is nothing in the analytic concept of complex-valued covariance that would produce a spurious signal from pure noise as an artifact, as suggested here in irrelevant comments by Spencer and Saumarez.”
If the two series have a common confounding component, there is. You are ducking the issue again.
I use RAW data in analyses.
Yet you claim to use a ‘different’ smoothing
Leif agrees FULLY with the thrust about the relations existing among ALL of the other variables
These are all interrelated to begin with and thus bring nothing to the discussion and are just red herrings.
Having to post this article was like having to take out the trash. Just something unpleasant that had to be done.
Looks more like dumping the trash here.
I’m a volunteer Leif. Gravy train riders don’t dictate the terms under which I submit to interrogation. Cheers.
Paul Vaughan says:
May 19, 2011 at 8:06 pm
I’m a volunteer Leif. Gravy train riders don’t dictate the terms under which I submit to interrogation. Cheers.
It is called to chicken out. After having been found out. [snip – play nice ~ac]
http://rcada.ncu.edu.tw/
“About RCADA
Data analysis is indispensable to every science and engineering endeavor, but it always plays the second fiddle to the subject area. The existing methods of data analysis either the probability theory or the spectral analysis are all developed by mathematicians or based on their rigorous rules. In pursue of the rigorous, we are forced to make idealized assumptions and live in a pseudo-real linear and stationary world. But the world we live in is neither stationary nor linear. For example, spectral analysis is synonymous with the Fourier based analysis. As Fourier spectrum can only give meaningful interpretation to linear and stationary process, its application to data from nonlinear and nonstationary processes is problematical. And probability distributions can only represent global properties, which imply homogeneity (or stationarity) in the population. As scientific research getting increasingly sophistic, the inadequacy is become glaringly obvious. The only alternative is to break away from these limitations; we should let data speak for themselves so that the results could reveal the full range of consequence of nonlinearity and nonstationarity. To do so, we need new paradigm of data analysis methodology without a priori basis to fully accommodating the variations of the underlying driving mechanisms.”
Paul Vaughan says:
May 20, 2011 at 7:32 am
To do so, we need new paradigm of data analysis methodology without a priori basis to fully accommodating the variations of the underlying driving mechanisms
Physical scientists do not have a ‘priori basis’ and no new paradigm is needed as the data themselves always have the last word. Of much greater importance is honesty, reproducibility, and disclosure of methods, data, and algorithms. You could try to approach those goals a bit more instead of refusing to explain what you are claiming.
http://rcada.ncu.edu.tw/6%20Instantaneous%20Frequency.ppt
Leif Svalgaard wrote (May 20, 2011 at 7:59 am):
“Physical scientists do not have a ‘priori basis’ […]”
The author you’re quoting [ http://rcada.ncu.edu.tw/ ] was commenting about mathematical scientists, not physical scientists.
Paul Vaughan says:
May 21, 2011 at 8:22 am
The author you’re quoting [ http://rcada.ncu.edu.tw/ ] was commenting about mathematical scientists, not physical scientists.
It was not my quote, but yours. There are no such critters as mathematical scientists. There may be mathematicians or statisticians deluding themselves into believing they are doing science.
Every time a scientist performs statistical inference, that scientist is making assumptions. The author [ http://rcada.ncu.edu.tw/ ] is drawing attention to untenable statistical model assumptions used by scientists (including physicists) to generate misleading p-values & confidence intervals.
Paul Vaughan says:
May 21, 2011 at 9:25 am
drawing attention to untenable statistical model assumptions used by scientists (including physicists) to generate misleading p-values & confidence intervals.
No scientist is dumb enough to believe in p-values or the like. These are only indicative not deciding. The statistical model assumptions are not relevant, the physical model is. Physicists do not make ‘statistical inferences’, but try to compare observations with predictions based on physical laws or hypotheses about proposed mechanisms.
Leif Svalgaard asserted (May 21, 2011 at 9:41 am):
“No scientist is dumb enough to believe in p-values or the like.”
Are you sure about that?
Leif Svalgaard continued (May 21, 2011 at 9:41 am):
“These are only indicative not deciding.”
They’re not even indicative if base assumptions are fundamentally flawed.
Paul Vaughan says:
May 21, 2011 at 11:38 am
“No scientist is dumb enough to believe in p-values or the like.”
Are you sure about that?
