Figure 1
Quite often integrating data is useful.
In an odd moment I trivially integrated one of the results from a recent blog post, a casual look at Hadcrut 4. This produces a strange and unexpected result, strange because the structure of the shape is highly complex, ambiguous even though it looks fairly trivial. (I might write on this complexity later)
The data used was published as spreadsheet two of Talkshop article Met Office Hadcrut 4: solar linkage (supplemented copy linked at the end of the current blog article)
As such this post today has nothing whatsoever to do with Hadcrut 4, which provided a fixed frequency switching wave used to decode sunspot data.
That is what I wrote yesterday. Sometimes the two handling this blog actually communicate, I sent the draft to Rog. Today he came back “By using integration you are also supporting my work on integration of the SSN as a proxy for OHC I think, though my series isn’t polarity sensitive.”
I’d forgotten that and yes it would fit, although none of this is hard proof until definite mechanisms are shown to be so, why discussion is needed.
Reproduced from the existing Talkshop article, Figure 8
Trace ssn is the item of interest now, that is what is integrated.
Now here is the Ocean Heat Content Tallbloke (Rog) is talking about.
Graphic supplied by Tallbloke
Compare with figure 1, it looks feasible. As I understand it the concept involves a constant which has been guessed estimated as the mean sunspot value based on history [*] ssn = 40 which is the value above which OHC accumulates and below which de-accumulates.
* See first comment by Tallbloke
Restoration of data bipolarity if valid automatically provides the constant, which is actually the mean value in the long term.
Underlying material
Eddy[1] reports various undulation underlying the notional 11 year sunspot cycle, perhaps these underlying changes are a cause of the drift off zero.
Bracewell in his analysis of the Elantina Elatina varves shows how solar activity was somewhat similar 680 million years ago
Figure 2
Fig 3 from Spectral Analysis of the Elantina Elatina varve series, R.N Bracewell, CSSA, 1988. [2].
Mackey[3] in his tribute to Fairbridge reminds us that apart from many posits over solar behaviour causal, that of Koutsoyiannis’ work adds caution that perhaps we are seing Hurst-like behaviour with scale changes and other discontinues.
This leads on to whether the time span of figure 1 can be extended.
As it stands, not by much into history because of the confused solar start prior to the 1820s where phase changes are implicated, in other words the 22 year seems to break down.
Given recent solar behaviour and suspicion the sun is repeating a confused episode, forward projection is unwise.
However, turning to an earlier exercise using longer annual ssn data, from year 1700. (ends 2008, was done a few years ago)
Figure 3
This does illustrate well enough but why is the result the other way up? Answer is there is no right and I used switching which was phased 180 degree differently.
Terrestrial magnetic change
The earth is the closest planet which has a significant magnetic field. Jupiter is the main player. Astronomy Notes have a useful page covering this. (“Venus has no magnetic field”; “Mars has an extremely weak magnetic field”; “Earth has a strong magnetic field”; “Jupiter has a HUGE magnetic field”)
Solar magnetics can be measured on earth from the direct effect here over a massive range of timescales, seconds onwards.
Measurement of the Earth’s magnetic field has been taking place from the 1500s so for interest here is a plot showing 1540 through 1900 for Paris.
Source [4]
Figure 4
Magnetic Declination for Paris, East-West and presumably dip.
There is dispute over the accuracy.
For Europe the British Sundial Society have a nice plot in their glossary which shows London, Paris and Rome magnetic variation all West maximum around year 1810 but even Napoleon wasn’t that god-like.
Open questions: what happened elsewhere in the world; does this part explain the poor weather, crop failures; how much if any is solar origin and in that case is the minima in sunspot activity connected around 1810?
Just before that was the 1790 solar phase anomaly.
As usual I am avoiding claiming anything is so, is more food for thought and discussion.
[update] I forgot to mention a comprehensive work which might give clues on additional items to consider where perhaps the date of publication leaves Yousef without knowledge of the future we know today yet what he writes seems to hold.
THE SOLAR WOLF-GLEISSBERG CYCLE AND ITS INFLUENCE ON THE EARTH
Shahinaz M. Yousef
Astronomy & Meteorology Dept.
Faculty of Science -Cairo University
September, 2000
[/update]
Post by Tim Channon (co-moderator)
1. CLIMATE AND THE CHANGING SUN
JOHN A. EDDY, Climatic Change 1 (1977) 173-190.
