LoD linked to solar radiation proxy, polar ice

Posted: June 27, 2012 by tchannon in Analysis, climate, Cycles, data, Dataset, Uncategorized, weather

Figure 1

Linkage of LoD to annual earth mass redistribution by global sea ice extent as a proxy.

Author: Tim Channon

LoD (Length of Day) contains a strong annual signal which is good shape match (r2=0.91 at a time lag of just over 5 months) with global sea ice extent as a proxy for annual mass redistribution, ultimately driven by variation in insolation and earth movement.

This suggests no lunar involvement, a disconnected between this part of the dataset and the rest.

The author noted a major mismatch between the spectra at earth distance for solar radiation and the same periods in LoD data. Recalling global sea ice looked similar this was compared and found to be a good match.

Northern snow cover and Arctic sea ice extent are closely allied. Unfortunately there is no global snow cover dataset (confirmed in a private conversion with Rutgers Snow Lab).

The sea ice dataset (NOAA/NSIDC d02135) is low resolution but is the only long term global dataset. This is sufficient for the present analysis.

Software was used to synchronise to and clone with accurate amplitude and phase the annual cycle of LoD and sea ice extent data to the 5th harmonic producing a pair of data models. Daily LoD was re-referenced to the sample rate of the monthly sea ice data.

This was normalised and plotted with a data time offset at a suitable lag, 5 months, then empirically fine tuned using a Farrow interpolar. Best r2 is at 5.16 months lag, value 0.91, a few cycles are shown as figure 1.

Visual confirmation

A direct visual confirmation of the above is important. This required processing of the dataset to remove major confounding features which are unrelated.

LoD data needed removal of the majority of the lunar orbit signal and long term change.

This was accomplished with suitable low and high pass filters.


Figure 2

Period in years, left to right, high pass, low pass LoD, low pass sea ice, all end corrected, of no importance here. The high pass is a compromise attempting to avoid the 0.1666/2 sample rate but allow the 0.2y 5th harmonic. the data not meeting Nyquist anyway. Low pass is arbitrary and keeping the known 2 to 5 year variations. A lot of weather noise is allowed.


Figure 3

Filtered datasets over a common time span but without relative time lagging.

LoD data contain a lot of weather noise where as usual the huge 1983 En Nino is clearly present.


Figure 4

Time lagged processed data plotted for visual comparison, r2=0.67

None of this provides insight into what exactly is moving mass  and might or might not involve snow/ice, which is frozen water originating as liquid elsewhere.

I’m expecting dispute from certain readers who have other ideas on what is going on, so be it, is how progress is made.


Figure 5

Spectra, the annual components and the effect of the bandpass filter.


LoD data as XLS
LoD data as OpenOffice ODT (actually ODS) (WordPress disallows .ods but allows .odt (wordprocessor), either rename the suffix or simply open, OO figures it out)

LoD data as XLS
Sea ice data ODT (see above)

The NOAA/NSIDC data source is about as cussed as it could be, bizarre file and directory structure, pairs of files by month in different directories. I don’t think they want anyone to actually see the data, only their political spin presentation.

How accurate is it? Not particularly, needs better than monthly but is from a mishmash of satellites anyway.

Also note missing data is not marked.

And read the notes in the files because the data is broken as is, needs an offset added for some of the time.

Alternatively trust me. (scripted download and mangle into a time series)

There is more data if you need it, intermediates, and so on, ask.

  1. tchannon says:

    The author comments:

    I decided to publish even though I am not entirely happy with the results. Better to show something and then I can move on to other things.

    Dispute is perfectly okay. If I am wrong this is far from the first time.

  2. Ninderthana says:


    You work appears to be very thorough and your arguments logically set out. Congratulations on a job well done!

    A few points to note:

    1. The result you have obtained has already been put forward by Prof. Nikolay Sidorenkov.

    Sidorenkov, N.S. (2009), The interaction between Earth’s rotation and geophysical processes.
    WILEY-VCHVerlag GmbH & Co. KGaA, Weinheim, 2009. 317 pp.

    However, I believe that the way [and venue in which] you have explained it will get the message out to a much larger audience.

    2. I believe that my earlier explanation

    [see https://tallbloke.wordpress.com/2012/06/19/earth-motion-lod-and-sorce-mystery/#comments
    Ninderthana says: June 23, 2012 at 3:20 am]

    still stands: i.e. That the semi-annual and annual changes in LOD can be explained by momentum exchanges between the solid Earth and the atmosphere and vice-versa.

