Readers may find the title familiar, that’s because Basil Copeland and I also did a paper looking at solar signatures in climatic data, which has received a lot of criticism because we made an analytical error in our attempt. But errors are useful, teachable moments, even if they are embarrassing, and our second attempt though, titled,
hasn’t been significantly challenged yet that I am aware of. Basil and I welcome any comments or suggestions on that work.
In our work, we used Hodrick-Prescott filtering to extract the solar cycle signal from the HadCRUT temperature dataset. In this paper the data are extracted from the ECA&ECD database (available via http://eca.knmi.nl ). According to the paper, they are “using a nonlinear technique of analysis developed for time series whose complexity arises from interactions between different sources over different time scales”. Read more about it in the paper. In both our paper, and in this one, a solar signature is evident in the temperature data. – Anthony
Evidence for a solar signature in 20th-century temperature
By Jean-Louis Le Mouel, Vincent Courtillot, Elena Blanter, Mikhail Shnirman (PDF available here)
J.-L. Le Mouël et al., Evidence for a solar signature in 20th-century temperature data from the USA and Europe, C. R. Geoscience (2008), doi:10.1016/j.crte.2008.06.001
Abstract
We analyze temperature data from meteorological stations in the USA (six climatic regions, 153 stations), Europe (44 stations, considered as one climatic region) and Australia (preliminary, five stations). We select stations with long, homogeneous series of daily minimum temperatures (covering most of the 20th century, with few or no gaps).We find that station data are well correlated over distances in the order of a thousand kilometres. When an average is calculated for each climatic region, we find well characterized mean curves with strong variability in the 3–15-year period range and a superimposed decadal to centennial (or ‘secular’) trend consisting of a small number of linear segments separated by rather sharp changes in slope.
Our overall curve for the USA rises sharply from 1910 to 1940, then decreases until 1980 and rises sharply again since then. The minima around 1920 and 1980 have similar values, and so do the maxima around 1935 and 2000; the range between minima and maxima is 1.3 °C. The European mean curve is quite different, and can be described as a step-like function with zero slope and a ~1 8°C jump occurring in less than two years around 1987. Also notable is a strong (cold) minimum in 1940. Both the USA and the European mean curves are rather different from the corresponding curves illustrated in the 2007 IPCC report.We then estimate the long-term behaviour of the higher frequencies (disturbances) of the temperature series by calculating the mean-squared interannual variations or the ‘lifetime’ (i.e. the mean duration of temperature disturbances) of the data series.We find that the resulting curves correlate remarkably well at the longer periods, within and between regions. The secular trend of all of these curves is similar (an S-shaped pattern), with a rise from 1900 to 1950, a decrease from 1950 to 1975, and a subsequent (small) increase. This trend is the same as that found for a number of solar indices, such as sunspot number or magnetic field components in any observatory. We conclude that significant solar forcing is present in temperature disturbances in the areas we analyzed and conjecture that this should be a global feature.
…
We find that station data are well correlated over distances in the order of a thousand kilometres. When an average is calculated for each climatic region, we find well characterized mean curves with strong variability in the 3-15-year period range and a superimposed decadal to centennial or ‘secular’ trend consisting of a small number of linear segments separated by rather sharp changes in slope. Our overall curve for the USA rises sharply from 1910 to 1940, then decreases until 1980 and rises sharply again since then. The minima around 1920 and 1980 have similar values, and so do the maxima around 1935 and 2000; the range between minima and maxima is 1.38C. The European mean curve is quite different, and can be described as a step-like function with zero slope and a 1.8C jump occurring in less than two years around 1987. Also notable is a strong (cold) minimum in 1940. Both the USA and the European mean curves are rather different from the corresponding curves illustrated in the 2007 IPCC report.
…
We then estimate the long-term behaviour of the higher frequencies (disturbances) of the temperature series by calculating the mean-squared interannual variations or the ‘lifetime’ (i.e. the mean duration of temperature disturbances) of the data series. We find that the resulting curves correlate remarkably well at the longer periods, within and between regions. The secular trend of all of these curves is similar (an S-shaped pattern), with a rise from 1900 to 1950, a decrease from 1950 to 1975, and a subsequent (small) increase. This trend is the same as that found for a number of solar indices, such as sunspot number or magnetic field components in any observatory.
