QBO rough analysis

Posted: September 13, 2015 by tchannon in Analysis, wind

This is a quick rough and ready analysis of an QBO data since Paul Vaughan asked. Here are all the things you never wanted to know.

QBO ( Quasi-Biennial Oscillation) is a strange entity, wind direction alternates. The data is an index, artificial computation and in this case part of a reanalysis. This article might add some insight http://www.geo.fu-berlin.de/en/met/ag/strat/produkte/qbo

A problem I see with simple data such as at one pressure level and location is the many other changes over time. Perhaps the pressure level should vary a little. It’s a multi-dimension entity anyway.

I’m taking it as-is with no more comment.

Image

Figure 1, straight plot of monthly data, which runs from 1948. No units are given so assume metres/second. Data used

The author has several bespoke software works useful for analysis, in C, unpublished so reproducing this work would be difficult.

On considering the data the period before 1970 is ignored. There is no information on technology changes or data reliability.

Paul Vaughan’s posit involves lunar modulation. If I take the largest 2.3 year term and find the amplitude modulation that gives 15.6 years which is not lunar. Not shown here.

The periodic terms circa 2.3 years are a triplet. Here is the evidence.

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Figure 2. Evidence of a triplet.

Given the data length only vague Fourier spectra can be done but the author has an innovative method of analysis as shown in figure 2.

Blue trace is the 1970 onwards data, which shows a hump with signs of more than one item present. The software finds an exact best match in a least squares sense. (RMSE). Red trace is the residual after three terms have been subtracted from the data. Yellow trace is spectra of what was subtracted.

Windowing is necessary with a Fourier transform, the Kaiser-Bessel beta=3 windows used here is in the author’s opinion the best compromise which shows best detail of closely related periods, but rejection of artefacts is necessarily moderate.

The software outputs various files. Here is a plot of the above.

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Figure 3, overlay of three term result and input data, hindcast has been allowed but is very unlikely to be correct.

In this case it seems reasonable to try and produce an analytic signal, a strange but important facility used in signal processing. The authors software has never been fully developed out for fringe use so this is pushing things given the awkward nature of climatic data.

The first move is bandpass filter the QBO data because high and low frequencies make a mess of things. This was done with diagnostics implying a good wanted signal from 1.8 years through 3.2 years.

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Figure 4

What is an analytic signal? It is the signal and the 90 degree phase shifted version of the signal, with a twist, the 90 degrees applies to all frequencies. Mind bending things are close. This is usually produced via an Hilbert Transform[ation].

Now, if you happen to have a signal and it’s quadrature, another name for a 90 degree phase shifted version there are magical mathematics available.

First lets prove it worked. Best note the ends of the data go bad, I’ll plot them anyway.

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Figure 5, plain plot of quadrature signals

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Figure 6. Another way of looking at it. Should be circular.

Trick mathematics? Know that Pythagoras chap? Simple sine and cosine allow direct computation of the envelope, a continuous amplitude signal, nothing else needed, a direct method.

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Figure 7, The envelope. As I mentioned earlier ignore the data ends.

Another family but more tricky is instantaneous frequency, phase and delay, all requiring phase unwrapping of the data, an indeterminate problem, very hard to do. This is why I bandpass filtered, reduces the problem. Did my code work?

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Figure 8, Instantaneous frequency (actually period, bespoke software inverts frequency)

What happened 2001? Probably gone through a singularity.

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Figure 9, phase, unwrapping was successful. (you’d see abrupt discontinuities)

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Figure 10, the least interesting plot, a metric, usually a straight line

Finally answer a question

period phase amplitude
2.3396747739 0.7220279978 12.1855647167
2.1996734721 3.6371639858 6.624010329
2.5320954646 2.3449830156 5.6962092807

Phase reference January 1948

What to make of that lot?
Not really anything to add, no insight. If it means anything you tell me.

Post by Tim

Comments
  1. Tim,
    There may be a lot more but well hidden in the damn averages. Is QBO or (Quasi-Biennial Oscillation), (quasi bi-annual oscillation?) but meteorology speak for an approximately 27.6 month or 840 day cycle interval cyclic wind? Your data seem to be monthly ‘average’ 30 kPa altitude equatorial north/south wind velocity. This ‘thing’ that Paul has discovered may very well be a wide spread atmosospheric 3D volumetric repeating wind phenomenon, transporting H20 in all 5 phases to all places. This but expresses itself locally at the equator to incompetent academic meteorologists as a vaguely apparent N/S stratospheric wind speed oscillation.
    Perhaps to Paul such does critically imply all manner of total interplanetary Solar system mass motions involving gravitational accelerations. Can you politely ask him?

  2. Ian Wilson says:

    The the three periods (in ascending time) to 4 significant figures:

    Period 1 = 2.200 years = 26.40 months
    Period 2 = 2.340 years = 28.08 months
    Period 3 = 2.532 years = 30.38 months

    How does this compare to the 4th sub-multiple of the three dominant long term tidal cycles?

    8.850 years / 4 =2.213 years = 26.55 months
    9.300 years / 4 = 2.325 years = 27.90 months
    10.147 years/ 4 = 2.537 years = 30.44 months

    I’d say that there is a good match.