    Semi-annual cycle in LOD is caused by seasonal momentum exchanges between atmosphere and the solid Earth that are due seasonal asymmetries between the mean latitude and strength of the mid-latitude westerly winds.

    However, the annual cycle in LOD may be caused by the net shift in polar ice that are caused by
    the ~ 7 % change in solar insolation that results from the Earth’s movement from perihelion to aphehilon. This redistribution in angular momentum is likely to be larger than that produced by an expansion or contraction of the atmosphere due to the same effect.

  3. Ninderthana says:


    Also, the semi-annual seasonal asymmetries between the mean latitude and strength of the mid-latitude westerly winds must play a role in producing the semi-annual changes that are seen in
    the sea-ice extent.

  4. steveta_uk says:

    Surely global sea ice extent isn’t a proxy for annual mass redistribution – it literally IS annual mass redistribution.

  5. Joe Lalonde says:


    If you want to understand the process you are looking at, many, many factors have to be in consideration. Just plotting data with no regard to any factors is the current path science has taken.
    Land mass difference between the northern and southern hemispheres and sun distance are just two.
    Water at the 48 degree latitude flows differently than the rest of the latitudes due to centrifugal force and the density of the material. Gases being a different density is not bound by this and move more freely. Circulation is mostly by our planets tilting and their is a lag time when gases swing back and forth but gases themselves change in density with heat and cold.
    Our poles should be a great deal hotter due to the tilting, velocity difference and lag time of planetary tilting and solar intensity of the sun’s rays. But they are not. Why?
    The atmosphere is also bent which fails to give direct intensity solar heat. It takes a great deal of energy to melt ice but the stored heat that the poles hold when tilting releases a great deal when in darkness.

    Two paths of science…

  6. tchannon says:


    I really don’t know how direct it is. There will be great devil in the detail.

    Seems to me that confidence there is an effect enables more detailed work toward unravelling a mystery, start to pick apart the different effects.

    Quite possibly there is more information on earth orientation where from that maybe it is possible to extract a polar tilt caused by the mass shift. If so perhaps the north and south data can be separated.

    There might also be a way of getting some kind of >1y signal from slower changes in whatever is causing the 1y change.

  7. tchannon says:

    So you are not completely against this, good. My guess is we are talking about much the same things, different leg of the elephant.

    I’ll say something about the direct lunar effects. Last year it was Paul Vaughan who asked me to look in detail at the fast lunar data, forming part of his guest post on WUWT. It did not go down well there for other reasons.

    I was able split the doublets in the data frequency domain, quite a few of them; a long and hard task, one by one. This is beyond normal techniques, the separation barely apparent via Fourier Transform. On computing with the results these checked nicely as modulation products, with the expected number appearing, of ~18.6y, the time for the moon to complete one Metonic/Saros cycle, back to the same position as before.

    A side effect of detail work is removal of factor after factor from the dataset, I do it by subtraction. What remains might contain more or ultimately noise/artefacts. This of course only works for fixed items (or stationary in statistics parlance).

    A lot of what I am doing is a consequence of developing software which exactly locks to a single item, so accurately the item can be point by point subtracted. Figure 1 shows such items, which do subtract out, can eyeball that is true, ie. is obviously right, therefore they can be taken in isolation and compared. In this case awkward because one dataset is crude monthly and the other day data. Now get the timing spot on.

    I will now reveal the origin of the needle plot in the previous article. One dataset is the modelled annual cycle in LoD and the other recurrence computed directly from the LoD data. Snag is the recurrence computation is affected by the calendar timing scatter. Got it close then gave up. Unimportant.

  8. Roger Andrews says:

    Hi Tim

    Could you please send me the monthly LOD data you used? I want to try something.

  9. tchannon says:

    See if I can find the time to get the data up.

    LoD monthly was incidentally produced so it doesn’t exist as a straight entity. As part of a final filter stage I said decimate to monthly. Sort something out.

    Need to clean up otherwise the files will be highly confusing.

  10. tchannon says:

    RA, LoD uploaded. Done as a new document.

  11. tchannon says:

    Uploaded sea ice data as well.

    If this is not sufficient, ask.

    Sound of steam. Darn WordPress just did the dirty on me again, reformatted all the text into one block losing all breaks. Horrible touching anything. Lots of breakages.

  12. Roger Andrews says:


    Thanks for your efforts. Everything worked fine for me.