…
We conclude that significant solar forcing is present in temperature disturbances in the areas we analyzed and conjecture that this should be a global feature.
We have also shown that solar activity, as characterized by the mean-squared daily variation of a geomagnetic component (but equally by sunspot numbers or sunspot surface) modulates major features of climate. And this modulation is strong, much stronger than the one per mil variation in total solar irradiance in the 1- to 11-year range: the interannual variation, which does amount to energy content, varies by a factor of two in Europe, the USA and Australia. This result could well be valid at the full continental scale if not worldwide. We have calculated the evolution of temperature disturbances, using either the mean-squared annual variation or the lifetime. When 22-year averaged variations are compared, the same features emerge, particularly a characteristic centennial trend (an S-shaped curve) consisting of a rise from 1920 to 1950, a decrease from 1950 to 1975 and a rise since. A very similar trend is found for solar indices. Both these longer-term variations, and decadal and sub-decadal, well-correlated features in lifetime result from the persistence of higher frequency phenomena that appear to be influenced by the Sun. The present preliminary study of course needs confirmation by including regions that have not yet been analyzed.
Paul Vaughan (17:41:33) :
You are underestimating the audience.
There are several classes in people in the ‘audience’:
1) people with agendas
2) people peddling pet ideas
3) people seeking knowledge
4) trolls
Which one(s) of the classes am I underestimating?
I’m not interested in social harmony. If I know something [or think I do] I’ll hold forth on it. When I see pseudo-science, I’ll try to point that out and explain why it is worthless. Even when confronted with rude persons that repeatedly will not give straight answers to straight questions, I’ll try to be patient. Contrary to your accusation I have no agenda.
Re: Leif Svalgaard
Repeating the answer from 12 days ago:
“Investigating relationships possibly involving SIM is worthwhile, in part since future SIM can be accurately predicted.”
I will also reiterate the qualifier:
“I’m not saying I agree with the more speculative comments Dr. Charvatova makes.”
…And I’ll stress this again:
One needs to maintain unwavering awareness of confounding when investigating what Dr. Charvatova calls “SIM”, since SIM is confounded with other indices (some of which are physically meaningful).
–
EOP (Earth Orientation Parameters) are affected by solar system dynamics & terrestrial weather patterns. This is not in dispute.
All of those “classes of people” [see Leif Svalgaard (18:11:10)] are capable of understanding that it does not take much of a nonlinear distortion to impact – or destroy – a linear correlation. Linear methods alone are insufficient for thoroughly investigating nonlinear relations.
Some of the relentless focus on amplitude needs to be diverted to phase, scale, conditioning, rate of change, & gradients.
Clearly the physicists (& all others) are overlooking important mechanics — otherwise we’d have all the answers and WUWT would need to find a new theme. I state this objectively, not maliciously.
I encourage you to refrain from disparagingly attacking other disciplines that may be able to help point you in the right direction in your search for missing mechanisms. This is a complex interdisciplinary problem.
If you look into what I am saying about the terrestrial Chandler wobble phase reversal, you will discover substance (even if you ignore the solar system centre of mass). If you think I’m peddling a statistics-based theory of barycentric influence on solar activity, you have fantastically misunderstood.
Despite your claims, I have doubts about your agenda; however, there’s an area of high priority where it seems we agree:
The truth takes precedence over social harmony.
Paul Vaughan (21:06:41) :
Good to see that you have toned down the rhetoric a tad, and to actually say something worthwhile, rather than pontificating on Santa Claus and non-drinking horses.
Repeating the answer from 12 days ago:
And what took you so long to remind me? Why would you play hide and seek with this for so long?
“Investigating relationships possibly involving SIM is worthwhile, in part since future SIM can be accurately predicted.”
And where does she actually say that? I must have missed it, and I do not think that this is her central thesis, if there even is one. As I have stated, predictability in itself does not seem to be a reason for investigating something. Otherwise you could claim that relationships with SIM need to be investigated for almost anything,
I will also reiterate the qualifier:
“I’m not saying I agree with the more speculative comments Dr. Charvatova makes.”
