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.
Paul Vaughan says:
April 13, 2011 at 7:10 am
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).
A simple way to address that is to give your understanding of ‘extent’ right here, in your own words.
Looking at “the superposition of millions” isn’t necessarily going to improve your vision if you & your colleagues have overlooked something fundamental.
Tell us what that might be. The method we use works very well in extracting the amplitudes and phases of all these waves. We use those to calculate the sound speed [and bulk movements] in the solar interior.
Paul Vaughan says:
April 13, 2011 at 7:21 am
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).
And so is the solar record. At the very least one could ask that both records be analyzed the same way [another of of my criticisms of the Le Mouel paper], after all they are simple time series.
One minor point: changes in the distribution of mass of the earth alter its rotational inertia but not its angular momentum; the momentum can only be altered by tidal friction through displacement of the earth/moon and earth/sun, whence long term LOD increase. Internal mass movement with its associated altered inertia is both short term and reversible. Momentum loss due to tidal friction is irreversible.
So now Le Mouel et al. would be a good choice. A few comments back it was not:
Third, the cosmic ray data compared with are not correct. They seem to have been manipulated to improve the fit
Regardless, it’s just absurd that basic physics should stop functioning beyond 11 years periods. And my own graphs of long-term changes do show that Temp~Integral of TSI http://virakkraft.com/TSI-integral-temp.png
lgl says:
April 13, 2011 at 1:23 pm
So now Le Mouel et al. would be a good choice. A few comments back it was not
None of the claimed correlations, yours included, are good choices as they are all spurious. But since you are a believer, it might work for you. Are you saying that it didn’t?
Regardless, it’s just absurd that basic physics should stop functioning beyond 11 years periods.
It doesn’t, but the effects are so minute that they drown in the noise.
And my own graphs of long-term changes do show that Temp~Integral of TSI
With a 25-yr lag (1/4 of the 100-yr slow solar cycle) or a 550-yr lag [1/4 of the even slower Hallstatt cycle]?
All you show is that solar cycle mean wiggles can be cherry picked to match some T means [Loehle’s T are also ‘integrals’ of T], but only for a limited period after 1200AD. Ignoring [and not even daring to show] what happened in the 1200 year before that.
“”””” Carla says:
April 13, 2011 at 5:40 am
George E. Smith says:
April 12, 2011 at 3:49 pm “””””
Not sure just what it was I said, that you are referring to Carla. I found nothing following the above that was anything that I said.
“”””” A G Foster says:
April 13, 2011 at 6:36 am
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. “””””
One would infer from that statement, that you are implying that there are times scales at which the earth is speeding up (or at least NOT slowing down) “”””” due to the recession of the moon, and the transfer of angular momentum from earth to moon ?” “””””
What would be the mechanism for that ?
As to your original premise that the melting of polar (land) ice would slow down the rotation because of sea level rise in the equatorial regions, I am still thinking on that question. It does seem that the prompt response would be water addition to the equator, supporting your thesis. But would there not be a simultaneous elastic bounce of the land, raising the poles, and shrinking the equatorial diameter; followed by a slower inelastic continuation of that reshaping.
In any case; food for thought; and I thank you for that stimulus.
Leif
Ok ΔT=q/C is not true and J=J/s
Try explaining your pseudo-science to guys working in the field and publishing. These for instance: http://www.wri.org/publication/content/7684 How many publications do you have on the oceans thermal inertia? But of course you know this too better than the specialists anyway.
“”””” 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
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. “””””
Interesting point lgl; that “around three months”.
As an old analog circuits practitioner, I can conjure up the flow of a current, through a resistive conduit to a capacitive (or capacious) storage element, having an RC time constant that is large compared to the 12 months cycle time of the driving signal frequency. One would then expect the “Voltage” on the Capacitor, being a measure (via the Capacitance) of the total stored charge (energy) to lag the current by exactly 90 degrees phase shift.
So I posit, that the “lag time” is not simply “about three months”; but is in fact precisely one quarter of a cycle.
So the about three months lag is NO accident.
lgl says:
April 13, 2011 at 2:57 pm
How many publications do you have on the oceans thermal inertia? But of course you know this too better than the specialists anyway.
