Paul L. Vaughan, M.Sc.
Without a good handle on its simple geometry, a seemingly complex time series can appear as a changeling yielding to the pressures of mysterious statistical manipulation.
For example, a fundamentally important seminal observation reported by Le Mouël, Blanter, Shnirman, & Courtillot (2010) revealed the quasistationary 11 year solar cycle in the rate of change of length of day (LOD’), but newcomers taking a preliminary look at daily resolution LOD’ are more likely to fixate on the 18.6 year lunisolar envelope.
Multiscale variance summaries highlight obvious envelopes:
Zooming in, a semi-annual envelope is also evident:
(WIDE GRAPH ABOVE –Click to view elongate graph^1 & then click again to magnify.)
(WIDE GRAPH ABOVE –Click to view elongate graph^2 & then click again to magnify.)
A parsimonious weekly-to-monthly timescale model of daily LOD’, explaining ~93% of the variance (r = 0.965), can be constructed using the following information (with model terms in bold italics):
| Year | Period (days) | Half-Period (days) | Defined by… |
| Tropical | 365.24219 | 182.621095 | equinoxes |
| Lunar Month | Period (days) | Half-Period (days) | Defined by… |
| Tropical | 27.321582 | 13.660791 | equator/equinoxes |
| Nodal or Draconic | 27.212221 | 13.6061105 | ecliptic |
| Anomalistic | 27.55455 | 13.777275 | apogee/perigee |
| Synodic | 29.530589 | 14.7652945 | new/full moon |
(27.321582)*(27.212221) / (27.321582 – 27.212221)
= 6798.410105 days = 18.61343046 years
(6798.410105)*(13.6061105) / (6798.410105 – 13.6061105)
= 13.63339592 days
(27.55455)*(13.660791) / (27.55455 + 13.660791)
= 9.132933018 days
Noteworthy envelopes apparent in the variance structure of LOD’ relate to:
1) lunar nodal cycle (LNC) = 18.6 years
2) lunar apse cycle (LAC) = 8.85 years
3) terrestrial year (1 year)
4) harmonics (e.g. 0.5 years & 4.42 years)
| Beat Period | (years) | Tropical | Nodal | Anomalistic | Synodic |
| 27.321582 | 27.212221 | 27.55455 | 29.530589 | ||
| Tropical | 27.321582 | – | 18.6134 | 8.8475 | 1.0000 |
| Nodal | 27.212221 | 18.6134 | – | 5.9970 | 0.9490 |
| Anomalistic | 27.55455 | 8.8475 | 5.9970 | – | 1.1274 |
| Synodic | 29.530589 | 1.0000 | 0.9490 | 1.1274 | – |
| Beat Period | (years) | Tropical/2 | Nodal/2 | Anomalistic/2 | Synodic/2 |
| 13.660791 | 13.6061105 | 13.777275 | 14.7652945 | ||
| Tropical/2 | 13.660791 | – | 9.3067 | 4.4238 | 0.5000 |
| Nodal/2 | 13.6061105 | 9.3067 | – | 2.9985 | 0.4745 |
| Anomalistic/2 | 13.777275 | 4.4238 | 2.9985 | – | 0.5637 |
| Synodic/2 | 14.7652945 | 0.5000 | 0.4745 | 0.5637 | – |
Beat Period = (A*B) / ( |A-B| )
| | indicates absolute value
The model:
| Relative | Cumulative | ||||
| Term | Period (days) | Amplitude | r^2 | r | Contribution |
| 1 | 13.660791 | 1 | 0.713 | 0.844 | | polarity | |
| 2 | 13.63339592 | 0.41 | 0.824 | 0.908 | LNC |
| 3 | 9.132950896 | 0.30 | 0.881 | 0.939 | LAC alternation |
| 4 | 27.55455 | 0.26 | 0.926 | 0.962 | LAC alternation |
| 5 | 14.7652945 | 0.08 | 0.931 | 0.965 | semi-annual |
(WIDE GRAPH ABOVE – Click to view elongate graph^3 & then click again to magnify.)