And this is much too vague and void. State what you agree with and what you disagree with.
…And I’ll stress this again:
One needs to maintain unwavering awareness of confounding when investigating what Dr. Charvatova calls “SIM”, since SIM is confounded with other indices (some of which are physically meaningful).
I’m sure that every scientist that reads her papers is fully aware of this.
EOP (Earth Orientation Parameters) are affected by solar system dynamics & terrestrial weather patterns. This is not in dispute.
It is not in dispute, but also not relevant for solar/geomagnetic activity.
Some of the relentless focus on amplitude needs to be diverted to phase, scale, conditioning, rate of change, & gradients.
There has to be an amplitude first, before there can be a phase, etc. Most scientists do not consider just a correlation to mean anything. Equally important are energy and coupling considerations: does the purported impetus carry enough energy to cause the claimed effects and is there a possible physical coupling to mediate the relationship.
Clearly the physicists (& all others) are overlooking important mechanics — otherwise we’d have all the answers and WUWT would need to find a new theme. I state this objectively, not maliciously.
I don’t think anybody is overlooking anything. It is just that the relationships are complicated and we don’t have enough data to guide the theory. Your statement seems to imply that everything we need is sitting just in front of our noses and that we are just ‘overlooking’ the obvious.
I encourage you to refrain from disparagingly attacking other disciplines that may be able to help point you in the right direction in your search for missing mechanisms. This is a complex interdisciplinary problem.
Attacking which other disciplines? Any discipline that can bring something to the table is welcome. I just don’t see much positive brought forward. I myself have fairly solid knowledge about atmospheric physics, solar physics, and geomagnetism, covering most of the disciplines involved.
If you look into what I am saying about the terrestrial Chandler wobble phase reversal, you will discover substance (even if you ignore the solar system centre of mass). If you think I’m peddling a statistics-based theory of barycentric influence on solar activity, you have fantastically misunderstood.
The goal of communication is to state something clearly so that misunderstandings don’t occur. If they do, the onus is on the person making the statement to be clear. And I do not think solar activity has anything to do with the reversal [for energy and coupling reasons].
Despite your claims, I have doubts about your agenda
This is unhelpful. If you think there is an agenda, state what you think it is and what you base that belief on.
Let me illustrate how to communicate: “I think that A is occurring and here is my reasons for thinking so […]. Do you think that B has any influence on A”.
Contrast this with:
“In increments perhaps. To get started: Does A affect B?
Increasing the pace: Do you think it is reasonable to claim that C does NOT show up in A?”
Re: Leif Svalgaard (22:06:57)
You still appear to be on the attack. It won’t be sensible to address all of your comments, but I’ll address a few points:
1)
You appear to have misunderstood (or misread) the following:
Paul Vaughan: “If you think I’m peddling a statistics-based theory of barycentric influence on solar activity, you have fantastically misunderstood.”
I will reiterate here that my earlier comments are about terrestrial phenomena.
2)
Leif Svalgaard (22:06:57) “Most scientists do not consider just a correlation to mean anything.”
Surely you realize you are wasting my time with such elementary notes.
3)
Leif Svalgaard (22:06:57) “Your statement seems to imply that everything we need is sitting just in front of our noses and that we are just ‘overlooking’ the obvious.”
Yes. That is the nature of complexity – i.e. it’s not necessarily easy to figure out even if simple.
When you girls have finished pulling each other’s pigtails perhaps you might both turn your prodigious intellects to the salient matters in hand.
Syd Levitus and the mystery of the missing ocean heat content.
Retension of the heat of insolation in the oceans.
Paul’s 1931 centred phase switch and the anomalous SST increase 1920-1940 not matched by a Nino cool phase 1945-1975 decrease in SST.
Bob Tisdale’s step changes in global temperature and the spreading, return and re-emergence of heat from the Pacific Warm Pool.
Leif Svalgaard (18:11:10) :
Paul Vaughan (17:41:33) :
You are underestimating the audience.
