By Dr. Nicola Scafetta
It is time to update my widget comparing the global surface temperature, HadCRUT3 (red and blue), the IPC 2007 projection (green) and my empirical model (black thick curve and cyan area) based on a set of detected natural harmonics (period of approximately: 9.1, 10-11, 20 and 60 years) which are based on astronomical cycles, plus a corrected anthropogenic warming projection of about 0.9 oC/century. The yellow curve represents the harmonic model alone without the corrected anthropogenic warming projection and represents an average lower limit.
The proposed astronomically-based empirical model represents an alternative methodology to reconstruct and forecast climate changes (on a global scale, at the moment) which is alternative to the analytical methodology implemented in the IPCC general circulation models. All IPCC models are proven in my paper to fail to reconstruct all decadal and multidecadal cycles observed in the temperature since 1850. See details in my publications below.
As the figure shows, the temperature for Jan/2012 was 0.218 oC, which is a cooling respect to the Dec/2011 temperature, and which is about 0.5 oC below the average IPCC projection value (the central thin curve in the middle of the green area). Note that this is a very significant discrepancy between the data and the IPCC projection.
On the contrary, the data continue to be in reasonable agreement with my empirical model, which I remind, is constructed as a full forecast since Jan/2000.
In fact the amplitudes and the phases of the four cycles are essentially determined on the basis of the data from 1850 to 2000, and the phases are found to be in agreement with appropriate astronomical orbital dates and cycles, while the corrected anthropogenic warming projection is estimated by comparing the harmonic model, the temperature data and the IPCC models during the period 1970-2000. The latter finding implies that the IPCC general circulation models have overestimated the anthropogenic warming component by about 2.6 time on average, within a range between 2 to 4. See original papers and the dedicated blog article for details: see below.
The widget also attracted some criticisms from some readers of WUWT’s blog and from skepticalscience
Anthony asked me to respond to the criticism, and I am happy to do so. I will respond five points.
- Criticism from Leif Svalgaard.
As many readers of this blog have noted, Leif Svalgaard continuously criticizes my research and studies. In his opinion nothing that I do is right or worth of consideration.
About my widget, Leif claimed many times that the data already clearly contradict my model: see here 1, 2, 3, etc.
In any case, as I have already responded many times, Leif’s criticism appears to be based on his confusing the time scales and the multiple patterns that the data show. The data show a decadal harmonic trending plus faster fluctuations due to ElNino/LaNina oscillations that have a time scale of a few years. The ENSO induced oscillations are quite large and evident in the data with periods of strong warming followed by periods of strong cooling. For example, in the above widget figure the January/2012 temperature is out of my cyan area. This does not mean, as Leif misinterprets, that my model has failed. In fact, such pattern is just due to the present La Nina cooling event. In a few months the temperature will warm again as the El Nino warming phase returns.
My model is not supposed to reconstruct such fast ENSO induced oscillations, but only the smooth decadal component reconstructed by a 4-year moving average as shown in my original paper figure: see here for the full reconstruction since 1850 where my models (blue and black lines) well reconstruct the 4-year smooth (grey line); the figure also clearly highlights the fast and large ENSO temperature oscillations (red) that my model is not supposed to reconstruct.
As the widget shows, my model predicts for the imminent future a slight warming trending from 2011 to 2016. This modulation is due to the 9.1 year (lunar/solar) and the 10-11 year (solar/planetary) cycles that just entered in their warming phase. This decadal pattern should be distinguished from the fast ENSO oscillations that are expected to produce fast periods of warming and fast period of cooling during these five years as it happened from 2000 to 2012. Thus, the fact that during LaNina cooling phase, as right now, the temperature may actually be cooling, does not constitute a “proof” that my model is “wrong” as Leif claimed.
Of course, in addition to twist numerous facts, Leif has also never acknowledged in his comments the huge discrepancy between the data and the IPCC projection which is evident in the widget. In my published paper [1], I did report in figure 6 the appropriate statistical test comparing my model and the IPCC projection against the temperature. The figure 6 is reported below
The figure reports a kind of chi-squared statistical test between the models and the 4-year smooth temperature component, as time progress. Values close to zero indicate that the model agrees very well with the temperature trending within their error range area; values above 1 indicate a statistically significant divergence from the temperature trending. It is evident from the figure above that my model (blue curve) agrees very well with the temperature 4-year smooth component, while the IPCC projection is always worst, and statistically diverges from the temperature since 2006.
I do not expect that Leif changes his behavior against me and my research any time soon. I just would like to advise the readers of this blog, in particular those with modest scientific knowledge, to take his unfair and unprofessional comments with the proper skepticism.
- Criticism about the baseline alignment between the data and the IPCC average projection model.
A reader dana1981 claimed that “I believe Scafetta’s plot is additionally flawed by using the incorrect baseline for HadCRUT3. The IPCC data uses a baseline of 1980-1999, so should HadCRUT.”