Center for Astrophysics, Harvard College Observatory and Smithsonian Astrophysical Observatory,
Cambridge, Mass. 02138, U.S.A.
2. Bracewell, here
3. MACKEY, R., 2007. Rhodes Fairbridge and the idea that the solar system regulates the Earth’s climate. Journal
of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), 955 – 968. Gold Coast,
Australia, ISSN 0749.0208
4. Terrestrial Magentism, secular variation of the United States and at some foreign stations. T. C. Mendenhall, United States Coast and Geodetic Survey, Washington. 1890.
(FTP access, PDF 9.3M, 151 pages)
Amended spreadsheet, new sheet with new result here.
Tallbloke's Talkshop 
Tim, this is an exciting article. More new science being pioneered on the talkshop. Your result looks great, and it’s all the more exciting for me because it confirms my own result from integrating sunspot number (thanks for including my plot).
Just a quick aside on this:
As I understand it the concept involves a constant which has been guessed
The ‘ocean equilibrium value’ is around 40SSN. This is not only the average monthly sunspot number during periods when the ocean temp is stable, but it’s also the average monthly sunspot number over the entire SIDC dataset from 1749 to 2010. I don’t guess, I do engineers estimates. 😉
You have ‘done it properly’ as this sentence in your post shows:
“Restoration of data bipolarity if valid automatically provides the constant, which is actually the mean value in the long term.”
So, we got to the same place anyway. 🙂
check out this bloke’s channel. Updated every day giving solar weather, earthquake data and other Earth weather reports.
It seems Tim has designed a measure of even-odd cycle asymmetry persistence.
A “Reconstruction of the solar magnetic secular minima of the last two millennia, taking as reference point the Maunder minimum (1680 for all periodicities)” is summarized in Table 1 of
The 120-yrs solar cycle of the Cosmogenic Isotopes
V. M. VELASCO1, B. MENDOZA1, J.F. VALDES-GALICIA1.
1Instituto de Geof´ýsica, Universidad Nacional Aut´onoma de M´exico, C.P. 04510
vmv@geofisica.unam.mx
http://indico.nucleares.unam.mx/getFile.py/access?contribId=1263&sessionId=40&resId=0&materialId=paper&confId=4
The 120 year cycle, with a predicted minimum in 2040, leaves its signature in the smoothed Interplanetary Magnetic Field (IMF B).
-Gerry Pease
Rog,
I’ll edit the post.
An aside I didn’t mention is the Leif contention over sunspot numbers.
This is perhaps interesting since the effect of changing all phases has no effect on the sign. It merely changes the slope, which is of no consequence. An inflection, maybe.
I also didn’t mention that if this is about magnetics it might be that this is partially localised on earth leading to the (I think) novel idea of local cosmic ray effects, ie. regional cloud variation. Given most datasets are actually regionally biased herein is a possible explanation for some contradictions. Can’t see any major effect though.
From the paper Gerry cites:
“The results obtained from the wavelet transformation shows that there are no periodicities of 80−90 yrs (Gleissberg cycle) or 205 yrs (de Vries or Suess cycle) in these series.
This suggests that these periodicities may be the result of applying transformations (for example Fourier) to time series that do not fulfill the condition of stationarity.”
Well, there’s a stick in the methodological wheel. The authors instead find periodicity matching the “vukcevic formula”.
“The Gnevyshev-Ohl rule is an empirical rule according to which the sum of sunspot numbers over an odd cycle exceeds that of the preceding even cycle.[1] The rule breaks down under certain conditions. [2]”
http://en.wikipedia.org/wiki/Gnevyshev-Ohl_rule
Caution: Even-odd asymmetry should not be confused with north-south asymmetry.
Paul V: Well, fancy that! 😉 Tim C found a strong 206 year component in the Steinhilber et al TSI reconstruction from paleo data however.
Tim, tell us which polarity activity has been biasing towards. the ‘southward component’ by any chance?
Alternative sun spot record.
The above graph posted at the end of my lunar-solar article here and was derived from daily sun spot area data , filtered with a 90 day gaussian to remove some of the hairiness.