There are several classes in people in the ‘audience’:
1) people with agendas
2) people peddling pet ideas
3) people seeking knowledge
4) trolls
I’m not sure which of these groups Leif pigeonholes me into, probably (2), but for the record, I’m not sold on or selling any particular theory. I’m trying to use some basic arithmetic to elucidate some of the lacunae in the present state of knowledge and get some fundamental issues with thermodynamics in order, as it seems to me the AGW crowd have misled themselves and us with an overly atmosphere-centric view of the earth’s heat engine. Sunlight mostly passes straight through the atmosphere and warms the ground and ocean, which then warms the atmosphere.
I’m a reasonably bright guy with an engineering background and a broad based science degree who suffered a reorganisation of his brain when punted off the road into a tree by an out of control car three years ago this week. I still have some insight but struggle with higher maths and stats and would appreciate some feedback and assistance with what appear to me to be fairly important issues WRT to the energy budget of this rock we call home.
A bit of co-operation whereby I chuck half baked ideas over the net and people with quick minded maths and stats skills bat them back with added value would be most welcome. At the moment, Paul intimates discoveries but fails to deliver any ‘look at my graph’ moments, and Leif is in auto-denigrate mode. Come on, lets crack the problem and collect the nobel prize as a collective effort.
Thank you.
tallbloke, based on your comments, you might be interested in the following:
Zhou YH, Yan XH, Ding XL, Liao XH, Zheng DW, Liu WT, Pan JY, Fang MQ, He MX, Excitation of non-atmospheric polar motion by the migration of the Pacific Warm Pool. Journal of Geodesy, 78, 109-113, 2004.
http://www.shao.ac.cn/yhzhou/ZhouYH_2004JG_PM_Warmpool.pdf
Yan, X.-H., Y. Zhou, J. Pan, D. Zheng, M. Fang, X. Liao, M.-X. He, W. T. Liu, & X. Ding (2002). Pacific warm pool excitation, earth rotation and El Nino southern oscillations. Geophysical Research Letters, 29(21), 2031.
http://www.agu.org/pubs/crossref/2002/2002GL015685.shtml
I’ve just located a copy of the Levitus et al. (2009) paper. If there is some particular figure or paragraph in the paper you think worthy of special attention, feel welcome to be very specific in pointing it out, otherwise I’ll be putting the paper aside as I have plenty on my plate.
I’ll consider looking into webspace for posting graphs. This text-only submission format is quite limiting.
“… BUT THE CORRELATIONS BREAK DOWN AFTER …”
Of course the correlations break down! That is *exactly* what you would expect if you are looking at LINEAR shadows of NON-linear relations! It suggests a problem with assumptions. Only once all of the terms, interactions, & dimensionality are *fully* worked out will equations be linearizable. Perhaps some fluid is being treated as Newtonian when it should be treated as visco-elastic. And perhaps also some terms in some differential equations are being set to zero when this is not *always valid. Perhaps some mass is being treated as a point when it should be treated as a series of concentric shells with differential response to gravitational accelerations. Perhaps some probability density functions are being assumed to be of one form when they are really of another. Until the morphology of the various nonlinearities are all worked out you NEED to pay some more respect to phase relations Leif — and I’ve given you some big clues — if you haven’t turned up anything interesting with the clues I’ve shared about the Chandler wobble phase reversal, then I know you haven’t made much of an effort.
Paul Vaughan (07:36:14) :
you NEED to pay some more respect to phase relations
Phase is very important and most of the time plays a big role in disproving a correlation when the phase changes all the time.
and I’ve given you some big clues
which is precisely the problem. If you have something to say, say it, don’t give clues, drop hints, asking one to have to ‘discover’ substance in what you say, intimate discoveries, or other circumspections. Oftentimes, the failure to be able to say what the ‘discovery’ is, is a sign of lack of substance.
You can be constructive by showing me where Charvatova says what her ‘central thesis’ is.
Surely you realize you are wasting my time with such elementary notes:
“Most scientists do not consider just a correlation to mean anything.”
You are taking this out of the context of what followed:
“Equally important are energy and coupling considerations: does the purported impetus carry enough energy to cause the claimed effects and is there a possible physical coupling to mediate the relationship.”
About non-linearity: Any system that has existed for billions of years is to first order linear. Non-linear effects are perturbations on the linear effects.
@Paul Vaughan… Can you give me a link to the whole process? I see the theory very interesting, but my knowledge on it is fragmented. Thanks!