    Anyway, I was having trouble with the concept of how sea water freezing and thawing in place could generate a mass redistribution large enough to cause measurable changes in LoD, and looking around for an alternative explanation I came up with the idea that seasonal variations in global sea level, which are only on the order of 15mm but which affect a very large area of sea, might do the trick. So I plotted your LoD data against detrended monthly sea levels (from the CLS/ENACT analysis, don’t know how good these data are) and got:

    There’s a correlation, but it’s nothing like as good as the correlation you got with sea ice extent. I think what’s happening here is that seasonal sea level variations are dominantly steric in origin, in which case the inertial impacts of increases in sea level will be compensated for by decreases in sea water density.

    But I’m still not sure how sea water freezing and thawing in place redistributes mass. Can anyone enlighten me?

  13. Edim says:

    Roger, when it freezes in place, it stays in plays place (more or less), while on the other hand, liquid water moves and can distribute itself evenly. Maybe.

  14. wayne says:

    Tim, sorry to point to this but polar sea ice is about the last thing you could say was calling a variance in the LOD. Sea ice, though 1/9th the volume us raised above the surface but that is because the density of the ice under the water is 1/9 as dense cancelling this as affecting the overall inertia or another way to say is the angular momentum moment arm. Also any mass displacement at the poles would be magnitudes less than an equal mass displacement vertically were it to occur in the tropics (the merry-go-round example, on at the center, the other at the edge, same quantity of mass displaced).

    Why did you rule out my possible explanation of the springtime movement of huge volumes of water from the oceans at sea level to an average of 400+ meters into lakes and rivers worldwide. Seems that effect would dwarf the freezing and thawing of polar ice even though they occur at the same time and would leave the same signature?

  15. tchannon says:


    That’s why I use the word proxy three times.

    You take it to be a proxy for non-floating ice and perhaps rain. Maybe.

  16. tchannon says:

    Added Figure 5, some spectra.

  17. vukcevic says:

    I have not looked into LOD in any significant way, but if I did so here are some points I would consider :
    – Mass of the inner and outer core and mantle in % terms
    – Earth core is asymmetrical (east is melting, west is solidifying)

    – making thermal circulation unevenly distributed and as consequence the Earth’s magnetic field is more concentrated to the more liquid side i.e. east.

    – by seismic tests (normally earthquake waves) it has been shown that there are variations in the rotation rate of the inner parts, which may be subject to number of tidal effects (from daily to decadal).
    – Considering total mass of the inner critical elements in relation to the much smaller mass of oceans and atmosphere, I would expect that the larger percentage of the LOD is due to their angular acceleration and de-acceleration on a daily, annual etc basis.
    Just a passing reflection.

  18. Bart Leplae says:

    The Moon is receding from Earth (3.8 centimeters per year) as a result of tidal effects on the Earth.
    The energy loss as associated with the LOD increase is balanced with the energy increase associated with the receding Moon.

    If the Earth would be completely covered with ice, then the Moon would not be receding from the Earth and the LOD of would not be increasing (as fast).

    So if the magnitude of the tidal effects is correlated with the extent of the global sea ice, wouldn’t this may explain why the LOD is indirectly correlated with the extent of the global sea ice?

  19. vukcevic says:

    May I add a note to my post:
    Sometime ago I found that LOD is related to the Arctic geomagnetic field:
    http://www.vukcevic.talktalk.net/LOD-GMF.htm (GMF is created in fluid part of the Earth’s interior by thermal convection I mentioned in my post.
    I also (more importantly) found that the Arctic temperature is strongly correlated to the average of the Arctic’s GMF.
    No one doubts that extent of the Arctic ice is related to the Arctic temperature.
    So does the Tim’s finding makes sense from point of view of the Earth’s interior functions?
    From the above it appears that it does.
    For some more details I just came across see:

    Click to access bloxham_areaps98.pdf

    Note: Figure 3 Change in the length of day derived directly from geodetic observations (solid line) and that are predicted from calculations of the core angular momentum arived from geomagnetic observations.

    This would fully support observations I made in the post above.

  20. tchannon says:

    I would not be at all surprised of a linkage with magnetic fields but this is a chicken and egg problem. For example if there is an association between magnetics and snow cover where the magnetic association is with climatic variation. Or as you suggest to do with internal mass.

    I can produce the exact phase angles relative to insolation. That isn’t enough to figure out much without the full earth orientation, thinking here being that if there is a spin rate change involving an unbalanced off equator mass it must produce a wobble. I think doing this is beyond me.

    The longer LoD data (pre-1962) is in a bad state, a long story which I won’t go into. A poor data match would not surprise me.