    It know from observation that roughly half the QBO events have periods of ~ 26 months
    and the other half periods of ~ 30 months giving an average QBO length of ~ 28 months.

    Prof. Nikolay Sidorenkov has also found a direct connection between supra-multiples of the ~ 1.2 year chandler wobble (CW) with both the Quasi Biannual Oscillation (QBO) and the ENSO.

    I’ll say it again:

    Nikolay Sidorenkov has pointed this out for decades and I have alluded to it on multiple occasions over the last five years:

    N. Sidorenkov, Astronomy Reports, Vol. 44, No. 6, 2000, pp 414 – 419, translated from Astronomischeskii Zhurnal, Vol. 77, No. 6, 2000, pp 474 – 480

    2013: http://astroclimateconnection.blogspot.com.au/2013/06/linking-orbital-configuration-of.html

    2010: http://astroclimateconnection.blogspot.com.au/2010/03/why-do-long-term-periodicities-in-enso.html

  3. Ian Wilson says:

    Another way of looking at the matching of the periods [to four significant figures] that Tim has measured to the long term tidal cycles:

    Period 1 x 4 = 2.200 years x 4 = 8.800 years – compares to 8.850 years for the Apsidal precession
    Period 2 x 4 = 2.340 years x 4 = 9.360 years – compares to 9.300 years for half the Nodal precession
    Period 3 x 4 = 2.532 years x 4 =10.128 years – compares to 10.147 years for Perigee-Syzygy Cycle

    Errors are:

    Period 1 x 4 – 0.05 years
    Period 2 x 4 – 0.06 years
    Period 3 x 4 – 0.02 years

  4. Ian Wilson says:

    Nikolay Sidorenkov’s 2000 paper is available at:

    http://link.springer.com/article/10.1134%2F1.163865

    The paper is pay walled but you can view the first two pages [of three or four] and see the graph on page 2 to get an idea what he was saying over 15 years ago.

  5. Ian Wilson says:

    Technically the multiples should be:

    Period 1 x 4 = 2.200 years x 4 = 8.800 years – compares to 8.850 years for the Apsidal precession
    Period 2 x 4 = 2.340 years x 4 = 9.360 years – compares to 9.300 years for half the Nodal precession
    Period 3 x 8 = 2.532 years x 8 =20.256 years – compares to 20.293 years for Perigee-Syzygy Cycle

    Errors are:

    Period 1 x 4 – 0.05 years
    Period 2 x 4 – 0.06 years
    Period 3 x 8 – 0.04 years

    Sorry.

  6. Ian Wilson says: September 13, 2015 at 7:53 am
    ———————————————————————————————————-
    Technically the multiples should be:

    Period 1 x 4 = 2.200 years x 4 = 8.800 years – compares to 8.850 years for the Apsidal precession
    Period 2 x 4 = 2.340 years x 4 = 9.360 years – compares to 9.300 years for half the Nodal precession
    Period 3 x 8 = 2.532 years x 8 =20.256 years – compares to 20.293 years for Perigee-Syzygy Cycle

    Errors are:

    Period 1 x 4 – 0.05 years
    Period 2 x 4 – 0.06 years
    Period 3 x 8 – 0.04 years
    ————————————————————————————————————
    Ian,
    Can it be that there are no errors, except for the earthling’s insistence of periodic and on rationality (integer ratios)? I am from an engineering, observational POV.
    Spinning near spheres must nutate (wobble), always. Much different than precession from torque orthogonal to spin axis. Spinning atoms wobble little, mass in centre, little moment of inertia. Spinning beryllium thin shell, “all moment of inertia”, refuses even to have a spin axis constrained to its own spatial geometry. Flywheels with very an-isotropic moment of inertia, must also nutate near twice rotation rate, along with the understandable precession with the application of torque orthogonal to spin axis. Planets with massive liquid centres, must remain very, very weird!
    BTW, Who the hell is buying the next round?
    All the best! -will-

  7. Paul Vaughan says:

    Point of clarification:

    I wasn’t suggesting there’s an 18.6 year envelope in QBO.

    Rather I was commenting on Paul Pukite’s exploration of QBO record aliasing …and what would be expected theoretically from a simple consideration of geometry based on those suggestions.

    Tim’s contribution helps explore Pukite’s & related ideas.

    These things Tim does (Hilbert, analytic, quadrature, etc.) can be taken an order of magnitude further with unconventional wavelet methods, but Tim’s analysis gives a traditional perspective that differs from Pukite’s exploration …and light from many useful directions aids synthesis.

    The suggestion I left was to look at LOD …and of course we know the 18.6 year envelope is crystal clear there.

    https://tallbloke.wordpress.com/2015/09/10/cheeky-pukitee-nicking-knowledge-without-acknowledgement/

    To first order QBO is nailed. Beyond that we’re not finished exploring …so light from many useful angles is welcome.

    Unfortunately there isn’t time to pioneer a whole lot of software…

    – –

    FYI I’ve given an update on Atlantic Hurricanes on the Suggestions-13 thread.