Re: Leif Svalgaard (08:29:47)
It appears you would rather hurl insults than conduct the wavelet analysis I suggested as step 1. Once someone confirms step 1, I will be in a position to communicate about step 2 productively. If no one here can reproduce step 1, then I’m addressing the wrong forum.
Re: Nasif Nahle (09:03:03)
I had basic insights into this research problem as early as September 2008, but in the past 2 weeks, a pile of clean results avalanched on me after a key realization – and I’m still digging out. I’m used to communicating via software called FirstClass, which handles images beautifully. I’m finding this text-only medium quite limiting, but as I’ve indicated to tallbloke, I’ll look into webspace access. Even if I secure webspace access, it is going to take me weeks-to-months – perhaps years – to organize my work & pursue the new leads I’ve turned up — and an audience will have to have intuition about cross-wavelet acoustics to appreciate some of the findings. In the meantime, if someone can confirm that they have reproduced my step 1, I imagine that will be of interest to others who need to see reproducibility.
I have been advised by one of my senior colleagues to stop responding to Leif Svalgaard.
Paul Vaughan (09:54:26) :
I have been advised by one of my senior colleagues to stop responding to Leif Svalgaard.
Very sensible advise.
Paul Vaughan (09:54:26) :
have been advised by one of my senior colleagues to stop responding to Leif Svalgaard.
Whereas, I [in stark contrast] am always willing to answer straight questions [past and in future] without circumspection, if I’m able or have an opinion, as I have done too many times to recount here, except for mentioning the last few instances, like what caused the aa-spike in 1930 and giving a link to ESK data.
Paul Vaughan (07:19:50) :
tallbloke, based on your comments, you might be interested in the following:
Zhou YH, Yan XH, Ding XL, Liao XH, Zheng DW, Liu WT, Pan JY, Fang MQ, He MX, Excitation of non-atmospheric polar motion by the migration of the Pacific Warm Pool. Journal of Geodesy, 78, 109-113, 2004.
http://www.shao.ac.cn/yhzhou/ZhouYH_2004JG_PM_Warmpool.pdf
Paul, thanks for the link to the paper, it is indeed interesting to me in general, and to some extent confirms the links between AAM, ENSO, loD and various planetary wobbles I’ve been trying to draw attention to for a year or so. I’m glad to see you have run with that line of enquiry with your stats abilities.
Of particular interest to me was the sheer distance the measured centre of the Pacific warm Pool moves on an annual and interannual basis. Obviously the ~10 degree north/south movement is dominated by Earth’s inclination to it’s orbital plane which is ~23.5 degrees. The latitudinal movement of up to ~20 degrees on such short timescales is intriguing. The PWP has an area greater than the continental U.S. What shifts it so far and fast? Trade winds drive surface currents, but we are talking here of a body of warm water with a depth of up to 400m! Perhaps the body of water is not moving so much as the applied heat intensity is shifting and cloud variability is the primary driver of this phenomenon, both in terms of regulating heat input from the sun, and rate of heat-energy emittance from the ocean.
I can conceive of ways a study of cloud location change, PWP centre movement and heat content, thermocline depth and near surface temperature may help us get a handle on the timescale of ocean heat retention and rates of energy absorption to deeper levels. I will try to find out if these problems have been worked on, but as I noted earlier, the atmosphere-centric tendency of the AGW crowd means these things have been neglected more than they should.
There are free image hosting services on the net you could make use of while you look into getting your own hosting arrangements sorted out. I have used photobucket.com which has now added some useful features including online image editing facilities, and comments dialogue.
Please try not to fall out with Leif Svalgaard. I have in the past sometimes found him unnecessarily rude, but he is nonetheless a world class scientist who has been generous in sharing his research results with lay members of the climate interested community who have sometimes accused him of having an agenda. Unfairly in my view. Take a breath, put the ego issues aside, and thank him for the links he has provided for you. Then put some graphs on photobucket and prove him wrong. No-one will be more pleased than he.
Is there an acoustic cross wavelet 101 online you can point me to? – I’d like to be able to understand your graphs when you post them.
Thanks.
tallbloke (11:36:17) :
Then put some graphs on photobucket and prove him wrong. No-one will be more pleased than he.