This reader also referred to a figure from skepticalscience, shown below for convenience,
that shows a slight lower baseline for the IPCC model projection relative to the temperature record, which give an impression of a better agreement between the data and the IPCC model.
The base line position is irrelevant because the IPCC models have projected a steady warming at a rate of 2.3 oC/century from 2000 to 2020, see IPCC figure SPM.5. See here with my lines and comments added
On the contrary, the temperature trending since 2000 has been almost steady as the figure in the widget clearly shows. Evidently, the changing of the baseline does not change the slope of the decadal trending! So, moving down the baseline of the IPCC projection for giving the illusion of a better agreement with the data is just an illusion trick.
In any case, the baseline used in my widget is the correct one, while the baseline used in the figure on skepticalscience is wrong. In fact, the IPCC models have been carefully calibrated to reconstruct the trending of the temperature from 1900 to 2000. Thus, the correct baseline to be used is the 1900-2000 baseline, that is what I used.
To help the readers of this blog to check the case by themselves, I sent Anthony the original HadCRUT3 data and the IPCC cmip3 multimodel mean reconstruction record from here . They are in the two files below:
itas_cmip3_ave_mean_sresa1b_0-360E_-90-90N_na-data
As everybody can calculate from the two data records that the 1900-2000 average of the temperature is -0.1402, while the 1900-2000 average of the IPCC model is -0.1341.
This means that to plot the two records on the common 1900-2000 baseline, there is the need to use the following command in gnuplot
plot “HadCRUT3-month-global.dat”, “itas_cmip3_ave_mean_sresa1b_0-360E_-90-90N_na.dat” using 1:($2 – 0.0061)
which in 1850-2040 produces the following graph
The period since 2000 is exactly what is depicted in my widget.
The figure above also highlights the strong divergences between the IPCC model and the temperature, which are explicitly studied in my papers proving that the IPCC model are not able to reconstruct any of the natural oscillations observed at multiple scales. For example, look at the 60-year cycle I extensively discuss in my papers: from 1910 to 1940 a strong warming trending is observed in the data, but the warming trending in the model is far lower; from 1940 to 1970 a cooling is observed in the data while the IPCC model still shows a warming; from 1970 to 2000, the two records present a similar trending (this period is the one originally used to calibrate the sensitivities of the models); the strong divergence observed in 1940-1970, repeats since 2000, with the IPCC model projecting a steady warming at 2.3 oC/century , while the temperature shows a steady harmonically modulated trending highlighted in my widget and reproduced in my model.
As explained in my paper the failure of the IPCC model to reconstruct the 60-year cycle has large consequences for properly interpreting the anthropogenic warming effect on climate. In fact, the IPCC models assume that the 1970-2000 warming is 100% produced by anthropogenic forcing (compare figures 9.5a and 9.5b in the IPCC report) while the 60-year natural cycle (plus the other cycles) contributed at least 2/3 of the 1970-2000 warming, as proven in my papers.
In conclusion, the baseline of my widget is the correct one (baseline 1900-2000). My critics at skepticalscience are simply trying to hide the failure of the IPCC models in reconstructing the 60-year temperature modulation by just plotting the IPCC average simulation just since 2000, and by lowering the baseline apparently to the period 1960-1990, which is not where it should be because the model is supposed to reconstruct the 1900-2000 period by assumption.
It is evident that by lowering the base line a larger divergence would be produced with the temperature data before 1960! So, skepticalscience employed a childish trick of pulling a too small coversheet from a too large bed. In any case, if we use the 1961-1990 baseline the original position of the IPCC model should be shifted down by 0.0282, which is just 0.0221 oC below the position depicted in the figure above, not a big deal.
In any case, the position of the baseline is not the point; the issue is the decadal trend. But my 1900-2000 baseline is in the optimal position.
- Criticism about the chosen low-high boundary levels of the IPCC average projection model (my width of the green area in the widget).
Another criticism, in particular by skepticalscience, regards the width of the boundary (green area in the widget) that I used, They have argued that
“Most readers would interpret the green area in Scafetta’s widget to be a region that the IPCC would confidently expect to contain observations, which isn’t really captured by a 1-sigma interval, which would only cover 68.2% of the data (assuming a Gaussian distribution). A 2-sigma envelope would cover about 95% of the observations, and if the observations lay outside that larger region it would be substantial cause for concern. Thus it would be a more appropriate choice for Scafetta’s green envelope.”
There are numerous problems with the above skepticalscience’s comment.
First, the width of my green area (which has a starting range of about +/- 0.1 oC in 2000) coincides exactly with what the IPCC has plotted in his figure figure SPM.5. Below I show a zoom of IPCC’s figure SPM.5
The two red lines added by me show the width at 2000 (black vertical line). The width between the two horizontal red lines in 2000 is about 0.2 oC as used in my green area plotted in the widget. The two other black lines enclosing the IPCC error area represent the green area enclosure reported in the widget. Thus, my green area accurately represents what the IPCC has depicted in its figure, as I explicitly state and show in my paper, by the way.