eLOD’ = estimated LOD’
The above tables & figures, while certainly nothing new to science, have been summarized here for the benefit of those striving to efficiently develop the foundations necessary to appreciate and build upon the recent seminal work of Le Mouël, Blanter, Shnirman, & Courtillot (2010). From their conclusions:
“The solid Earth behaves as a natural spatial integrator and time filter, which makes it possible to study the evolution of the amplitude of the semi-annual variation in zonal winds over a fifty-year time span. We evidence strong modulation of the amplitude of this lod spectral line by the Schwabe cycle (Figure 1a). This shows that the Sun can (directly or undirectly) influence tropospheric zonal mean-winds over decadal to multi-decadal time scales. Zonal mean-winds constitute an important element of global atmospheric circulation. If the solar cycle can influence zonal mean-winds, then it may affect other features of global climate as well […]”
[Typos: 1) “evidence” should read “observe”. 2) “undirectly” should read “indirectly”.]
Caution
Exclusive &/or excessive focus on the first moment (the mean) should not be at the expense of attention to higher moments (such as the variance), as the following graph should emphasize:
SOI = Southern Oscillation Index (an index of El Nino / La Nina)
[ ] indicates boxcar averaging [applied here to highlight interannual variability]
When studying the preceding graph, it is important to understand that the blue line is the normalized interannual average of the black line. (Take a minute to think about this carefully.)
To reinforce this point, here is another graph of the normalized mean at the semi-annual to annual timescale:
The occurrence of such patterns in the mean despite the maintenance of stationary variance limits suggests a need to carefully consider which equators (geographic, celestial, magnetic, meteorological, etc.) are relevant to the phenomena under study. (See for example Leroux (1993).)
Multimoment multiscale spatiotemporal integration reveals nonrandom harmonic pattern-summary discontinuities, exposing the comedy tragically advocated by deceitful &/or naive theoreticians who are in part constrained by a dominant culture that clings seemingly religiously to maladaptive traditions such as unjustifiable assumptions of randomness, independence, uniformity, linearity, etc. that are routinely misapplied (for example to conveniently render abstract conceptions mathematically tractable).
Bear in mind that for some phenomena, such as ice-jacking freeze/thaw cycles, the properties of the variance play a critically fundamental role in dynamics.
Conclusion
With awareness of key wavelengths and a solid conceptual understanding of the effect of integration across harmonics, we arrive at something truly simple: Earth, Sun, Moon.
Both of the ~11 year waves summarize the semi-annual wave, which summarizes biweekly & monthly LOD’ variations bounded by lunisolar limits.
While the magenta wave is isolated via complex wavelet methods, the sky-blue wave is accessible to any member of the general public with an understanding of this article, 5 minutes to spare, & a spreadsheet.
Acknowledgement
Tim Channon generously shared LOD’ models developed using his synthesizer software. Access to Tim’s models facilitated expeditious cross-checking of lunisolar theory, mainstream literature, & data.
Suggestion
I encourage responsible readers to download & archive daily LOD data. Scientifically-engaged citizens can keep a vigilant watch on potentially-arising future data vandalism.
Data
LOD
International Earth Rotation Service (IERS)
http://www.iers.org/IERS/EN/DataProducts/EarthOrientationData/eop.html
Related Reading
Li, G.-O.; & Zong, H.-F. (2007). 27.3-day and 13.6-day atmospheric tide. Science in China Series D – Earth Sciences 50(9), 1380-1395.
http://www.scichina.com:8080/sciDe/fileup/PDF/07yd1380.pdf
Sidorenkov, N.S. (2007). Long-term changes in the variance of the earth orientation parameters and of the excitation functions.
http://syrte.obspm.fr/journees2005/s3_07_Sidorenkov.pdf
Sidorenkov, N.S. (2005). Physics of the Earth’s rotation instabilities. Astronomical and Astrophysical Transactions 24(5), 425-439.
http://images.astronet.ru/pubd/2008/09/28/0001230882/425-439.pdf
Gross, R.S. (2007). Earth rotation variations – long period. In: Herring, T.A. (ed.), Treatise on Geophysics vol. 11 (Physical Geodesy), Elsevier, Amsterdam, in press, 2007.
http://geodesy.eng.ohio-state.edu/course/refpapers/Gross_Geodesy_LpER07.pdf
http://geodesy.geology.ohio-state.edu/course/refpapers/Gross_Geodesy_LpER07.pdf
Schwing, F.B.; Jiang, J.; & Mendelssohn, R. (2003). Coherency of multi-scale abrupt changes between the NAO, NPI, and PDO. Geophysical Research Letters 30(7), 1406. doi:10.1029/2002GL016535.
