LoD, AAM and sea ice relationships

Posted: July 20, 2012 by tchannon in atmosphere, Cycles, data, general circulation, Ocean dynamics, weather

This continues a look at commonality between dataset with a clear linkage on the annual cycle.


Figure 1

Figure 1 is part of the result of rework based on better knowledge.

Previously I posted about the annual cycle and LoD/sea ice. Some of what I wrote was wrong in detail, a risk with actually doing things rather than copying others.

I’m not sure on how much detail to show.

Recently Paul Vaughan suggested via email it would be interesting to look at AAM (Atmospheric Angular Momentum) but this time he referenced an actual dataset, which helps. I tend to be reluctant over artificial datasets, in this case with very dubious underpinnings, including models which are assumptions, all based on sparse and inconsistent data.

I was aware there is a common view in the sciences involved that AAM part drives LoD (earth Length of Day, spin variation) but I have never seen more than opinion.

I am also sceptical for several reasons, a situation not helped by a lack of a coherent mechanism for the linkage, as well as ignoring the huge and moving mass of the oceans.

So I want to see for myself. I’ve split this article with the discussion about data processing in bottom part.

Figure 1 is troubling. When I looked at lead/lag AAM/LoD, using what ought to be accurate daily data it shows a good correlation very close to in phase.


Figure 2

I’d already looked at monthly, using daily Figure 2 confirms what it indicated, where according to this LoD lags AAM by about 10 days, very close to in phase and it seems regardless of a fixed time constant. I expected an elastic effect if one really does drive the other but this is essentially completely the same.

Alternatively I completely misinterpret what the AAM data really is. What I also need is a mechanism, how does one drive the other?

Simple investigative technique, what does the product (point by point) say, Figure 3


Figure 3

This is overwhelmingly unipolar, strange if one drives the other, pointing at a fixed time offset. Given the extensive computations needed for each dataset I am disinclined to take them as accurate.

What else?


Figure 4

Spectra from unfiltered daily data, figure 4, are essentially the same. Most noticeable difference is on the relative 0.5y. Given LoD is quantised to little more than 4000:1 some difference is expected.

Figure 5 shows a known major difference which is specifically excluded from most of the compare plots, such as monthly derived. (I am not looking at lunar)


Figure 5

LoD has very clear lunar spectra which I very clearly and precisely showed in another work elsewhere by splitting the doublets (invisible here) and correctly they show an 18.6 year repeat. There is no lunar component in AAM data. If this does exist it is not in the global average, (perfectly possible) it poses a need by those chasing lunar effects to explain this away.

The strong ~13 day strangely has a spectra null for AAM, suggesting a curiosity, an absence can be telling.

This also poses the question of why if LoD/AAM are so tightly linked at a short timescale there is no lunar effect in both?

Sea ice

Bringing in the sea ice from the previous article I am still of the opinion this is closely linked to LoD and as a driver, with the mechanism of latitudinal mass transfer. An error I made was mentioning the difference in north/south ice when actually it is the sum, ie. total.

Someone remarked they would like the see the effect of variable proportions of north/south. I agree, had a play but from what I could see this is of interest without changing much in this context. Here is an opportunity for others to explore. (showing anything here would take time)

A useful addition here is an article I published last year on my own blog where this attempts to show why the annual Arctic extent shape is very tightly a simple function driven by the sun except in hindsight that is not strictly correct. It has more to do with the tilted earth axis, which in current times is close in antiphase to sun/earth distance variation.


This gives me an idea for a future avenue to explore: as the earth orbital parameters drift so will the shape of any polar ice extent. This could be modelled. A change in seasonal shape might be illuminating re ice ages. Extending thought further for a moment, this will impact paleo proxy results which will vary in their behaviour, eg. rock deposits from iceberg melt.

Food for thought in there in the implications for fauna and flora in history, coping with different environments for the reproduction cycle. Darwin has spoken many times leading to what we have today.