I’m working on the premise that the underlying process that is being monitored by the SSN or SSa proxy is proportional to the square root. ie SSN manifestation is the square of what is causing this visible trait we have been counting for centuries.
It was noted by Ray Tomes some time ago that the noise level at max and min SSN meant it would lend itself better to spectral analysis if the root was taken.
Bart also noted in his detailed power distribution spectral analysis , reposted here, that his method that is usually done on the square of the whatever is being analysed, worked better on straight SSN. This again suggests that SSN already is the square of the underlying process.
That does not necessarily mean that it is the sqrt that drives terrestrial climate but it does suggest we should at least be looking at sqrt(SSN) to understand its variation.
One thing that is notable in my graph is that the base line shows more variability that straight SSN and has been dropping off in recent decades. Global warming has also been dropping off.
The graph plotted rate of change of SST since it was simply aiming to show the phase relation of the respective cycles . I was not aiming to link magnitude.
On the most summary view it appears that sqrt(SSa) may be related directly to temperatures rather than rate of change. I may take a closer look at that.
Tim, it may be interesting to compare minima in that data to your change over dates.
On the topic of sunspot activity 1802-1805 and the 1793 solar phase anomaly:
– 1793 : sun was at a ‘maximum velocity’ > connected with the phase anomaly
– 1802 : sun was at a ‘minimum velocity’ > connect with the start of the solar minimum
The variations of sun velocity mainly reflect the 19.86-yr synodic period of Jupiter and Saturn.
In my latest paper , “Why does the current Sunspot Cycle stagnate?” http://www.gsjournal.net/Science-Journals/Essays/View/4598 , I included the hypothesis that the Sun polar magnetic field is induced through the variations of the Sun velocity. This periodicity is different from the SSN periodicity (x 2).
tallbloke (March 2, 2013 at 9:13 pm)
“Tim, tell us which polarity activity has been biasing towards. the ‘southward component’ by any chance?”
Clarification: In my G-O rule comment above I’m referring to heliographic asymmetry. Indeed heliomagnetic asymmetry is conflated with G-O, as TB hints. Apologies for any misunderstandings that may have arisen from the lack of specs. (It’s just that as soon as most see “solar asymmetry” they automatically think of sunspot area asymmetry, which is heliographic, not heliomagnetic. I was cautioning about that.)
[…] Bias in solar activity, the combination of Hale, Wolf and Wolf … […]
TB, oceans will integrate incoming energy over time but you need to allow for is dissipating.
You need to fade out older values, typical physical thing would be an exponential decay of to be determined time constant.
If you can do a weighted mean , set up coeffs that are 1 at last date and fade off over a decade or two. The mean will be proportional to the integral so it will give you the right form.
Thanks for the suggestions Greg, I’ve been meaning to further develop the original idea I had for ages.
As I recall there has been talk in formal science circles of power 1.4 and this does seem to have merit.
It so happens I have live power law on the data here. This does have a large effect on detail without changing the basic message. I’m going on keeping things simple, do it straight.
Rog,
Which polarity?
You want the truth, complete truth?
I haven’t faintest idea. This is so easy to get wrong I sit on the wall.
Which way up does sun affect earth and which half or all of the earth? Got north and south polarities, no idea whether this is NN SS or NS NS
Tim, fair enough. 🙂
Paul, point taken.
Somewhere I have a file from Svalgaard with polarity separated Bz components. It affects Geomagnetism, and I remember Vuk having some looong arguments with Leif about it. If one phase of the solar magnetic Hale cycle is more effective than the other (as seems likely to me) then right there we have a partial explanation for ~60 year oceanic cycles, with two geo-effective cycles in one ~33 year period and one in the other.
Greg Goodman says:
March 2, 2013 at 11:03 pm (other thread)
10.8 || 12.88 -> 66 year beats. Origin of “60 year” cycles?
Greg Goodman (March 2, 2013 at 10:10 pm)
“TB, oceans will integrate incoming energy over time but you need to allow for is dissipating.
You need to fade out older values, typical physical thing would be an exponential decay of to be determined time constant.
If you can do a weighted mean , set up coeffs that are 1 at last date and fade off over a decade or two. The mean will be proportional to the integral so it will give you the right form.”