Second, skepticalscience claims that the correct comparison needed to use a 2-sigma envelope, and they added the following figure to support their case
The argument advanced by skepticalscience is that because the temperature data are within their 2-sigma IPCC model envelope, then the IPCC models are not disproved, as my widget would imply. Note that the green curve is not a faithful reconstruction of my model and it is too low: compare with my widget.
However, it is a trick to fool people with no statistical understanding to claim that by associating a huge error range to a model, the model is validated.
By the way, contrary to the claim of sckepticalscience, in statistics it is 1-sigma envelope width that is used; not 2-sigma or 3-sigma. Moreover, the good model is the one with the smallest error, not the one with the largest error.
In fact, as proven in my paper, my proposed harmonic model has a statistical accuracy of +/- 0.05 oC within which it well reconstructs the decadal and multidecadal modulation of the temperature: see here.
On the contrary, if we use the figure by skepticalscience depicted above we have in 2000 a 1-sigma error of +/- 0.15 oC and a 2-sigma error of +/- 0.30 oC. These robust and fat error envelope widths are between 3 and 6 times larger than what my harmonic model has. Thus, it is evident from the skepticalscience claims themselves that my model is far more accurate than what the IPCC models can guarantee.
Moreover, the claim of skepticalscience that we need to use a 2-sigma error envelope indirectly also proves that the IPCC models cannot be validated according the scientific method and, therefore, do not belong to the realm of science. In fact, to be validated a modeling strategy needs to guarantee a sufficient small error to be capable to test whether the model is able to identify and reconstruct the visible patterns in the data. These patterns are given by the detected decadal and multi-decadal cycles, which have amplitude below +/- 0.15 oC: see here. Thus, the amplitude of the detected cycles is well below the skepticalscience 2-sigma envelope amplitude of +/- 0.30 oC, (they would even be below the skepticalscience 1-sigma envelope amplitude of +/- 0.15 oC).
As I have also extensively proven in my paper, the envelope of the IPCC model is far larger than the amplitude of the temperature patterns that the models are supposed to reconstruct. Thus, those models cannot be properly validated and are useless for making any useful decadal and multidecadal forecast/projection for practical society purpose because their associated error is far too large by admission of skepticalscience itself.
Unless the IPCC models can guarantee a precision of at least +/- 0.05 oC and reconstruct the decadal patterns, as my model does, they cannot compete with it and are useless, all of them.
- Criticism about the upcoming HadCRUT4 record.
Skepticalscience has also claimed that
“Third, Scafetta has used HadCRUT3 data, which has a known cool bias and which will shortly be replaced by HadCRUT4.”
HadCRUT4 record is not available yet. We will see what happens when it will be available. From the figures reported here it does not appear that it will change drastically the issue: the difference with HadCRUT3 since 2000 appears to be just 0.02 oC.
In any case for an optimal matching the amplitudes of the harmonics of my model may need to be slightly recalibrated, but HadCRUT4 already shows a clearer cooling from 1940 to 1970 that further supports the 60-year natural cycle of my model and further contradicts the IPCC models. See also my paper with Mazzarella where the HadSST3 record is already studied.
- Criticism about the secular trending.
It has been argued that the important issue is the upward trending that would confirm the IPCC models and their anthropogenic warming theory.
However, as explained in my paper, once that 2/3 of the warming between 1970 and 2000 is associated to a natural cycle with solar/astronomical origin (or even to an internal ocean cycle alone) the anthropogenic warming trending reproduced by the models is found to be spurious and strongly overestimated. This leaves most of the secular warming tending from 1850 to 2012 as due to secular and millennial natural cycles, which are also well known in the literature.
In my published papers, as clearly stated there, the secular and millennial cycles are not formally included in the harmonic model for the simple reason that they need to be accurately identified: they cannot be put everywhere and the global surface temperature is available only since 1850, which is a too short period for accurately locate and identify these longer cycles.
In particular, skepticalscience has argued that the proposed model (by Loehle and Scafetta) based only on the 60-year and 20-year cycles plus a linear trending from 1850 to 1950 and extrapolated up to 2100 at most, must be wrong because when the same model is extrapolated for 2000 years it clearly diverges from reasonable patterns deduced from temperature proxy reconstructions. Their figure is here and reproduced below
Every smart person would understand that this is another skepticalscience’s trick to fool the ignorant.
It is evident that if, as we have clearly stated in our paper, we are ignoring the secular and millennial cycles and we just approximate the natural millennial harmonic trending with a first order linear approximation that we assume can be reasonable extended up to 100 years and no more, it is evident that it is stupid, before than being dishonest, to extrapolate it for 2000 years and claim that our result is contradicted by the data. See here for extended comment by Loehle and Scafetta.