  21. adolfogiurfa says:

    Temperatures change as LOD changes:

    According to Prof. Leonid B. Klyashtorin´s paper made for the UN´s FAO.

  22. Good article!

    A related article just published is this:

    Mazzarella A., A. Giuliacci and N. Scafetta, 2012. Quantifying the Multivariate ENSO Index (MEI) coupling to CO2 concentration and to the length of day variations. Theoretical Applied Climatology.

    Look at my web-page [ http://www.duke.edu/~ns2002/ –mod]

    or here


  23. vukcevic says:

    I think doing this is beyond me.
    Tim, it is beyond me and beyond my interest, there is also Chandler’s wobble; number of chickens and even more eggs.
    Magnetic stuff is an enigma too. WUWT and Jo Nova blogs considered max temps from a small Australian town which has about 100 years of good correlation with polarized SSN (difficult to be anything but magnetic)
    I did a graph for it, now doing a bit more digging, but how it works in the Australian bush no idea, except it looks they used same min-max thermometer for about 100 years, must have been replaced recently with digital stuff (it’s now remotely controlled) and guess what, correlation has disappeared.

  24. tchannon says:

    Hopefully I am getting back to normal (Me? Normal?)
    Solved the network backup problem, been painful but the first hurdle passed with zero errors. Have to backup 100GB tomorrow, do more tests. (then find the money)

    You can see the Graeff stuff, with another part to come, one reason why I have been busy. Rog is on family business, how long I don’t know. Have to put up with me.

    I’ll try and find some posts on other topics for certain users. Part of it is me not paying attention to anything going on elsewhere. Sleep problems? Ongoing but the builders next door have finished so the noise and dust is down. No longer micro-sleeping. Used to go through that on massive PCB layout sessions and similar.

  25. tchannon says:


    CO2 data is a subject where I have put in many months of work over years with a remarkable unpublished result.

    For Mauna Loa the annual cycle is extremely constant, as such containing no information. The long term characteristic is also highly predictable.

    There are actually two different datasets although this is not obvious but highly critical at the precision I was working. The primary work was modelling the early archived hourly data, 250k points. With one trivial change to cater for the change in dataset proxy this forecasts with rising r2 to date, r2 rising to >0.999, over 20 years of extrapolation. At that it is still annual cycle accurate. The rest is unpublished, other than the maximum error over the whole period is <2.1 ppm,. non accumulative.

    Obviously there is weather noise if not much.

    Now, the CO2 is spread unevenly geographically, is quite interesting. One observation is a likely connection with Arctic ice, I figured that if you walk from Alaska you will arrive at Mauna Loa with the CO2. Strangeness in the Arctic makes sense given various factors, including solubility increasing with lower water temperature and ice expelling gas on forming, taking in on melting.
    Lot of snippets surround this.

    There could be why LoD and CO2 seem to meet.

    Work on various dataset add some weight but is disputed by certain parties who insist on vegetative causals and of course the assumption that long term change is human induced. Actually a human assumption that we are important. Doesn't fit well with my finding.

    This is probably material for future blog posts, a lot of items.

  26. segeiMK says:

    This article suggests that CO2 cycle is generated by daylight hours vs darkness and availability (no ice) of the solar input to phytoplankton – O2 decrease as photosynthesis increases (consuming CO2) O2 decrease as the phytoplankton respires in the dark releasing CO2 and consuming oxygen

    another post ::
    … looking at the monthly plots shows that the peak at alert Alaska occurs some 2 months before the peak at Mauna Loa. Indicating that CO2 is pretty much in synch.

    This shows that the CO2 minima are occurring roughly at the same time over 33 years at Barrow but at La Jolla California the minimas are occurring significantly earlier

  27. tchannon says:

    Bit of a poser.
    I’ve put together a mass of annual waves with computed phase angle relative to solar radiation as the timing reference.

    Don’t know how to present this.

    Takes deep breath.

    SORCE 1y
    SORCE 0.5y (ignored as uninteresting)
    Earth axial tilt (1y)
    Sea ice north 1y
    Sea ice north 0.5y
    Sea ice south 1y
    Sea ice south 0.5y
    LoD 1y
    LoD 0,5y

    Getting this reasonably accurate is going to be fun.
    Am calculating phase on the fly, not dead accurate but probably inside a degree. Which phase leads is a matter of the human brain figuring. Similarly what exactly does the phase of 0.5y mean in this context.

    Any ideas. I could just hack something together and let folks refine it.

  28. […] LoD linked to solar radiation proxy, polar ice […]