Maraun, D.; & Kurths, J. (2005). Epochs of phase coherence between El Nino-Southern Oscillation and Indian monsoon. Geophysical Research Letters 32, L15709. doi10.1029-2005GL023225.
http://www.cru.uea.ac.uk/~douglas/papers/maraun05a.pdf
Leroux, M. (1993). The Mobile Polar High: a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes. Global and Planetary Change 7, 69-93.
http://ddata.over-blog.com/xxxyyy/2/32/25/79/Leroux-Global-and-Planetary-Change-1993.pdf
Trenberth, K.E.; Stepaniak, D.P.; & Smith, L. (2005). Interannual variability of patterns of atmospheric mass distribution. Journal of Climate 18, 2812-2825.
http://www.cgd.ucar.edu/cas/Trenberth/trenberth.papers/massEteleconnJC.pdf
Abarca del Rio, R.; Gambis, D.; & Salstein, D.A. (2000). Interannual signals in length of day and atmospheric angular momentum. Annals Geophysicae 18, 347-364.
http://hal-insu.archives-ouvertes.fr/docs/00/32/91/24/PDF/angeo-18-347-2000.pdf
Abarca del Rio, R.; Gambis, D.; Salstein, D.; Nelson, P.; & Dai, A. (2003). Solar activity and earth rotation variability. Journal of Geodynamics 36, 423-443.
http://www.cgd.ucar.edu/cas/adai/papers/Abarca_delRio_etal_JGeodyn03.pdf
Le Mouël, J.-L.; Blanter, E.; Shnirman, M.; & Courtillot, V. (2010). Solar forcing of the semi-annual variation of length-of-day. Geophysical Research Letters 37, L15307. doi:10.1029/2010GL043185.
Vaughan, P.L. (2010). Semi-annual solar-terrestrial power.
Technical Aside
For those interested in exploring LOD’ variance patterns that are not necessarily evident at first glance, another noteworthy envelope is the following:
(13.777275)*(13.63339592) / (13.777275 – 13.63339592)
= 1305.478517 days = 3.574281812 years
This polar-equatorial eclipse cycle is evident in the sequence of diagrams here:
http://eclipse.gsfc.nasa.gov/5MCLE/5MCLE-Figs-10.pdf (1733-2151)
From:
Espenak, F.; & Meeus, J. (2009). Five millennium canon of solar eclipses: -1999 to +3000 (2000 BCE to 3000 CE). NASA Technical Publication TP-2009-214172.
http://eclipse.gsfc.nasa.gov/SEpubs/5MCLE.html
h/t to WUWT commenter “lgl” for initially drawing attention to this pattern some time ago.
Earlier & Future Articles
I wrote the following articles before (a) acquiring access to Le Mouël, Blanter, Shnirman, & Courtillot (2010), (b) coming across Leroux (1993), and (c) re-reading Sidorenkov (2005) with consequently improved awareness:
1) http://wattsupwiththat.com/2010/08/18/solar-terrestrial-coincidence/
2) http://wattsupwiththat.com/2010/09/04/the-north-pacific-solar-cycle-change/
3) http://wattsupwiththat.com/2010/09/11/solar-cycle-length-its-rate-of-change-the-northern-hemisphere/
Related articles could have been written on All India Rainfall Index & other variables, but the audiences’ handle on the solar, lunisolar, & spatiotemporal nature of interannual variations was revealed to be inadequate in comments here:
4) http://wattsupwiththat.com/2010/10/11/atlantic-hurricanes-the-sun/
[Some audience members may benefit from careful consideration of issues raised by Tomas Milanovic at Dr. Judith Curry’s blog Climate Etc.]