None that I know of [and I know a lot]]. Perhaps you know some dumber ones?
Leif Svalgaard continued (May 21, 2011 at 9:41 am):
“These are only indicative not deciding.”
They’re not even indicative if base assumptions are fundamentally flawed.
Nobody has base assumptions that are fundamentally flawed a priori. We judge the base assumptions by the agreement with observations. Or rather, don’t bother with assumptions if the predictions come out even half right.
Leif Svalgaard says: May 21, 2011 at 8:43 am
There may be mathematicians or statisticians deluding themselves into believing they are doing science.
Well said Leif!!!!!
Leif, you’re again misinterpreting the term “assumptions” as if it’s referring to a physical model (& I expected you would do this).
To clarify yet again:
I’m referring to the statistical models upon which statistical inference is based. ALL of these models are founded on ABSTRACT assumptions, REGARDLESS of who is using them.
As for your other misrepresentations & misunderstandings: They are too numerous to address.
Paul Vaughan says:
May 21, 2011 at 2:00 pm
I’m referring to the statistical models upon which statistical inference is based. ALL of these models are founded on ABSTRACT assumptions, REGARDLESS of who is using them.
No, only if the user cares about and expresses abstract model assumptions. Usually he does not, because he knows that statistics [no matter how abstract] doesn’t prove a thing. Can at best give an indication or vague quantification of a relationship that must be established by physical understanding. In economics, statistics reigns because there is no underlying theory or laws.
Leif, like many people, you appear unaware that all statistical inference is based on abstract model assumptions. You also seem to misunderstand that I am an advocate of statistical inference. On the absolute contrary, I am sternly cautioning AGAINST it in contexts where its “reasoning” is based on untenable assumptions (and to be honest I’m not much of a fan of it any context).
Paul Vaughan says:
May 21, 2011 at 4:44 pm
Leif, like many people, you appear unaware that all statistical inference is based on abstract model assumptions.
I’m trying to tell you that physicists do not rely on or base their work on statistical inferences, but on physical theory and observation. A feeling for how little value statistics has you might consult http://www.leif.org/research/Reply%20to%20Lockwood%20IDV%20Comment.pdf
especially paragraph [16].
economics has the law of supply and demand and theories such as the net propensity to consume. newtons law of gravity acts infinity fast at infine distance. newton recognized the physical impossibility.
in science the concept of “understanding” is an illusion. the more we discover, the more questions are raised. we continue to underestimate the size of infinity. like ether, we invent dark matter and dark energy to fill the void.
the value of science is not in “understanding”, it is in our ability to predict accurately, no matter how this is accomplished. If history is a guide, 500 years from now everything we think we “understand” about the physical world will have long since been dumped into the rubbish bin.
ferd berple says:
May 21, 2011 at 5:21 pm
economics has the law of supply and demand and theories such as the net propensity to consume.
Yet their predictions fail spectacularly.
in science the concept of “understanding” is an illusion. the more we discover, the more questions are raised.
It takes understanding to raise more questions.
Leif,
Upthread you were demanding inference.
Now you’re trashing it.
Seems you change stripes as convenient.
–
ferd berple wrote (May 21, 2011 at 5:21 pm)
“the value of science is not in “understanding”, it is in our ability to predict accurately […]”
No interest in predicting, only in exploring. If others are interested in predicting, no problem with that.
ferd berple wrote (May 21, 2011 at 5:21 pm)
“the more we discover, the more questions are raised.”
Exactly.
Paul Vaughan says:
May 22, 2011 at 9:50 am
Seems you change stripes as convenient.
Seems you have left reasonable discourse behind and resorting to person characterizations.
Leif Svalgaard wrote (May 22, 2011 at 9:59 am)
“Seems you have left reasonable discourse behind and resorting to person characterizations.”
On the contrary. Upthread you demanded statistical inference. Now you are saying statistical inference isn’t useful. I have objectively noted the inconsistency.
Paul Vaughan says:
May 22, 2011 at 12:06 pm
On the contrary. Upthread you demanded statistical inference.
On the contrary, perhaps show where I demanded that. I said that physicists don’t do such inferences.
Leif Svalgaard wrote (May 22, 2011 at 12:22 pm)
“[…] physicists don’t do such inferences.”
Nonsense. You’re now suggesting physicists calculate neither p-values nor confidence intervals?