As said above in those models the secular and millennial cycles were excluded for purpose. However, I already published in 2010 a preliminary reconstruction with those longer cycles included here (sorry in Italian), see figure 6 reported below
However, in the above model the cycles are not optimized, which will be done in the future. But this is sufficient to show how ideologically naïve (and false) is the claim from skepticalscience.
In any case, the secular trending and its association to solar modulation is extensively addressed in my previous papers since 2005. The last published paper focusing on this topic is discussed here and more extensively here where the relevant figure is below
The black curves represent empirical reconstruction of the solar signature secular trending since 1600. The curve with the upward trending since 1970 is made using the ACRIM TSI composite (which would be compatible with the 60-year cycle) and the other signature uses the PMOD TSI composite which is made by manipulating some of the satellite records with the excuse that they are wrong.
Thus, until the secular and millennial cycles are accurately identified and properly included in the harmonic models, it is the studies that use the TSI secular proxy reconstructions that need to be used for comparison to understand the secular trending, like my other publications from 2005 to 2010. Their results are in perfect agreement with what can be deduced from the most recent papers focusing on the astronomical harmonics, and would imply that no more that 0.2-0.3 oC of the observed 0.8 oC warming since 1850 can be associated to anthropogenic activity. (Do not let you to be fooled by Benestad and Schmidt 2009 criticism that is filled with embarrassing mathematical errors and whose GISS modelE performance is strongly questioned in my recent papers, together with those of the other IPCC models) .
I thank Anthony for the invitation and I apologize for my English errors, which my above article surely contains.
Relevant references:
[1] Nicola Scafetta, “Testing an astronomically based decadal-scale empirical harmonic climate model versus the IPCC (2007) general circulation climate models.” Journal of Atmospheric and Solar-Terrestrial Physics, (2012). DOI: 10.1016/j.jastp.2011.12.005
[2] Adriano Mazzarella and Nicola Scafetta, “Evidences for a quasi 60-year North Atlantic Oscillation since 1700 and its meaning for global climate change.” Theor. Appl. Climatol. (2011). DOI: 10.1007/s00704-011-0499-4
[3] Craig Loehle and Nicola Scafetta, “Climate Change Attribution Using Empirical Decomposition of Climatic Data.” The Open Atmospheric Science Journal 5, 74-86 (2011). DOI: 10.2174/1874282301105010074
[4] Nicola Scafetta, “A shared frequency set between the historical mid-latitude aurora records and the global surface temperature.” Journal of Atmospheric and Solar-Terrestrial Physics 74, 145-163 (2012). DOI: 10.1016/j.jastp.2011.10.013
[5] Nicola Scafetta, “Empirical evidence for a celestial origin of the climate oscillations and its implications.” Journal of Atmospheric and Solar-Terrestrial Physics 72, 951–970 (2010). DOI: 10.1016/j.jastp.2010.04.015
Additional News and Links of Interest:
Global Warming? No, Natural, Predictable Climate Change, Larry Bell
http://scienceandpublicpolicy.org/images/stories/papers/reprint/astronomical_harmonics.pd
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@Willis
I totally appreciate your position. I sincerely hope Dr Scafetta responds. He has an interesting theory and he has clearly put a lot of work into it. I think we could all learn a lot if he responds to you.
Hi Geoff
For long time I searched for 59.5 years signal in the temperature data, never found a significant one. As you can see the GISP spectrum
http://www.vukcevic.talktalk.net/GISP2spec.htm
has 57.6 and 61.5, which are symmetrical in respect of 59.5 (sidebands) , but they are pretty weak in comparison to the nearby ones, may be coincidence, the symmetricity argues against it, but even so there are about 10 or 11 stronger periods within 38-100 year range, so 61.5 can’t be that important.
Forced oscillation are not necessarily locked to but can be symmetrically displaced around the central frequency as in here
http://www.vukcevic.talktalk.net/SSN-Vfspec.htm
analogous to above (57.6- 61.5 years case), but here the strength of the two sideband signals makes relationship highly likely, however the proof can’t ever be 100% verifiable.
One has to take a reality check and if something is not very convincing most likely isn’t terribly important.
I don’t agree with Willis that tides do not matter, multi-decadal tidal oscillations are an important factor.
Dr. Svalgaard is also wrong to say there is no 88 year signal in the temperature records, it is one of the strongest periods in both CET and GISP2.
I have mentioned elsewhere to Dr. Scafetta, a possible but strong 62 year negative feedback between the Arctic and Equator
http://www.vukcevic.talktalk.net/AEc.htm
more likely to be related to Bart’s idea of Rossby (or planetary) waves resonance .
In conclusion, I am not siding with anyone however clever they may (or may not) be, just observing and noting reality as I see it, and when necessary re-adjust .
MAVukcevic says:
March 14, 2012 at 4:26 am
Vuk, I think it is very obvious because of solar system variance that FFT analysis is fruitless in many cases.