Le Mouël, Blanter, Shnirman, & Courtillot’s (2010) game changing observation rendered earlier results much less mysterious:
For capable individuals striving to render these & related findings disgestible by a mainstream audience, I strongly recommend:
A) gleaning the primary point made by Schwing, Jiang, & Mendelssohn (2003) about the effect of windowing parameters on apparent phase, which can be reversed by spatial patterns, not just temporal evolution.
B) heeding the advice of Maraun & Kurths (2005) about “periods of coupling which are invisible to linear methods.”
Future posts in this series (if it continues) may draw attention to:
a) nonrandom relations between interannual terrestrial oscillations and interannual [not to be confused with decadal] rates of change of solar variables.
b) the guaranteed potential for naive investigators to be irrecoverably derailed by Simpson’s Paradox due to stubborn &/or blind adherence to seriously misguided conventional mainstream statistical inference paradigms & malpractices that rigidly & dogmatically insist on falsely assuming independence when none exists.
c) the [counterintuitive &/or paradoxical for some] influence of grain & extent – & aggregation criteria more generally – on summaries of spatiotemporal pattern.
“Grain” & “extent“?…
Grain is another term for spatiotemporal resolution. Important: Extent is a term which concisely encompasses the properties of spatiotemporal summary windows. The vast majority of mainstream researchers are either absolutely ignorant or insufficiently cognizant of the effect of extent on integrals across spatiotemporal harmonics (including the nonstationary variety). The consequences are serious: blindness and rejection of valid findings on nonsensical grounds.
Best Regards to All.
Leif
No it doesn’t, but I never said TSI is the net energy transfer. Of course you have to subtract the loss but that still doesn’t mean 1 J in must result in 1 J out over the same time period. The loss is always delayed because of the heat capacity so temperature will always lag the energy input.
Dr. Svalgaard you are a man of immense patience it seems. Hope some of this sinks in around here so that there is less noise and more real science.
“so the climate must already have an 11-yr cycle [due to other things] for the solar cycle to be creating resonance.”
There is no problem with this. The cyclic ocean currents (for example) operate on time scales similar to the solar cycle. Over time, those that are in phase with the solar cycle will tend to strengthen and persist and those that are out of phase will tend to weaken and die.
Over time this will encourage the formation of semi-permanent ocean currents that resonate with the solar cycle.
ENSO for example averages about 2x the frequency of the solar cycle. The longer ocean cycles also appear to be close integer multiples of the solar cycle, similar to the resonance we see in orbital cycles.
“You can’t find patterns finer than the grain or coarser than the extent.”
Averaging temperature over 30 years to yield climate pretty much guarantees you are not going to find any 11 year solar cycles affecting the climate. Sampling theory says you probably will be limited to finding 60 year cycles or longer.
“you are a slow learner, apparently”
If you are in fact a scientist as you claim then there is no need for this. It makes it appear you are out of your depth when you resort to insult to try and win your point.
lgl says:
April 12, 2011 at 1:30 pm
so temperature will always lag the energy input.
I guess this didn’t sink in:
“Explain that to Paul and Le Mouel who claim
1: no lags
2) direct correlation with cosmic rays and LOD’ [assumed to be climate related – although Paul never commits to anything]. http://www.leif.org/research/Courtillot-GRL-Cosmic-Rays.png or the discussion here: http://wattsupwiththat.com/2011/03/17/tisdale-update-on-ocean-heat-content/
Some, a very small part, will stay deep for centuries, but most clearly will not.”
GeoChemist says:
April 12, 2011 at 1:31 pm
Dr. Svalgaard you are a man of immense patience it seems. Hope some of this sinks in around here so that there is less noise and more real science.
No such luck can be hoped for, I’m afraid.
ferd berple says:
April 12, 2011 at 1:32 pm
There is no problem with this. The cyclic ocean currents (for example) operate on time scales similar to the solar cycle. Over time, those that are in phase with the solar cycle will tend to strengthen and persist and those that are out of phase will tend to weaken and die.