Absolute spot on. Then I would have learned something. And that is what it is all about.
Paul Vaughan (18:11:23) :
The Chandler wobble period plummeted from ~1921 until ~1942. The phase reversal was in ~1931 and can be linked (statistically – I’m still waiting for a physicist to explain the mechanism) to a very unique combination of the following: (1) terrestrial polar motion, (2) solar system dynamics, & (3) the lunar nodal cycle. The alignment is precise and unique in the entire polar motion record (1846-present) – i.e. there is no other such spike.
With awareness of this, some of you should be able to pull several threads together (e.g. precipitation, length of day, polar motion, atmospheric angular momentum, SOI, NAO, solar variation, temperature [global, regional, minimum, maximum, average, extreme monthly minimum, & extreme monthly maximum], rate of change of carbon dioxide concentration, …)
I did take note of this post and await more details. 🙂
One thing which may interest Paul with regard to this is that according to my solar activity cumulative running total method, the count reached a minimum in around September 1935 following a decline since around 1875, and rose to a peak around 2000. To me, this would indicate that the swiftly rising temperature 1920-1940 was the result of a terrestrial redistribution of energy, rather than having a direct solar energy emission cause. How much of the terrestrial redistribution of energy was due to motions induced by non-terrestrial sources I leave to Paul to elucidate and demonstrate.
Here is the best wavelet tutorial of which I know:
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
It is worth going down every link-branch on that site in all detail. The site pitches at a truly introductory level. Someone with no background could spend weeks looking at other wavelet sites and get nowhere – and then get all the wavelet basics in a few hours on this site. There are a LOT of BAD wavelet sites that are just scrapes of other bad wavelet sites – it is epidemic.
The links between LOD, GLAAM, & ENSO are well-established and can be traced back decades in the literature. You might want to dig into the references listed in papers 1, 4, & 5 which I listed at Paul Vaughan (16:56:10). You may also have noted links provided by Richard Mackey (to Lambeck) & Ian Wilson (to Sidorenkov) during recent months — and the following (which includes tons of good references) is likely to be of interest:
R.S. Gross (2007). Earth rotation variations – long period (3.09). In: T. Herring & G. Schubert (eds.), Treatise on Geophysics, Volume 3, Geodesy, pp. 239-294.
ftp://euler.jpl.nasa.gov/outgoing/EarthRotation_TOGP2007.pdf
You may also be aware that Klyashtorin & Sharp make use of the polar motion harmonics I explained above:
ftp://ftp.fao.org/docrep/fao/005/y2787e/
ftp://ftp.fao.org/docrep/fao/006/y5028e/
–
If anyone knows of any very concise summaries of the spatiotemporal extent & phasing of the 1930s drought (that affected at least North America), please let me know. Also, if anyone knows of any “respected” regional &/or global precipitation series, I will appreciate links.
Related:
“Currie (1996), who employs filtering techniques commonly used in electrical engineering, seems to contend that significant lunisolar components are detectable in a very wide variety of terrestrial time series, including virtually all climate series. He investigates terrestrial geographic sites individually (thousands of them) and cautions that zonal &/or global averaging masks locally detectable signals that are intermittently out-of-phase with those at different locations, even ones relatively nearby. […] Currie (1996) suggests that “on decadal and duodecadal time-scales the spectrum of climate is signal-like rather than noise-like, as radically assumed by statisticians and mathematicians the past 70 years.”” (Vaughan 2008)
Currie, R. G. (1996). Variance contribution of luni-solar (Mn) and solar cycle (Sc) signals to climate data. International Journal of Climatology, Vol. 16, No. 12, 1343-1364.
An outline for anyone reproducing what I have described above as “Step 1”:
1.
Polar motion time series can be obtained here:
http://hpiers.obspm.fr/eop-pc/products/combined/C01.html
2.
Difference both x & y and find the root mean square. (This creates an index of polar motion radius with the trend removed.)
3.
Do a complex Morlet transform with wavenumber = 2pi on the interval (3.5a, 9.5a). [Note: a = annum.]
4.
Convert the real & imaginary arrays into modulus & argument arrays.
5.