Discussion is welcome, as is help.


This describes what I have done with the data.

Assume LoD and sea ice are similar to this recent article.


datafile http://ftp.aer.com/pub/anon_collaborations/sba/aam.ncep.reanalysis.1948.2009

Data is sampled 4x daily, 1948 through end 2009. Documentation/description is very poor so I played around to guess my way to a reasonable solution.

There are 9 data columns, 3 triplets of xyz, with z a dominant figure, not clear which axis is which or whether this is linear or rotational. Units are not known, figures in the 1e24 range.

What is stated is mass with or without barometric compensation, plus motion, whatever that is.

I chose to use uncompensated, don’t want yet another dubious hack, however there is barely any difference barometer or not.

The xyz is awkward so I decided to simply do |xyz|, alternative looks too close to quaternions, don’t go there.

Laws of inertia/motion, compute ((motion^2/mass)/2 which ought to give inertia/momentum, ie. energy. Curiously this gives a result very close to 1.00e24 as though it is centred on that value. This was a worry, the signals are unipolar but variation in momentum is bipolar. The result looks sensible.

From that I get 1948 onwards at 4 samples per day, awkwardly large.

Accurately decimate to daily 1962 onward to match LoD dataset.


Figure 6

Output runs 1st Jan 1962 to 31st Dec 2009, daily samples. Few climatic or meteorological (or science for that matter) datasets are validly sampled.

Data for plotting and some compares was further decimated to monthly


Figure 7

Long term variations vary widely with these datasets but the primary interest here the annual cycle, so a high pass was applied, for consistency an identical filter to monthly data. (since sea ice is monthly data)

As a second effect this kills dataset offset from zero.


Figure 8

Filters use automatic end compensation, don’t like it, don’t use the results or ignore a few months at the ends.


Not provided at the moment, too much. Ask for specific things.

Posted by co-moderator

  1. Ninderthana says:


    There is no lunar component in AAM data. Exactly – My understanding is that the Lunar tidal component is deliberately excluded from the AAM calculation.

    The powers that be have decided that on periods less than 5 years, the Earth/Atmosphere/Oceans experience no external torques other than lunar/solar tides. Hence, the gurus regularly remove the lunar/solar tidal components (with periods less than or equal to 18.6 years) from the LOD and AAM data. Then, they make the assumption that the lack of an external torque means that the overall total angular momentum of the Earth/atmosphere/oceans is conserved. Hence, all variations in LOD/AAM under five years just involved the transfer of angular momentum from the solid Earth to the atmosphere/ocean system – with most of the exchange being between the solid Earth and atmosphere.

    Of course, blind Freddy can see that they are assuming that solid Earth, the Earth’s liquid core, the atmosphere and the oceans are all responding in exactly the same way to the solar/lunar tides on time scales less than five years. What if any one of these were to respond differently to the external tidal influence than anyone of the others? Under these circumstances you might expect the solar/lunar tides to play an important role in the angular momentum transfers between the atmosphere and the solid Earth – particularly on time scales ~ five years and longer.

  2. tchannon says:

    That would be deliberate removal. I’m a little surprised such people could do that and survive through what I have done without leaving a fingerprint.

  3. Hans says:

    Tim and all,

    I think that treating LOD variations is a very important issue and in my opinion almost anyone has fallen into a number of traps that are involved in examining complex systems. Here are some comments dealing with your two sentences below.

    “lternatively I completely misinterpret what the AAM data really is. What I also need is a mechanism, how does one drive the other?”

    This is treated in the paper “Richard D. Rosen and David A. Salstein, “Variations in atmospheric Angular Momentum on Global and Reginal Scales and the length of Day, Journal of Geophysical Research, Vol. 88, 20pp, June 20, 1983

    Spectral analysis is used on AAM (empirical orthogonal function (EOF) or principal compontent analysis) and the amplitude is shown in latitudinal belts. Maxima are around +/-30 latitude (in w2inter) and is about double the southern one in the northern hemisphere.