You have this backwards. The natural cycles involve huge amounts of energy and will not weaken and die because of some gnat pissing on them. It will be the solar influence that either will or not will not have any effect if not in the right phase. Hence what we see is normally the dominant natural cycles. There is also the coincidence problem that since the rotation of the Earth changes over time [it slows down] we live in the special period where the natural cycles just happen to match that of the Sun.
cycles also appear to be close integer multiples of the solar cycle, similar to the resonance we see in orbital cycles.
In fact a solar cycle is a close integer multiple of the yearly cycle. Perhaps that explains the seasons. What do you say? Yet another cyclomania theory confirmed.
GeoChemist, see what I mean.
ferd berple says:
April 12, 2011 at 1:52 pm
Averaging temperature over 30 years to yield climate pretty much guarantees you are not going to find any 11 year solar cycles affecting the climate.
People find cycles no matter what the averaging interval is…
“you are a slow learner, apparently”
If you are in fact a scientist as you claim then there is no need for this.
I have carefully explained this to you several times. It is, of course, possible that the fault is mine for not explaining it well enough, but then I would have expected you to ask for clarification. Ah, well, perhaps one should not project one’s own approach onto others.
Leif
Give us one example of heating of water where temperature does not lag the energy input.
lgl says:
April 12, 2011 at 2:39 pm
Give us one example of heating of water where temperature does not lag the energy input.
It is not about a lag, but about how big it is. Also, if I stop the energy input, how long time after that does the temperature keep going up?
lgl says:
April 12, 2011 at 2:39 pm
Give us one example of heating of water where temperature does not lag the energy input.
The ARGO measurements of ocean temperatures with depth shows that the seasonal variation penetrates hundreds of meters deep with a lag of only a few months, so lags are small.
http://www.jcommops.org/FTPRoot/Argo/Doc/PO_Roem_2009_ArgoClim.pdf
“”””” A G Foster says:
April 11, 2011 at 8:54 pm
Lots of confusion around here. One poster confuses LOD=sunrise to sunset with sidereal LOD, equals one spin of the earth relative to a star. I’m surprised at George Smith, but I will try to enlighten him. When polar ice melts the earth changes shape: mass (ice) which was concentrated at the poles, with a short arm of inertia, is spread evenly around the ocean surface, averaging something like 63 degrees latitude. If the the mantel were totally elastic nothing would happen, but it isn’t. It is part elastic, part plastic, so there is an instantaneous change of shape (more oblate) followed by slow inelastic recovery (back to round, or oblate spheroid). The earth has been speeding up in recent years due to Glacial Isostatic Adjustment from a combination of the Last Glacial Maximum and the Little Ice Age. “””””
I’ll have to think on that.
We are constantly told that when all the Greenland ice slips off into the ocean and melts that the Greenland land will rebound.
Presumably a similar thing happens if the Antarctic ice melts, and if the weight of all that ice stops pushing on Antarctica, so it rises, surely the equatorial radius of the earth will diminish.
If the ice caps are currently melting as we are assured by the NSIDC is happening, then your scenario would be happening, so the earth should be slowing down; yet you say it is speeding up.
It’s not clear to me you’ve made your case; but as I said, I will think on it.
Should not the earth be slowing down due to the recession of the moon, and the transfer of angular momentum from earth to moon ?
Leif, I’ve reviewed your comments and this is a note to confirm that we have different definitions of extent. Your example of Simpson’s Paradox is a different variety from the 2 specific types I have in mind. I take responsibility for not having enough time to explain that properly. It would take 10 to 1000 times more time than I can presently volunteer to make myself more clear on some of these points. I accept the responsibility.
Re: izen
You appear to be under the impression that some relations are controversial to the mainstream when in fact they are well accepted by the mainstream. See for example the literature links I listed above. Here’s another:
Zhou, Y.H.; Zheng, D.W.; & Liao, X.H. (2001). Wavelet analysis of interannual LOD, AAM, and ENSO: 1997-98 El Nino and 1998-99 La Nina signals. Journal of Geodesy 75, 164-168.
http://202.127.29.4/yhzhou/ZhouYH_2001JG_LOD_ENSO_wavelet.pdf
I appreciate your interest in these phenomena. Thanks sincerely for your contributions to the discussion.