I am repeating this post because it was held in the sin bin because the word Landshe…t was included, which normally places such posts late in the conversation and interrupts intelligent discussion. It is high time this blog recognized this part of science has some merit, especially since the science has moved on greatly since Theodor’s days. In fact the new theory is way beyond Theodor’s pioneering concepts.
Willis Eschenbach says:
March 14, 2012 at 1:53 am
Oh, wait … Geoff Sharp, I’ve heard that name before … weren’t you the brilliant fellow who was claiming upthread that the synodic cycle of Saturn/Jupiter was 60 years, when in fact it’s 19.87 years? … Yeah, that was you. And now you want to tell me I’M out of my field? I got schooled and instructed in this stuff by Ted Landsch…t himself, but I’m the one that’s out of my field
Your style belittles you. I am surprised Anthony still puts up with you after your recent fiasco. You have absolutely no understanding of planetary theory and you have learned nothing from Theodor, you failed last time when not able to recognize 2nd order harmonics. Instead of shooting your mouth off, try educating yourself.
Willis,
as I have told you many times, before criticize a paper and the work of somebody you need to study it.
Yesterday I spent half day telling you this obvious fact that every smart and less smart person would be able to understand by himself without any necessary input from somebody else.
Finally, in late evening you finally downloaded a paper of mine. However, instead of studying it, you simply skimmed it in just a few minutes.
Essentially, you are spending more time in writing in this blog criticizing my work than in properly studying my papers first to educate yourself first.
About your question and insinuations of the type “I am totally unable to replicate your Figure 10b.”
That is because you did not read how I got that figure. Use the recepie written in the paper, and you will get it.
Your own update “[UPDATE: Ahhh, I see what you have done. My bad. I noticed it on my first read, but I couldn’t believe it.”
is nothing but the most clear evidence of how superficially and arrogantly you are acting: you open your mouth laud before properly studying the subject.
Contrary to your expectations, I have no duty to lecture you for free and waste my time.
Study carefully my papers, study the relevant literature and come back.
You may be interested in starting from very very far given your total ignorance on the topic and your need to deeply educate yourself first. For example, you may need to start from
“Abu Ma’Sar on Historical Astrology: The Book of Religions and Dynasties on Great Conjunctions (Islamic Philosophy, Theology, and Science) (Mnemosyne, Bibliotheca Classica Batava) ”
Which is a book from 886 AD
http://www.amazon.com/Abu-MaSar-Historical-Astrology-Conjunctions/dp/9004117334/ref=sr_1_2?ie=UTF8&qid=1331730766&sr=8-2
just to discount you from the Indian, Chinese, Egyptian and Babylonian studies on the topic.
Then pass through all medieval literature on the topic up to and including the works of Kepler.
And go on.
Then, of course you still need to read my papers well to understand what I have done.
Have a good reading, Take your time. It will take a while!
@ur momisugly Agnostic says: March 14, 2012 at 3:22 am
Sorry, agnostic. If Willis wants me to interact with him:
1) He needs to acknowledge that he have criticized my works without reading them first (as everybody here has understood) and he needs to deeply apologize with me, with Anthony and with all readers of this blog.
2) He needs to promise to stop to behave like an arrogant fat-brained guy and carefully study my papers (as well as the papers of other people) before talking and wrinting.
3) He needs to withdraw this article here on this web-site
http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/
where he have criticized my work with Loehle, without carefully reading it. Note in particular that I kindly showed him the strong limitations of his reasoning in my comment
http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-709115
and Willis never felt the duty to respond my point, and was criticized by many other readers for that.
He again needs to apologize to me and Loehle, to Anthony and to all readers of the web-site.
In comparison you can read this comment on airvent on my same paper with Loehle
http://noconsensus.wordpress.com/2011/10/15/cycles-in-temperature-trends/
where Jeff clearly is surprise of the superficiality of Willis.
In conclusion, if Willis wants me to interact with him, he needs first to prove me that he is not a buffoon. I do not have time to loose with buffoons.
Bart says: March 14, 2012 at 1:46 am
thank you, but I know what I am doing. Just be patient to see the development of the theory.
Agnostic says: (March 13, 2012 at 3:02 pm) “@Willis, I think what you are running into here is something of a culture clash.”
I do not think so.
Also in American culture when somebody publicly criticizes somebody else’s work without first educating himself on what the latter has truly written it is considered highly unethical and slandering. In America, people can sue for much less than what Willis did.
Just for comparison, everybody knows that Peter Gleick has written on Amazon a strong criticism to the book of Donna Laframboise
http://www.amazon.com/review/R3DB7LHRMJ14G5
But a lot of readers have immediately noted that he did not actually read the book. Everybody properly accused Gleick of lack of integrity.
You can also read the strong criticism against Gleick’s behavior by Curry here
http://judithcurry.com/2011/10/19/laframboise-on-the-ipcc/
Willis, by criticizing my work without have spent any time reading the papers first, has acted exactly in the same way of Gleick.