The specialists operate with temperature forcing of several degrees. As the solar activity induced ΔT is one to two orders of magnitude smaller, any effects will be correspondingly smaller, and unobservable. Try your wiggle matching on the full dataset and see for yourself. The issue is not the oceans thermal inertia, but the much too small solar forcing. For the ocean heat content to vary appreciably [the lag is a red herring], the energy input [your q] has to vary appreciably too, and it doesn’t. In your ΔT=q/C, for ΔT to be negative [which it is at times, right?], your q has to be negative. Perhaps you really mean ΔT=Δq/C. And since Δq ~ ΔTSI, you mean ΔT ~ ΔTSI, which is, in fact very nearly the case, as ΔT/T = 1/4 ΔTSI/TSI, where T and TSI can be regarded as constant compared to the Δs.
Given the bunfights I assume no-one is interested in an elephant.
Nothing to do with Paul Vaughan as such, I decided out of curiosity to produce a more comprehensive model etc. and reconstruct to LoD.
Anyone seriously interested I’ve made it available here. Dead horse watchers, nit pickers, the lazy, etc. do not bother. Some might find it educational.
http://daedalearth.wordpress.com/2011/04/14/length-of-day-modelling-the-lunar-and-annual-effect/
A G Foster wrote, “[…] Richard Gross […] I understand he is now working on the ice problem.”
Excellent news. Thanks for sharing.
Tim Channon wrote, “I decided out of curiosity to produce a more comprehensive model etc. and reconstruct to LoD. […] http://daedalearth.wordpress.com/2011/04/14/length-of-day-modelling-the-lunar-and-annual-effect/ “
Thanks for sharing that Tim. What did you find most noteworthy &/or interesting about your results? And did the exercise arouse any noteworthy curiosities tempting further exploration?
izen wrote,
“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. […] thought you were claiming a causal path from LOD to climate, rather than the other way round.”
I get that reaction a lot and I find the reaction itself quite interesting.
The sign of the phase relationship between interannual SOI & interannual LOD is not static as many seem to think. SOI is just a part of AAM (a big part, but certainly not the only part). In studying interannual phase relations of various climate indices, the interesting thing is the nonrandom distribution of phase differences. There is a preference for co-phasing or anti-phasing (with switching). Loosely speaking, this is something like the eddies on opposite sides of a global jet swirling in opposite directions (…and then the position of the jet moves).
I haven’t presented related results here, but they are a much bigger topic than the current post. There is coherence with the rate of change of solar variables. The ‘messy’ aspect of the 11 year envelope we’ve been discussing relates to these changes. I’ve audited many claims about cycles since November 2007 and pursued many curiosities arising along the way; most of them run into dead ends of one form or another, but the ones I describe in this comment keep getting cleaner as I look more carefully (an activity for which I no longer have much time, unfortunately).
Thank you sincerely for your thoughtful comments.
Paul Vaughan says:
April 13, 2011 at 9:20 pm
I’ve audited many claims about cycles since November 2007 and pursued many curiosities arising along the way; most of them run into dead ends of one form or another
If you audit 20 claims, just by chance you’ll find one that looks significant at the 95% level [without really being it]… It looks like you just found yours.
George
Right, in an ‘ideal’ setting it will be precisely one quarter of a cycle. In real world there are losses so it will always be a little less than 1/4. Temp will peak when the net energy transfer goes below average and not when the solar input goes below average.
Leif
Δq ~ ΔTSI
No, J still isn’t J/s
For the ocean heat content to vary appreciably, the energy input has to vary appreciably too
No, that’s the nice thing with integrals. With an 0.1W/m2 imbalance for 400 years q=6.3*10^23 J I’d call that appreciably.
George E. Smith April 13, 2011 at 3:03 pm
George,
You wrote:-
Here is a paper by Walcott, R. I. (1973) Structure of the Earth from Glacio-Isostatic Rebound; Annual Review of Earth and Planetary Sciences, Vol. 1, pp15-37
The question you pose of “simultaneous elastic bounce of the land” is addressed by these statements.
However the deformation of the solid Earth by ice sheet loading is so extensive that both the elastic crust and plastic mantle are involved. Continental ice sheet melting and water redistribution to the oceans resulting in a volumetric change in sea-level at the equator is virtually instantaneous compared to the process of land level rise due to plastic rebound of the mantle following unloading.
See the post glacial uplift graph on p17 where the ongoing 7,000 year uplift of the rocks that supported the former ice sheets is recorded.
In his discussion of the gravitational data (p20) Walcott comments that estimates of the remaining rebound are 300m for the Laurentide & 120m for Fennoscandinavia.