Leif & lgl,
regarding what Leif wrote: “direct correlation with cosmic rays and LOD’”
This is a misunderstanding. This is not what is being claimed. Reading other comments here I can also see that most are still fixating on patterns in the mean and not realizing that the ~11 year pattern is an envelope. There are several other ways to demonstrate the pattern. Certainly we’re going to need more cooperation to understand one another better. I apologize for my constraint: shortage of time. It concerns me that some will misunderstand and misrepresent what they perceive as a “direct correlation with cosmic rays and LOD’”.
lgl, Leif is correct that I might have some issues with your conceptions of heat storage & lags. However, I’ve miles of data exploration to go before I will be anywhere near a point where I can appropriately articulate my suspicions about multidecadal variations.
A G Foster wrote, “See the more careful remarks of Walter Munk […]”
Thanks for that link.
Paul Vaughan says:
April 12, 2011 at 9:22 pm
fixating on patterns in the mean and not realizing that the ~11 year pattern is an envelope.
Except that is is not. You [and they] subtract all the other components and isolate the semiannual amplitude. This is not an envelope. It would be an envelope if the the semiannual variation would be a modulation of all the rest, but it isn’t. The semiannual variation rides on top of all the rest.
BTW, in mainstream solar physics we are extracting information about the solar interior by analyzing the superposition of millions of simultaneous standing waves all over the visible disk of the Sun, all with different lifetimes, frequencies and spatial extents. The ultimate in spatio-temporal integration over harmonics! Perhaps even better: solving the inverse problem: finding the patterns and the physics in the chaos. We find no reason to use the special jargon that newcomers to such analysis have obscured the methods and concepts with.
Leif
Also, if I stop the energy input, how long time after that does the temperature keep going up
The integral of energy input will peak when you stop it so that’s when temperature peaks. If you let the water cool down and repeat the process, you will see that the energy input curve leads the temperature curve by 1/4 period.
Same with the diurnal cycle: http://curry.eas.gatech.edu/currydoc/Webster_JC9.pdf fig.4 Temperature lags several hours.
The ARGO measurements of ocean temperatures with depth shows that the seasonal variation penetrates hundreds of meters deep with a lag of only a few months
or around 3 months, 1/4 of a period, to be more precise.
So that’s three cases of temperature lag, still missing one with no lag.
What is the magic cycle length where there suddenly is no lag any more?
George E. Smith says:
April 12, 2011 at 3:49 pm
“”””” A G Foster says:
April 11, 2011 at 8:54 pm
..The earth has been speeding up in recent years due to Glacial Isostatic Adjustment from a combination of the Last Glacial Maximum and the Little Ice Age..
~
The melting of the ice and perma frost over that period has also helped to increase the Earth’s surface electric potential. Ice is not a good conductor..
~
Leif Svalgaard says:
April 11, 2011 at 1:38 pm
..closer your dipole is to the energy source ‘within’ your system, the more influence the solar electra magno reconnection regime, well have upon it.
The sun does influence the planets magnetically, but not the other way around. The planets and the interstellar medium do not influence the Sun via magnetic forces..
~
The Interstellar Magnetic Field shapes the heliosphere. That in itself is an influence upon it. The primary reconnection zone at the nose of the heliosphere is very simular to the reconnecton process we experience daily several times a time here at Earth. They think one of the differences in the reconnection processes is that the the sun is capable of more multiple reconnection regions. The primary being at the nose in the direction of solar orbit. Maybe that unravelling knot at the edge of the bubble was just a diminishing reconnection site.
George Smith says: “Should not the earth be slowing down due to the recession of the moon, and the transfer of angular momentum from earth to moon ?”