Find the maximum modulus for each time and note the timescale. (If using Excel, use the functions “max” and “match”.) [Note: This gives a series of group-wave periods corresponding to the polar motion beats visible in the original x & y.]
6.
Find the beat period of this series of modulus-maximizing timescales with the annual wobble using the Helmholtz acoustic equation.
7.
Convert from years to days.
8.
Make a simple time-plot of the resulting series.
This will draw undeniable attention to the Chandler wobble phase reversal.
Step 2 is to compare the resulting curve with precipitation series smoothed at 13 year bandwidth (the average period of the envelope of the polar motion group-waves). [Note: Be sure to check to see if the precipitation series need variance-stabilizing transforms – square root works well with the series I have investigated.]
In part due to the notes of Currie (1996, cited above) I have focused my attention on the heavy precipitation of the Pacific Northwest of North America, where the Pacific Ocean abruptly meets mountain ranges, resulting in heavy fall/winter rain/snowfall. A large anomaly in the 13a-time-integrated precipitation series matches the wavelet-derived Chandler period series. The spatial extent of the 1930s drought extended beyond the Pacific Northwest. I plan to expand the analysis to other sites & regions.
Good science is reproducible. I await feedback. If this result is already known to climatologists, I await references (and I have other clean results involving extreme monthly temperatures).
Note that the calculations do not (so far) depend on the solar system barycentre. Things get a lot more complicated. This is just an introduction.
Hi Paul,
I’ve downloaded the data and chucked it into a spreadsheet (openoffice calc).
I’m guessing step 2 amounts to a trigonometrical function but need help to grasp how you perform the ‘difference’ calculation.
It might help if I understood the units. Presumably x and y are coordinates representing the offset of the pole from the reference frame.
I hope you don’t mind taking the time to get me through this step by step. I’m certainly willing to spend the time to try to replicate and corroborate your results.
Thanks
I’ve started working through the wavelet tutorial. Thanks for the link.
One other thought, once we have the radius plotted against time, we could also take the first and second derivatives to look at velocity and acceleration of the polar motion. It seems to me these might have some bearing on the excitation of atmospheric and oceanic phenomena and may lead to some insight into the relationship between the slopes of the AAM curves and the rate of motion of the pacific Warm Pool.
tallbloke, your intuition about acceleration, etc. is good — differencing approximates a derivative. The differencing is this simple: Say your x series is in column A in Excel – then enter in cell B2 the following:
+A2-A1
Copy B2 & paste it all the way down column B.
–
LOD & AAM:
When you have time, I encourage you to study:
a) figure 1a in Schmitz-Hubsch & Schuh (1999)
http://www.uni-stuttgart.de/gi/research/schriftenreihe/quo_vadis/pdf/schmitzhuebsch.pdf
b) Figure 6 in Sidorenkov (2005)
http://images.astronet.ru/pubd/2008/09/28/0001230882/425-439.pdf
c) figures 1, 2, & 3 in Zhou, Zheng, & Liao (2001)
d) everything Richard Gross has to say in Gross (2007)
ftp://euler.jpl.nasa.gov/outgoing/EarthRotation_TOGP2007.pdf
You will see that the PWP (Pacific Warm Pool) is something Zhou & associates are looking at to explain “left-overs” not explained by AAM (Atmospheric Angular Momentum). If you dig into Gross’s work, you’ll see that he looks at OAM (Oceanic Angular Momentum).
It is important to keep in mind that most experts agree that AAM accounts for a large proportion of LOD variation.
There is plenty of quantified speculation about polar motion, but my impression from digging in the literature is that it is not as well understood as LOD, even though certain aspects of it are certainly very well-understood.
The paper that originally drew my attention to polar motion was the following:
Yndestad, H. (2006). The influence of the lunar nodal cycle on Arctic climate. ICES Journal of Marine Science 63(3), 401-420.
http://icesjms.oxfordjournals.org/cgi/content/full/63/3/401
Over time I have developed the view that, while Dr. Yndstad’s research is a very important contribution, there are problems with his interpretations; I believe there are confounded-influences on polar motion (no simple matter to disentangle). There are different factors with very similar harmonic scales that show up in polar motion phase relations analyses (details will have to wait for another day).