The best that everybody here can do to help Willis, it to rebut him by properly accusing him to have lost his integrity by his behavior, and that to restore such intergrity he needs to apologize without if or but.
Personally I see a 71-72yr temperature signal since a peak at c.1868:
http://www.woodfortrees.org/graph/hadsst2gl/from:1860
Astronomical analysis of such a cycle would come to a very different conclusion, especially if all four Jovian bodies are considered.
MAVukcevic says:
March 14, 2012 at 1:15 am
“Astronomy deals with precise numbers: 62 will not do for a 60 year cycle.”
Finite data record length can cause apparent shifting of the peak in a spectral estimate, but that requires a longer explanation than I care to give here. The difference between these is 3%. Estimation of the central location of a peak is not likely to be that precise.
Also, if the signal is driving a resonance with a slightly different natural frequency, the resonant peak may be the main one.
“As you can see the GISP spectrum… has 57.6 and 61.5…”
Splitting of lines in spectral estimation is a well known occurrence. It can happen even when the actual underlying signal is unimodal. This is just one of the phantoms that can emerge if you do not do a proper spectral analysis. As I tried to explain to Willis, there are many subtleties to spectral estimation which would take several chapters, if not an entire book, to explain, but he wants it all condensed into a blog post.
I will explain line splitting a little. The stochastic nature of the data means that an apparent (but spurious) amplitude modulation can appear. As any student with basic knowledge of trigonometry should know, a sinusoid which is amplitude modulated by another sinusoid is equal to the sum of two sinusoids. If the first sinusoid has a frequency f, and the second is df, then there will be apparent harmonics at f+df, and f-df. But, they are not necessarily real. Example: cos(theta)*cos(dtheta) = 0.5*cos(theta-dtheta) + 0.5*cos(theta+dtheta).
There are also finite data window effects. You can find more info on spectral line splitting in power spectrum estimation by performing a search, e.g., like this.
Nicola Scafetta says:
March 14, 2012 at 8:06 am
“Just be patient to see the development of the theory.”
I will wait and see what develops. And, I will spend the intervening time reading your publications so that I can comment and critique knowledgeably.
Bart says: March 14, 2012 at 10:57 am
Bart is right about the splitting of the spectral peaks. A modulated 60-year cycle will results is two spectral peaks symmetric to the 60 year cycle, because that is how power spectra would interpret the data. In fact, if we use vukceviv graph
http://www.vukcevic.talktalk.net/GISP2spec.htm
we find two large peaks at 54.4 and 67.2 years. If these two peaks represent a splitted cycle, the central cycle would be at
2/(1/54.4+1/67.2) = 60.13 years
which is the 60 year cycle, we are talking about.
Because the astronomical cycles are not rigorous single-harmonics and the climate system add its own chaotic response to the 60 year forcing, and GISP2 record is not a global surface temperature records but a very local one which also presents all internal local weather variability of the system and many other problems, by using this long record a spectral splitting may not be unreasonable.
In any case, the issues are discussed in my papers, in particular when I summarize the scientific litterature about the 60 year cycle during the Holocene and during the last 1000 years, that people like Vukcevic and Willis are invited to read.
@Nick: Looks to me now that your patience shattered the storm troopers….
The bottom construction of the 60 year cycle is sound as rock….for
building the upper construction, i.e. calculations on how cyclic forces pull/push
exactly at which day/year and how much [in miles/km] at the Earth’s orbit
to produce the noticable 0.4 C cyclic staircase shape in centennial
temp development….
All in the bag already…..as I wrote before…..well done…..
JS
Dr. Scafetta
& Bart
Amplitude modulation with sidebands (term I used in my previous post) not only that is well known, but it is part and parcel of the everyday radio transmission practice.
http://en.wikipedia.org/wiki/Sideband
You need to learn more about actual physical content of such processes and there is a whole science to it (sideband transmission engineering).
It was recognition of these cross-modulation patterns which enabled me to devise the SSN formula http://www.vukcevic.talktalk.net/NFC7a.htm
within 2-3 days of the first ever seeing sunspot cycle train in my daughters school project.
Nicola Scafetta says:
March 14, 2012 at 11:51 am
that people like Vukcevic and Willis are invited to read.
I do not need to read your work, for simple reason that is coming nowhere close to explaining how the sun and the Earth climate change are connected.
I worked it out nearly two years ago, and if you haven’t seen the graph for the North Atlantic Precursor than I suggest have a good look at:
http://www.vukcevic.talktalk.net/GTC.htm
Not much reading required, just study the graphs, it is all there.
MAVukcevic says: March 14, 2012 at 1:23 pm
Ok, Vukcevic. Do not read, that is OK. But do not criticize too. The two things go together.
About your graph, write a decent paper and try to publish it in a journal. It may be important.
MAVukcevic says: March 14, 2012 at 1:23 pm
In fact, if you do not read my papers first, you cannot know whether they addrees the issue of whether they come or not “close to explaining how the sun and the Earth climate change are connected.”