It depends on the time scale. We’re already speaking of scales that have little to do with PV’s contribution. Between secular and millenial scales you are correct, but we need to account for the current decadal scale–LOD has decreased in the last 40 years, and the simplest explanation is increased Antarctic snow. Gravity sensing is sufficiently inaccurate to allow for it, and core/mantle coupling is likewise poorly understood. The LOD decrease I speak of is beyond dispute: google “leap second” to see a Wikipedia chart of LOD since the introduction of the atomic clock. The causes are certainly not beyond dispute, but as I say, the simplest explanation is more snow, i.e., decreased melting. I’m a know nothing in the field but Walter Munk was one of the best–still alive but no longer current in the field. I suppose Richard Gross has replaced him, and I understand he is now working on the ice problem. –AGF
lgl says:
April 13, 2011 at 1:58 am
Leif:
“Also, if I stop the energy input, how long time after that does the temperature keep going up”
lgl:
“The integral of energy input will peak when you stop it so that’s when temperature peaks. ”
The actual timing of the peak depends on the system parameters (mass, heat capacity, rate of energy input). With a step change in energy input the system will approach a new equilibrium following an exponential decay and there will be no overshoot. But with a sinusoidal input, the system never reaches equilibrium so that the temperature continues to rise whenever the equilibrium temperature is higher than the system temperature, which is about 1/4 of the time. Thus the observed (and highly variable) time lags, which depend on the mass being affected. The earth’s oceans can be modeled (shudder) as series of masses corresponding to different layers with energy inputs decreasing with depth, and with the low mass, low heat capacity atmosphere on top. With such a system the observed lag times will vary with the frequency of the applied signal.
Sorry about the verbose reply, but its not a simple system.
@-Paul Vaughan says:
April 12, 2011 at 9:15 pm
“You appear to be under the impression that some relations are controversial to the mainstream when in fact they are well accepted by the mainstream. See for example the literature links I listed above. Here’s another:”
Zhou, Y.H.; Zheng, D.W.; & Liao, X.H. (2001). Wavelet analysis of interannual LOD, AAM, and ENSO: 1997-98 El Nino and 1998-99 La Nina signals.
Ah.
That makes things clearer.
I see I need to offer my sincere apologies for the earlier skepticism I was expressing.
I had got things COMPLETELY inverted as to what you might be claiming here.
For some reason I had infered that there was some claim that the variation in day length had some causal influence on SOI, ENSO and Zonal winds.
That of course would not just be controversial but ridiculous.
But what is really the subject of the research is how the SOI, ENSO etc have a causal effect on the LOD. As other posters have indicated with the point about how ice lost from ice-caps changes the angular momentum, the movement of water and atmosphere over the surface has an impact on the angular momentum and therefore a major ENSO event will show up in a LOD fluctuation.
There is also the fact that as LOD is influenced by tidal effects from the Sun and Moon and ENSO, zonal winds etc are also to some extent modulated by the same tidal effects the same influence shows up in both.
Again, I am sorry I got things completely backwards and thought you were claiming a causal path from LOD to climate, rather than the other way round.
lgl says:
April 13, 2011 at 1:58 am
What is the magic cycle length where there suddenly is no lag any more?
According to the article we are discussing [Le Mouel et al.], a good choice would be 11 years as they find no lag between cosmic ray intensity [and a negative lag of one year for sunspots] and LOD’. Svendsmark and friends see no lag either at that period. Your own graphs of long-term changes do not show a 25 year lag between the 100-yr long period of solar activity and temperatures, and so on.
Carla says:
April 13, 2011 at 5:40 am
The Interstellar Magnetic Field shapes the heliosphere. That in itself is an influence upon it.
But not on the Sun itself, as such changes cannot travel upstream in the solar wind, anymore than a log floating down a fast-flowing river cannot alter the flow at the headwaters.
Leif Svalgaard says:
April 13, 2011 at 7:07 am
[and a negative lag of one year for sunspots]
I wanted to say ‘negligible’ lag…
Leif, every time I find a new comment from you there are a dozen more misunderstandings to address. Looking at millions of things won’t help if you’ve got your fundamentals wrong. As I’ve indicated, you’re using a different definition of extent than the one to which I was introduced by the post-secondary education system (at both undergraduate & graduate level in different departments at different universities). You also appear in comments you address to Tim Channon to misunderstand that his synthesizer has isolated the 11 year pattern. It has not, but the more important misunderstanding is on the definition of extent. Looking at “the superposition of millions” isn’t necessarily going to improve your vision if you & your colleagues have overlooked something fundamental.
Leif, bear in mind that daily LOD’ is itself a summary of higher frequency oscillations (and that there is currently unresolved spatial variability in the measurement of the higher frequency oscillations).