That’s conceptually similar to what I’ve done with the thick orange curve on p.3 here. That’s for an exponential half-extent of 33 years. If you tune to a narrower or even much narrower window and then gaussian smooth, you’ll get the same result but with the recent multidecadal rise climbing higher from ~1976 before plateauing — i.e. the general form of the curve is robust across methodological variation.
TB’s method works well for SST from 60S to 90S where there’s less land impeding zonal midlatitude westerly flow (with a minor but noteworthy exception near ~1940). I believe the comparative difference gives us important information about the role of geography (especially the distribution of ocean & continents) in circulation & dynamic ocean memory pattern.
“Which polarity?” depends on which time of year from a terrestrial perspective, since both sun & earth are tilted. See the graph on p.1 here.
That was isolated from geomagnetic aa index annual variation, but it can also be isolated from HMF polarity data …actually way easier to do — do HMF rather than aa if you don’t know much about tuning multi-extent wavelets to detect the central limit (attractor) of hierarchically cyclic heteroskedasticity.
There’s a lot more to the HMF story hinted at in appendix C (p.7). When time/resources permit, I’ll share more of the details. At this stage I can’t rule out the possibility that what Tim illustrates here is related & important. In fact, what Tim illustrates is consistent with 2 illustrations I flagged as important in the past. I’ll have to find time to dig them out. I’ll try to share links before the end of tomorrow…
TB, I’ve hacked my gaussian convolution filter to do an exponential fading integration with a “neutral” offset value.
Not sure it’s the right answer but if you want to experiment…
In plotting and integrating and looking at long-term histories of the sun like this, remember to use the actual “dates” for each sunspot cycle – NOT the “average” 11.xxx year or 22.yyy year period. i suspect that CHANGES in the main relationships – if any is to be found at all – will be linked to the slowly changing differences and relationships that AFFECT those “average” sunspot cycle.
Make sense?
in other words, what ever might be changing solar activity in any way is almost certain to be changing sunspot cycles as well – so if the INFLUENCE is slowing changing, then the EFFECT of that influence will likely also be changing not only the magnitude of the sunspot cycles, but their individual periods and their durations as well.
Using a constant 11.xx average cycle length will disguise that influencing factor. Again, if it exists at all.
This answer any questions or raise more?
Pass is roughly 18 to 25 years, brutal and crude filter.
Phase appears to lead solar. Same if the synthesiser 22y is used.
If this is really so perhaps the part of the solar earth linkage is not centred on the assumed part of ssn or relationship with.
I am learning here, know as much as you.
RACookPE1978
This is all data driven, you need to track backwards on what I am doing.
The synchronous decode of circa 11 year comes from Hadcrut 4 data, not accurate but good enough (switching at near zero). The integrate then comes from the bipolar restored 22 year solar cycle, actual data. No tricks, I supply working data, wrong, show me, I make mistakes.
I’ve just put up a plot showing filtered which has no hard limit at 22 year, can move timing around, data again, but this is supposed to be global earth temperature… vs. solar. Spooky.
Okay so it is barely noticeable temperature, it is though a subset of the whole data.
Rog, there is some phase.
Tim , could you be more explicit about what you are calling integrated solar in your plot?
Tim, see this plot and comment about spectral corruption in Hadley data.
Greg,
Working code is supplied.
Solar in this context is sidc ssn restored to bipolar by means of synchronous demodulation. The bipolar result is then accumulated sample value by value producing the shape under discussion.
The whole scheme is very simple.
The justification of restoration is the magnetic solar cycle where a sunspot cycle occurs during each half phase of the magnetic cycle. In addition sunspots show reversed magnetic polarity, which is detect by optical effects in solar spectral emission lines.
I agree Hadcrut data is of dubious goodness, all of these global datasets are poor.
Follow up on the loose end I left above…
Tim included the following graph in the article above:
2 * 172.5 = 345 year (Bracewell 1988)
That triggered some recall.
Tons of terrestrial time series show a fundamental shift near ~1930. Most of them don’t extend far enough to show when similar shifts happened further back in time, but a few suggest an opposite sort of shift ~1765 or ~1770. Could there be a cycle with half-period 165, 171, or 179 years? Consideration of the following raises the question:
A) Figure 7b:
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.