Of course I am also talking about those mechanisms (modulation of the cloud cover etc), but you do not get it because you do not read the papers. But talk, talk and talk….
Joachim Seifert says:
March 14, 2012 at 12:41 pm
“The bottom construction of the 60 year cycle is sound as rock..”
Hardly, a 60yr cycle will only run two or three steps before it fizzles out. Try going from 1690 (very cold) in 60yr steps forward, it has lost it by 1870. There is no logic to three consecutive synodic periods of Jupiter and Saturn producing a 60yr cycle. Draw a 60yr sign wave and plot the three ~20yr J/S conjuncts on it, and it becomes apparent that if every third conjunct is on the 60yr wave peak, then the other two will be below the zero line. Explain that, how does one conjunct every 60yrs makes it hot and the other two make it cooler ?
To Ulrich:
There are 2 distinct cycles: The minor cycle, due to the 3-body gravitation
and interaction of the body Sun, then Earth, then Jup/Sat as third; maximum
effect 0.4’C and recurring over 1,000’s of years….
Scroll up the comments: it is superimposed on the large cycle, completely
different in its origin.The other, the major cycle has the present lenght of 790
years, and amplifies into the future glacial with a value of 17.88 years per full
period……
The cycle is transparently calculated in lit: ISBN 978-3-86805-604-4 on the
GERMAN Amazon.de
Both cycles interact with partial/entire addition/subtraction…….and you will get
the correct values….. If you take just the minor and try to mathematically extend
it over centuries without a heuristic grasp…. futile…
In any case, it seems trhat Warmist nonsense did not stick with you…..
Therefore: Understanding both natural cycles in full is the key to climate
science…..
…. Warmists will have lost in a few years, when natural cycles [and of course
the continuing cooling of climate, as the cycles clearly prove] hit the public
interest… 3 more cold winters and people are much more open to natural
cycles as today…
Cheers
JS
modulation of the cloud cover etc
Cloud modulation and many of the other et ceteras are not causes but the consequences of the climate change. I doubt that anyone can understand temperature changes without deep and detailed understanding what is going on in the North Atlantic. To climb the climate change ladder good advice is to start from the ground level up. People like Lindzen & co stumbling through the cloud cover minutiae and the CO2 feedbacks quandary are just chasing their own tails.
MAVukcevic says: March 14, 2012 at 2:27 pm
“Cloud modulation and many of the other et ceteras are not causes but the consequences of the climate change.”
Ok Vukcevic, there exists a large scientific literature that claims otherwise, but you do not know it because you do not read; you just talk, talk and talk…..
The issue is currently debated.
I am among those who claim that there exists a relatively strong cloud feedback to astronomical forcing regulated by solar/astronomical oscillations, and I base my conviction on my studies and on my reading of the scientific litterature.
Of course the cloud system also responds to purely terrestrial phenomena as claimed by the IPCC models that however do not agree with the data nor reproduce the correct cycles.
So, there is a contribution of both phenomena.
Ulric Lyons says:
March 14, 2012 at 1:46 pm
There is no logic to three consecutive synodic periods of Jupiter and Saturn producing a 60yr cycle. Draw a 60yr sign wave and plot the three ~20yr J/S conjuncts on it, and it becomes apparent that if every third conjunct is on the 60yr wave peak, then the other two will be below the zero line. Explain that, how does one conjunct every 60yrs makes it hot and the other two make it cooler ?
At least you understand the origin of the 60 year cycle.
If people would read Nicola’s paper they would see he measures the distance between Earth and Jupiter/Saturn. There is a 60 year cycle in this distance brought about from the 3 synodic repeats. This is also seen clearly when looking at the Sun/Jupiter distance via JPL data comparing perihelion/aphelion distances, the same 60 year cycle is evident.
Nicola only speculates on the mechanism involved in the modulation of cloud cover/ocean cycles and leaves the topic for future research. More can be found in my article.
http://tinyurl.com/2dg9u22/?q=node/233
Joachim Seifert says:
March 14, 2012 at 4:45 pm
“There are 2 distinct cycles: The minor cycle, due to the 3-body gravitation
and interaction of the body Sun, then Earth, then Jup/Sat as third; maximum
effect 0.4′C and recurring over 1,000′s of years….”
That is just waffle. You are not going to get a sign wave or saw tooth 60yr signal out of three Ju/Sa synodic periods with or without Earth. There is no 790yr cycle, 22 Sa/Ne synods is 789.125yrs but nothing else coincides with that period so there is no reason for it to stand out as a cycle.
With a competent understanding of planetary effects on solar activity, one can plot which months or even weeks will be colder in a given winter ahead: http://wattsupwiththat.com/2010/05/05/suns-magnetics-coming-alive-again/#comment-386968
One or two cycles is far too simplistic.