    It is stated in the article that: “We conclude on the basis of these comparisons that that indeed most of the variability in our timne series for M is real and that, as others have suggested, the atmosphere plays a dominat role in forcing changes in LOD on time scales of about a year and less.”

    This is a statement that has to be checked and it is very probably false. It is much more probable that the (frequency limited) correlations betweween LOD and AAM is the opposite of what is concluded, the moon is forcing changes within a limited frequency band and limited area of ears atmosphere.

    It should also be noticed ÁAM VARIATIONS are much more developed in the northern hemisphere than in the southern hemisphere. In the latter the jet winds are almost constant throughout the year. In the Norhern hemisphere they go down to zero during summer time. Any correlation between GLOBAL AAM and LOD is approximately a correlation between LOD and Northern hemisphere AAM. This is an important distinction.

    for a logn time scientists tried to figure out how momentum was transfered from the atmosphere and solid earth without success. The truth is probale that the energy only is moving in one direction.

  4. Hans says:

    Tim and all,

    There has been a keen interest in corelations between LOD and AAM for many years. These efforts have not lead to much substantial knowledge about spin-orbital coupling, probably because scientists don´t want to believe (investigate if) that such ones do exist.

    J.O.Dickey et al wrote “Extraterrestrial aspects of the 40-50 Day oscillation in LOD and Atmospheric Angular Momentum, Journal of Geophysical research, Vol. 96, Dec. 20, 1991, 16pp.

    A major fault is to remove “lunar influences from the data set. Another one is to treat “global AAM” instead of separating them in each hemisphere. The influence of our moon is the key to understand why LOD do exist. This investigation is far foo limited in frequency band to get an undeerstanding of the correlation between AAM and LOD which actually is very limited. No such limit do exist for LOD variations.

    It is stated: “Results suggest that two intraseasonal oscillations exist in the earth-atmosphere system: a tropical 50-day oscillation associated with the convectively driven MJ wave and a mid-latitude, 40-day oscillation associated with the interaction of nonzonal flow with topography.”

  5. Hans says:


    Signal processing can be a very potent tool to gain knoledge and you are for sure aware of that. However, interpreting the outcome is not always easy.

    A very ambitious investiagation of LOD spectral compontent was performed by Charles F. Yoder et al, “Tidal variations of Earth rotation”, Journal of Geophysical Research, Vol. 86, Febr. 1981, 11 pp.

    The amplituded of 62 (!!!) frequency components have been measured. The two dominant ones are 1 and 0.5 years. Then the basic onces at higher frequences are in order 27.56, 13.66, 13.63, 9.13 and 14.77 days.

    This makes me quite sure that you have identified a number of essential frequences in your figure 5 above. One is half the anomalistic month (27.55455/2 days), one is half the synodic month (14.765), 9.13 days is 1/3 of the siderial lunar piriod, 14.77 is half the synodic month nd the 4 double peaks are all produced by the influence of the half year periodicity which is the beat frequency of each of the double peaks.

    Observe that twice 13.66 is the lunar siderial period which is a fact that has to have an explanation. So far I haven´t seen any offical one why it should be a prominent cycle in LOD variations. It is interesting that you pointed out that the 18.6 year period (lunar perigee orbital period was idenfi´fied in your material despite filtering away other “lunar” frequencies. If you want raw data to treat with signal analyses look at maia.usno.navy.mil/ser/7/finals.all

    If you do feel that your data in figure 5 allow 4 digits for the peaks I would be very interested in getting these numbers and please don´t forget the negative peak at about 40 days which might be very important.

  6. Hans says:


    Your figure 1 raises a number of interesting questions that I might come back to. Mass displacement is for sure one reason to take into account for causing LOD variations but that can hardly be all.