Clearly the regional land surface adjustment following ice sheet melting is a slow long-term process with significant vertical effect.
Leif Svalgaard wrote, “If you audit 20 claims, just by chance you’ll find one that looks significant at the 95% level [without really being it]… It looks like you just found yours.”
You’re misleading people by assuming independence where none exists. Remember, I taught stats for years. You can’t fool me on this (but it seems you may be fooling yourself…)
Leif, you seem to be using the word extent the way many people use the word global (i.e. to refer to the whole series).
Here’s what I wrote above:
“Extent is a term which concisely encompasses the properties of spatiotemporal summary windows.”
There are bodies of literature, books, courses, etc. on the variation of pattern measures with variations in the properties of spatiotemporal summary windows.
Your choice to label people pursuing such legitimate work as a “cult” was in poor taste.
Let’s get this nonsense over with.
While I don’t have time to write an essay or short course for you, I can ask a pointed question to diagnose your deficiency. (If you were not so defiant & intransigent [“learning resistant” as you would say] – and if I had more time – I might be more patient, but under the circumstances I need to be practical…)
…So let me ask:
1) If you average pressure over some region of the world – and then you move the spatial window to another region while making it a different shape & size, will you necessarily get the same summary?
2) If you do a wavelet analysis with Morlet 2pi and then do the same analysis with Morlet 10pi, will you necessarily get the same summaries?
These are just 2 off-the-cuff examples with the answer “no”.
Elaborating succinctly is challenging (but maybe we are identifying here an important challenge for educators …discussion generally goes on for hours when profs introduce these concepts to newcomers)
In landscape ecology, a problem field researchers were having was that they were getting COMPLETELY different results depending on what summary windows they used (Simpson’s Paradox). This is no trivial matter warranting rude labeling of serious researchers – doing legitimate & IMPORTANT research – as a “cult” [Leif Svalgaard’s term].
Depending on the nature of the spatiotemporal heterogeneity, there can be abrupt scale breaks as one adjusts windowing parameters. Many researchers have never taken time to think about this carefully, in part perhaps because formal education on the subject remains in its infancy, still working its way in from the periphery on the mainstream radar.
I suggest taking some time to run systematic investigations, paying attention to how scale-dependent (window scale, to clarify) integration over harmonics (using a variety of kernels) affects summaries.
For those playing around with GIS (Geographic Information Systems), systematically investigate how changes of summary window sizes & shapes change pattern summary. (This exercise should give some idea of the importance of the main point raised by Schwing, Jiang, & Mendelssohn (2003).)
Paul Vaughan says:
April 14, 2011 at 5:26 am
Leif Svalgaard wrote, “If you audit 20 claims, just by chance you’ll find one that looks significant at the 95% level [without really being it]… It looks like you just found yours.”
You’re misleading people by assuming independence where none exists. Remember, I taught stats for years. You can’t fool me on this (but it seems you may be fooling yourself…)
If you always look at many variations of the same thing [search for your lost car keys under the lamp post] then you have not really ‘audited’ many relationships.
Paul Vaughan says:
April 14, 2011 at 6:38 am
“Extent is a term which concisely encompasses the properties of spatiotemporal summary windows.”
That is just mumbo-jumbo.
Your choice to label people pursuing such legitimate work as a “cult” was in poor taste.
A cult implies a group which is a minority in a given society, i.e. not part of the mainstream which you so vehemently deride for not embracing the spatio-temporal jargon and conceptual box.
1) If you average pressure over some region of the world – and then you move the spatial window to another region while making it a different shape & size, will you necessarily get the same summary?
As you say, “no”, but that is such a triviality that no self-respecting scientist [that I know of] would ever do such a silly thing.
Depending on the nature of the spatiotemporal heterogeneity, there can be abrupt scale breaks as one adjusts windowing parameters.
Again self-evident, and at least in the physical sciences this never is a problem as everybody knows this. This is a non-issue. Now, for economists, social ‘sciences’, and such, there may be problems, but you don’t solve that problem by mumbo-jumbo, but by simple examples you feed the students up front. This is not rocket science.
lgl says:
April 14, 2011 at 5:10 am
No, that’s the nice thing with integrals. With an 0.1W/m2 imbalance for 400 years q=6.3*10^23 J I’d call that appreciably.
And over 4 billion years it is even worse than we thought: 6.3*10^30 J. You cannot ignore the losses.
lgl says:
April 14, 2011 at 5:10 am
With an 0.1W/m2 imbalance for 400 years q=6.3*10^23 J I’d call that appreciably.