Geoff Sharp says:
March 14, 2012 at 5:53 pm
“At least you understand the origin of the 60 year cycle.”
No, I understand there is no reason for three 20yr sign waves to turn into a 60yr sine wave. Willis quite rightly has the same reservation too. I`m not even happy about a 60yr pattern in the temperature record, it looks more like 71/72yrs to me, which makes a lot more sense astronomically.
to Ulrich:
This post was enormously rich and produced really good insights….even Willis,
which is rarely the case, had to throw in the towel this time……
The post is almost at its end now and voila, here you come along, and instead
of having learned a lot about cosmic cycles with climate relevance….
no, nothing learned…… you just throw CO2-Warmist BS into the post….not
even worth a single letter of reply…..
Mind Warmism/Alarmism hide/hate cosmic cycles because those would
reduce/eliminate the GHG effect…. and you either just repeat Warmist
BS slogans [“NO CYCLES!] or are confused on cycles matter, applying
rudimentary “mathematics” of your gusto, explaining nothing and trying to
feel important…
This has no value…. sorry.
Cheers….
Ulric Lyons says:
March 14, 2012 at 6:58 pm
No, I understand there is no reason for three 20yr sign waves to turn into a 60yr sine wave. Willis quite rightly has the same reservation too.
I have clearly laid out the actual observed distance variations that occur in a 60 year cycle. This item is not up for discussion, it is fact proven via JPL. If yourself and Willis refuse to acknowledge the facts there is no point in further discussion.
MAVukcevic says:
March 14, 2012 at 1:05 pm
“It was recognition of these cross-modulation patterns which enabled me to devise the SSN formula http://www.vukcevic.talktalk.net/NFC7a.htm
within 2-3 days of the first ever seeing sunspot cycle train in my daughters school project.”
The SSN data is proportional to the absolute value of a process which alternatingly emanates energy from the Northern and Southern solar hemispheres. The major modes can be modeled as shown here, being two resonant systems driven by random noise. The natural frequencies of these dominant modes have corresponding periods of about P1 = 20 and P2 = 23.6 years.
The SSN squared PSD therefore displays peaks at frequencies associated with periods of P2*P1/(P2+P1) = 10.8 years, P2*P1/(P2-P1) = 131 years, P1/2 = 10 years, and P2/2 = 11.8 years.
Simulated outputs of the model show behavior very similar to actual SSN data. In these plots, we see the same type of random amplitude and phase modulation as observed in the real world data. It is this type of variation which accounts for the descrepancies between your static model and the observations.
If I had time to complete this analysis, I would use the SSN squared values as observables for a Kalman Filter, run the data backwards and forwards through it to initialize the states properly, and then I could project the SSN forward in time with error bounds produced by the Kalman Filter formalism.
But, this is a genuine instance of a well defined, amplitude modulated signal with prominently separated frequency peaks in a bimodal distribution. Your spectrum here… it’s just lines, barely better than a list of numbers. There’s no insight into how you picked these values or what a well prepared spectrum would look like.
Geoff Sharp says:
March 14, 2012 at 7:08 pm
“I have clearly laid out the actual observed distance variations that occur in a 60 year cycle.”
So there is a little 60yr wobble on the 20yr sine wave: http://www.landscheidt.info/images/scafetta_60.png
it`s not a 60yr cycle in it`s own right, and Neptune and Uranus will only come into a similar position relative to the Ju/Sa conjuncts at the Jose cycle period.
Joachim Seifert says:
March 14, 2012 at 7:20 pm
No cigar…
cheers, Ulric.
Ulric Lyons says: March 14, 2012 at 6:58 pm
The 60-year cycle is quite simple to get in multiple ways because it is implicit in the geometry itself of the combined orbit of Jupiter and Saturn. So, every function containing the orbits of Jupiter and Saturn will also present a 60-year cycle. If you use some observable this 60-year cycle looks small, if you use some other observable it looks big.
In my papers the issues are explained in details with alternative physical observables. In my papers the logic is to identify the frequency of these cycles, and for this purpose any function of the orbit is good. The purpose was not to identifies the actual function that more directly relates to the climate oscillations.
Willis and all those who, like him, arrogantly and dishonestly think that it is ok to criticize my work (as well as the work of anybody else) without reading it first and without understanding its logic and philosophy, continuously make the same mistake.
Their superficial look, misled by their poor imagination and poor knowledge of physics, fall only on the relative amplitude of the cycles, while the purpose in the paper was to look at the frequencies and their phases. In fact, the relative amplitudes change from observable to observable, but the frequencies do not: they are the invariable measures. Think at two different instruments that play the same music. And that is what it is happening to the climate system, it is syncronized to the astromonical frequencies; showing this syncronization was the purpose of my past papers.
Some my figures are in Geoff web-site clarify some of the issue showing alternative observables constructed with the different physical functions
http://tinyurl.com/2dg9u22/?q=node/233
More details on the issue require you to wait the development of the theory: be patient.