Click to access Abarca_delRio_etal_JGeodyn03.pdf
B) Figure 10:
alternate: http://ars.els-cdn.com/content/image/1-s2.0-S0273117707006382-gr2.jpg
Georgieva, K.; Tsanev, V.; & Kirov, B. (2000). Solar asymmetry, QBO and climate.
http://www.atmosp.physics.utoronto.ca/SPARC/SPARC2000_new/PosterSess3/Session3_3/Georgieva/doklad.htm
Also see Figure 8, but take careful note of how positive/negative correlation is summarized differently from in Figure 10.
alternate: http://ars.els-cdn.com/content/image/1-s2.0-S0273117707006382-gr1.jpg
The sorting algorithm used for Figure 8 correlations appears asymmetrical, strongly biased towards classification as “positive”. (I’ll need to look into this more carefully when time permits.) This doesn’t mean one or the other of the 2 summaries is somehow wrong; we just need to take care interpreting.
I believe we have here a problem of fundamental importance that can be cracked.
Errata Tim as usual flips spellings.. article s/Elantina/Elatina/ varve.
Sigh, I wish.
I’ve not looked at the fascinating Elantina varve recently. Seems more linked by search today.
Fairly recent
http://link.springer.com/article/10.1007%2FBF00206434?LI=true
Older
http://articles.adsabs.harvard.edu/full/1986MNRAS.223..457B
http://jpdesm.pagesperso-orange.fr/sunspots/sfaqs5.html
I point out I am not very interested in luni-solar unless something compelling turns up. I am not convinced as things stand. Fundamentally it is unfortunate there are several periodic systems with very similar frequencies.
Tim wrote in the article:
“[…] fixed frequency switching wave used to decode sunspot data”
…apparently prompting RACookPE1978 (March 3, 2013 at 3:37) to comment as follows:
“[…] Make sense? […] changing not only the magnitude of the sunspot cycles, but their individual periods and their durations as well. […] Using a constant 11.xx average cycle length will disguise that influencing factor.”
That’s part of the reason why I designed the metric summarized by the thick orange curve I mention above. I had to do theoretical work to figure out how to stabilize that measure as the arctangent function is so incredibly sensitive. So far as I’ve seen so far, even the very most sensible wavelet authors appear to overlook the source of the instabilities — e.g. these guys (Donner & Thiel 2007) are brilliant, but look at the wild fluctuations in their phase estimates:
Those seemingly wild fluctuations are actually perfectly structured bias. It turns out to be easy to completely overcome that problem.
There’s certainly room to improve on estimates based on the assumption of stationarity, but that doesn’t mean it was wrong to explore the structure of the integral under the assumption of stationarity. Ask a taxonomist: Often the most useful insights are comparative. Tim has flagged up an important, interesting problem. This provides a starting point of immeasurable value and invites others to try to carry the ball further.
—
Tim: Your 22a year temperature – sunspot phase difference is small enough that it looks like it could be wave-shape related. Maybe extension to anharmonic exploration (or something else) will illuminate further. You’ve certainly raised some interesting material.
Tim linked to Jean-Pierre Desmoulins’ page on “The Elatina varves controversy”. I don’t remember noticing this Desmoulins comment before:
“I would be even more grateful if their administrations could answer favourably my demand to have a file of the raw data of the varve thickness signals.”
Sometimes administrators can be excessively creepy & crusty. Where’s the balance point on classified information? And who exactly is benefiting from keeping info hidden?
Recently I was granted access to thermospheric density data. I quickly found something simple & clear that isn’t reported in the solar-terrestrial literature. The insight substantially influences my overall perspective on solar-terrestrial relations. I’m not free to elaborate due to the “Rules of the Road”:
http://cedarweb.hao.ucar.edu/wiki/index.php/Tools_and_Models:Emmert_sat_drag_neutral_mass_density
Would it really be such a threat having deeper insights out in public? Apparently some are quite worried that the answer might be yes, but personally I’ve seen no convincing evidence that their judgement is sound.
Paul, there are several printouts of a 1400 year section, presumably the clearest. These look workable for a data extract. Might do this sometime.
The dispute over what the data represents seems ot continue.
Folks, there is no rush with continuing what I have shown, more a matter of doing oddments when ideas arrive.
I have normalised the plot shown in comments a few items back. If I run from 1880 r2=0.56, is better than it looks on close examination.
Lots of loose ends.
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typo: “and other discontinues.” discontinuities