    Regards

  8. Ian Wilson says:

    Will,

    The errors of ~ 0.05 years are just a natural consequence of measurement error.

  9. Ian Wilson says: September 13, 2015 at 9:06 am

    (Will, ‘All the best! -will-‘)

    “The errors of ~ 0.05 years are just a natural consequence of measurement error.”

    Dr. Wilson, u-aizu.ac.jp,
    Respectfully, Good God, 18.25 days is approximately 2 beers/day from a 30 pack! Do you guys even have a ruler? The constant speed of 10 micron light, as one foot per nanosecond in vaccuo, relates to 3 inches per nanosecond in germanium. Or perhaps 3 inches inside = one foot outside, perhaps one foot inside, 3 inches outside. Or perhaps 3 x10^8 meters/sec outside, = 0.75 x 10^8 meters/sec inside, or perhaps 4 seconds inside = one second outside. Do you high academic priests have any idea of what you may be spouting?🙂

  10. Ian Wilson says:

    Will,

    As an engineer, you might try thinking of them as percentage errors. It sounds much better!

    Period 1 x 4 – 0.57 %
    Period 2 x 4 – 0.64 %
    Period 3 x 8 – 0.20 %

    I think that the actual error between the measured and expected periods is dominated by the inherent errors that come from measurement process. I think Tim will tell you that it is hard to improve on those measurement errors given the limited length of the data series.

    All I am saying is that the result is strongly suggested in that the spacing of the three spectral features is close to what you might expect if sub-multiples of the three lunar cycles were involved.

  11. tchannon says:

    The intermodulation of those three terms will produce the envelope. Note to Will, this is all taken as roughly. Those figures though are so accurate you could compute a time series fitting the published data and reproduce what was shown. Whether this is useful is another matter.

    Posting an article makes the information available for others, if of little chatter interest.

  12. Ian Wilson says: September 13, 2015 at 3:36 pm

    “Will,

    As an engineer, you might try thinking of them as percentage errors. It sounds much better!

    Period 1 x 4 – 0.57 %
    Period 2 x 4 – 0.64 %
    Period 3 x 8 – 0.20 %

    I think that the actual error between the measured and expected periods is dominated by the inherent errors that come from measurement process. I think Tim will tell you that it is hard to improve on those measurement errors given the limited length of the data series.

    All I am saying is that the result is strongly suggested in that the spacing of the three spectral features is close to what you might expect if sub-multiples of the three lunar cycles were involved.”

    Dr. Wilson,
    Thank you for your measured response to my outburst! I also suffer from frustration in getting a POV across. Yes “error in measurement” is generally presented as a percentage of the measurement. My previous was a question of ‘are these errors at all, or actual symptoms of the physical to be contemplated?’
    Will Janoschka says: September 13, 2015 at 8:39 am

    (‘Can it be that there are no errors, except for the earthling’s insistence of periodic and on rationality (integer ratios)? I am from an engineering, observational POV.
    Spinning near spheres must nutate (wobble), always. Much different than precession from torque orthogonal to spin axis. Spinning atoms wobble little, mass in centre, little moment of inertia. Spinning beryllium thin shell, “all moment of inertia”, refuses even to have a spin axis constrained to its own spatial geometry. Flywheels with very an-isotropic moment of inertia, must also nutate near twice rotation rate, along with the understandable precession with the application of torque orthogonal to spin axis.’)

    The obliquely spinning and orbiting earth and independently spinning atmosphere “must” respond in a deterministic fashion to any external torque upon it. Since the inner planets orbit mostly the mass of the Sun rather than the SS barycentre The motions of the Sun will have effects on all of the angular momentums of the Earth. The closer coupled Moon more greatly affects such balance.
    I suggest that an expected response to the torques be examined then the deviations from the expected be measured. From experience, not from books, torquing tuned spinning mass does not result in just a translation to smooth angular precession orthogonal to both the spin and torque axis. Nutation also occurs. The precession is in epicycles. In engineering such untoward is reduced with dissipative nutation dampers that act much like Earth’s liquid about the core, ocean sloshing, and perhaps, the atmosphere’s variation in jet-streams and vorticies.
    I have looked at the additional QBO data Tim pointed to. It is truly a mess, but there is 3D data there of finer measurement than monthly average of one pressure altitude. Errors in measurement will always be, but averaging is the enemy of understanding.

    tchannon says: September 13, 2015 at 5:32 pm

    “The intermodulation of those three terms will produce the envelope. Note to Will, this is all taken as roughly. Those figures though are so accurate you could compute a time series fitting the published data and reproduce what was shown. Whether this is useful is another matter.”

    Tim, Please investigate why such resonances do not destroy this planet. Why does the envelope dissipate, cancelling any hope for ratioing the three?

    “Posting an article makes the information available for others, if of little chatter interest.”
    Thank you Tim!
    All the best to both of you! -will-

  13. Paul Vaughan says:

    A lot of good questions are coming to mind with this quick QBO revisit… this is good …but too busy at paid-work and too many other things on the go, so no time to even record the questions …and all of this gets pushed way back on the back-burner …for some future month or year.