  7. tchannon says:

    Ah, someone is cutting through the rapid fire Graeff posts. I’m letting that run whilst some are it seems enjoying trying to make progress. Doesn’t help other readers though.

    My interpretation is LoD and AAM are essentially locked in phase therefore any coupling between them is extremely strong or they are caused by a common something else. The latter is unreasonable (come to lunar in a moment) but so it something as trivial as a low mass layer tightly driving a large chunk of rock.
    I assume LoD tightly drives atmosphere.

    If an elastic medium such as gas was doing work driving this ought to show strong phase effects.

    On the other hand it is rather likely there is a considerable mass transfer during a year to and from polar regions and such a mass transfer is more or less directly coupled to body earth, giving a trivial explanation for spin variation. This also has around a 90 degree phase shift, so it makes sense as a driver.

    Why is a more complex explanation needed?

    The moon, I’ll make that a separate reply.

  8. tchannon says:

    I mentioned an earlier work elsewhere. Some time ago Paul Vaughan asked me to look in detail at a dataset he provided of LoD. (when I checked it was first difference, makes little difference to what I was doing). The result was of some use and was mentioned in a WUWT article. A subsequent more detailed version exists.

    I’m not inclined to show much because this involves painstaking detailed work where there has to be a definite justification.

    Reasonable separation of lunar doublets, triplets etc. cannot be done using a Fourier Transform given the dataset low sample rate, length of suitable data and poor data resolution.

    I often show spectra here which is done by my own software which takes the sensible limit as far as I think is safe. This is partially about windowing where I insist on using a window where otherwise the ambiguity leads to spurious and highly misleading output.
    Most of these are chirp z-transform and use a version of the kaiser bessel window.

    For illustration purposes I picked a probable doublet with a period of around 13.6 days.

    The blue trace is what Fourier shows, almost separating into two, of different amplitude.

    As some of you know over some years I developed novel software which can so exactly lock to a term it can be subtracted out of a dataset and also producing a fourier model of the data. This has various uses.

    Given the extreme nature of this problem I have to guide the software. In this case is trivial, allow two terms and give it upper and lower limits on where the look.

    The red trace is the model output. Actually out put as a timeseries and the same chirp applied, plot both together.

    This is extremely accurate, producing period, amplitude and phase. Noise, interference, quantisation all act to limit how good.

    If I subtracted the model from the data the peaks would vanish, are cancelled out.

    if you are still with me, some numbers.

    Outputting to 6 places (arbitary)

    ignore A B
    period -var- 13.660991 13.633395
    frequency -const- 0.073201 0.073349
    phase -var- 2.868012 0.358860
    amplitude -var- 0.000356 0.000147

    Now sum and difference the periods

    sum diff years
    6.823590 6748.973603 18.478077

    Not spot on 18.6 years, but give me a break, know anyone else can do that?

    The effect of two very slightly different periods is a drift in and out of phase, adding or subtracting in effect, with a period of 18.6y

    Unfortunately plotting this directly is not possible, needs too many points and would alias on display at anything less.

  9. tchannon says:

    Ian says lunar is deliberately removed from AAM. I do not understand why anyone would publish a dataset like that without making it clear and giving a reason.

    AAM obviously is primarily random noise. Is weather isn’t it?

  10. Ninderthana says:


    From: http://ggosatm.hg.tuwien.ac.at/rotation.html

    The atmosphere is one of the fluid portions of the Earth and its angular momentum shows significant temporal variations due to large-scale mass redistributions and changes in the pattern of winds. If one disregards external torques exerted by other solar bodies, the collective angular momentum of all fluid layers (atmosphere, ocean, core, …) and the solid Earth (crust and mantle) has to be conserved. This means that changes in the angular momenta of the solid Earth and the fluid layers are of equal size but otherwise opposite. Changes in the angular momentum of the solid Earth, however, are visible as fluctuations of the rotation of our planet. In this way, atmospheric processes are responsible for a certain part of geodetic polar motion and observed changes in length of day (LOD).