Schwartz has a nice analysis of the energy balance:
http://folk.uio.no/clausn/APPC/Stephen_Schwartz.pdf
He finds a time constant of the order of a decade.
It doesn’t matter how large the ‘imbalance’ is. The temperature will not continue to rise.
In further response to G Smith at 2:52 (thankyou Mr. Mulholland):
Even when the earth is speeding up with a loss of rotational inertia, it is losing angular momentum through an entirely separate mechanism. That is, there is always tidal friction and loss of kinetic energy, but the angular momentum can only be transferred to the moon, or the earth/sun. In other words, while the earth speeds up, say from full moon to half moon or when post glacial rebound overtakes melting (both strictly terrestrial processes), it is still losing angular momentum to the moon. Again, the internal process are reversible–there is no change in angular momentum where the sun and moon are not involved. But the kinetic energy that was converted to heat will never be converted back to mechanical potential, nor will the moon ever get any closer.
Tidal friction from the mantle depends mainly on the rate of earth rotation (constant except over the aeons), while that from the seas depends on coastal configuration: continental drift and some slight influence from sea level and ice formation–not really quantifiable. It’s fairly constant and its average is well known–we only have to measure the rate of the moon’s recession by laser ranging. Before that ancient eclipses were used to calculate (negative) acceleration. But since the advent of the atomic clock we have been in a period of no average deceleration–slight acceleration, and this must be explained through terrestrial processes. Atmospheric coupling can’t account for more than a few years’ worth; core/mantle coupling patterns may have been identified but of course cannot be expected to permanently offset tidal friction, or to have recently kicked in to do the same. Again, ice balance is the prime suspect, and odds are high that polar ice is increasing. If sea level is really rising it must be due to thermal expansion.
From my limited perspective two of the strongest arguments against AGW are the LOD problem and the fact that only ice sheet extension (hence, temperature) explains the correlation between Milankovitch Cycles and CO2 fluctuations in the ice cores; that is, T forces CO2 or both are forced in tandem by ice sheet extension.
“”””” lgl says:
April 14, 2011 at 4:48 am
George
Right, in an ‘ideal’ setting it will be precisely one quarter of a cycle. In real world there are losses so it will always be a little less than 1/4. Temp will peak when the net energy transfer goes below average and not when the solar input goes below average. “””””
Sure lgl, I was not of course being critical of your “waffling” around the about three months thing; simply pointing out that there was a good model reason to expect it to be three months or a quarter cycle. And for all the reasons you mentioned, one wouldn’t be surprised to see the delay time vary somewhat, since the “circuit diagram” parameters, are themsleves not fixed.
But is not the roughly 1/4 year phase lag, a good indication that the solar input/ocean storage system, is a pretty damn good picture of what is going on with the vast majority of the thermal energy in the system. So a lot of these “other” perturbations are lttle more than a scrawny Mexican rat dog nipping at ones trouser cuffs.
I can see I will get into trouble by calling any tidal action a “strictly terrestrial process,” so I’d better explain myself. True, the moon is causing the fortnightly zonal tides, and all tides (along with the sun), but those tides are 99.99% or thereabouts reversible–frictionless–the earth recovers its spin speed when the tide goes down. Wouldn’t that pull the moon back in? That question is beyond my pay scale, but here are a few considerations: it is the longitudinal component of the zonal (north/south, fortnightly) tides that torques the moon; diurnal tides are more effective since they are both diurnal and primarily longitudinal. While part of the tidal energy is dissipated on the coasts, another part turns into the circumpolar current and is ultimitely dissipated on the ocean floor, and that current could be reduced or eliminated if the Strait of Magellan froze deep, reducing the rate of deceleration and allowing the core to catch up a little (in its deceleration). Then when the strait melted braking torque from the core would be reduced, but braking torque from the polar current would return to normal. It will be a while before any such mechanisms are detected, and this applies to irreversible mantle braking. The reversible effect of melting ice on LOD would also be transmitted to the core, so that the core/mantle torque varies according to the LOD and climate history. Electromagnetic core/mantle coupling may be influenced by the sun.
I don’t think the moon is affected by reversible tidal action–the earth’s center of gravity doesn’t move with tides. It is the constant tidal bulge which torques the moon, and a tiny part of that bulge is converted in the ocean to currents which flow past land. But I’m in over my head. –AGF