–
Regarding wavelets:
It would take me weeks of heavy, more-than-full-time engagement to develop a good “Wavelets in Excel for Beginners” website. For now, I suggest you focus on getting the basics.
The simplest way to think of it is that the wavelet can shrink and grow —- at each size which it can assume, it takes a trip through the data, pausing at each time-step to measure how well its shape correlates with the data. As you know, correlations range from -1 to +1 – so if the wavelet records -1, that means it matched that data perfectly in a given time-step-window (& at a given size), but that it had to flip over to do it.
For each wavelet size (timescale) there is a string of measurements. In a wavelet plot the strings of measurements are stacked vertically on the timescale axis. Don’t confuse time (horizontal axis) with timescale (vertical axis) on wavelet plots.
What I’ve just described is for a real wavelet. To get at phase information, complex wavelets (with a real & an imaginary part) are used. The imaginary part is phase-shifted by 90 degrees (seahorse-shaped) so that it sees “uphill” vs. “downhill” (upside-down seahorse) while the real part (mexican-hat-shaped) sees “peak” versus “valley” (upside-down mex-hat). This enables one to know – from a pair of correlations – things like “going uphill & approaching a peak” or “in a valley bottom & about to go uphill”, etc. —- i.e. it takes you a step beyond just knowing “on a peak” or “on the side of a hill” — it puts these states into a richer context.
The mexican hat & the seahorse are cooperative traveling buddies. They have different shapes, but they always stick together & assume the same size. These explorers are always curious to see how well their complementary shapes match their surroundings on the time-series-landscape as they slide & change size together. Mathematicians call them a “complex pair” because of their relative appearance, but their view of the world is simple.
Wavelets come in other shapes. The Morlet wavelet gets lots of attention. It can be adjusted to control how many waves it has in its sliding window. This means it can be adjusted to achieve good timescale-resolution – but at the expense of lost time-resolution. For graphs that illustrate this point nicely, see here:
http://www.clecom.co.uk/science/autosignal/help/Continuous_Wavelet_Transfor.htm
If you get the basics from the tutorial at …
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
…to the point where you can look at the regular timeplots on that site and see how they map onto the wavelet plots and vice versa, that will be enough to tide you over until you master wavelet transform calculations — i.e. at least you’ll be able to read others’ work while you are learning to write your own.
Advised: Go through the tutorial links in the order in which they are presented.
Wavelet concepts are simple, but since the edge-effect varies with timescale – i.e. the wavelet hangs further off the edges of a time series as it grows – computer-coding gets fussy. This is just a technical issue – so reading comes fast, but writing takes a little longer.
I don’t have multiple free weeks to explain all of the coding technicalities now – and “part-way” coding doesn’t cut-it with computers. I suggest moving at whatever pace you can, with the first priority being ability to read wavelet plots.
For now I’ll take questions on that. I’m hoping to be positioned to start posting graphs within hours-to-days (there is a technical issue – & I never underestimate them).
tallbloke (00:48:04) “[…] if I understood the units. Presumably x and y are […] I hope you don’t mind taking the time […]”
If you dig around in directories like …
http://hpiers.obspm.fr/iers/eop/
…and in publications, you’ll find the info you need.
“mas” is the abbreviation for milli-arcseconds (angle).
You may find this site to be a useful gateway:
http://hpiers.obspm.fr/eop-pc/
Accessible from there, the following page gives a good overview of EOP:
http://hpiers.obspm.fr/eop-pc/earthor/orientation.html
Let’s see if this link works:
http://www.sfu.ca/~plv/ChandlerPeriod.PNG
Paul, thanks for your excellent and clear explanations. Your graph does show up at your link and very interesting it is. I’ll read more on the tutorial site and at your other links so I can get more out of the nuances of the information your graph contains.
Speculative question: Could the polar motion on a longer timescale affect the position of the magnetic north pole? I remember Vukevic got excited about that and posted some maps on solarcycle24.com showing the path of the shifting magnetic north over the last 2000 years or so which had been produced by some researchers (from Canada I think).
I get what you mean about differencing now. It’s the same as the method I used to get the running cumulative total on the sunspot counts and sunspot area measurements.