    When studying the influence of the atmosphere on Earth rotation, it has become common practice to use the effective atmospheric angular momentum (AAM) functions, which were introduced by Barnes et al. (1983, Proc. R. Soc. Lond.) and can be directly calculated from globally-gridded meteorological data. The AAM consists of two components, usually referred to as matter and motion terms (or pressure and wind terms). The matter term describes the influence of atmospheric mass redistributions on the Earth’s inertia tensor, whereas the motion term corresponds to the relative angular momentum of the atmosphere with respect to the mean rotating reference system. In its most practical formulation, the two AAM components are estimated from surface pressure data and from the global fields of zonal and meridional wind velocities.

  11. Tenuc says:

    Tim, there could be a problem with the model used to produce the NOAA Reanalysis Observation dataset, as it doesn’t conserve total angualr momentum. Paper discussing the issues is available free here…

    Click to access Simon_Driscoll.pdf

    The Earth’s Atmospheric Angular Momentum Budget and its Representation in Reanalysis Observation Datasets and Climate Models
    “…We conclude that the NOAA Reanalysis Observation dataset, like many others, does not conserve angular momentum. It is thought that the error lies almost completely in the torques and that any error in the angular momentum is negligible.

    It is believed that major error lies in the gravity wave torque in the northern hemisphere winter (and that the choice of the gravity wave torque parameterization is not the main factor), along with the friction torque, which exhibits a large positive bias over all times (but particularly in the northern hemisphere winter), and also the mountain torque which, too, shows a large bias over the northern hemisphere winter.

    We note that there seems to be some large error coming from the data assimilation process, however, we are not able to pinpoint the cause(s)…”

  12. tchannon says:

    Already been that. That is what first alerted me to the questionable nature.
    Try this “The general goal of the AAM part of GGOS Atmosphere is to rigorously model atmospheric effects on Earth rotation for all time scales and improving the models which are involved in the estimation process. ”
    Why not simply calculate based on hard data?
    I assume this is because they can’t.

    Try this too “Investigating the relationship between effective AAM functions and Earth rotation parameters at diurnal and semi-diurnal frequencies and improving the existing transfer functions proposed by Brzezinski et al. (2002, Surveys in Geophysics).”
    Yet zero lunar.

    My word you have been digging. Grin. msc? No-one will blink. Methinks he and his supervisor were mighty cynical but couldn’t say it directly. Data 100 years apart gives the same answer, actual data is of a wildly different coverage… amused.

    Atmosphere 5 orders of magnitude smaller, quite.

    I still want to know why ice as a proxy is as good a fit and has a plausible chicken phase angle.

    Not a lot more I can do.

  13. Tenuc says:

    It is interesting that it is the NH winter which comes most under the spotlight from Simon Driscoll in the above paper. Few top-of-the-head thoughts…

    Perhaps conventional wisdom has cause and effect mixed up, though I’m not sure if there is actually a correlation between AM of atmosphere, ocean, solid earth and changes to rate of Earth spin – could all be responding to an unknown third ‘force’, with slightly differing effects and lags?

    Perhaps the change of state of water from a highly mobile fluid (both as vapour and liquid) to less mobile solid ice could cause problems to the standard conjecture, which appears to have the tail wagging the dog! The part of the Arctic ocean which does remain liquid also has less freedom of motion in the winter than in the summer when the ice starts to break-up and melt.

    Finally, I’m sure that turbulence and changes of AM from and to other forms of energy, such as heat, are also being underestimates – anything to do with climate tends to be very messy, producing observational data with lots of noise.

  14. I am not sure this will help, but the internal cycles have several variables that tend to help you see what you wish to see. So I have been playing with a method to help make some sense out of the internal noise.


    It is not perfected by any means, but it does appear to help spot internal inertia symmetry that appears to be more like noise. So you can not only remove ENSO for example but the harmonics to some extent.