Talkshop contributor ‘Bart’ has used a powerful mode of analysis of the sunspot record to reveal periodicities and also devised an elegant algorithm which can produce a time series very similar to the historical sunspot record. Bart does not explicitly link the two periods found to planetary periods as I have in the title of this thread to make it easy for Google to find us, but the two periods are very close to twice the orbital period of Jupiter and the synodic period of Jupiter and Saturn, which when averaged are close to the Hale cycle period. I got Bart’s permission to make an article, and Bart told me in comments here, that adjusting the two values to the exact planetary periods would make little difference to the result.

**Modeling the historical sunspot record**

I observed four significant peaks in the PSD of the SSN process at 10 years, 11.8 years, 10.8 years, and 131 years (unfortunately, the one at 131 years is obscured in the PSD I showed because I had to make the usual tradeoff between bias (resolution) and variance in my plot, and I chose to present a smoother version, the better to resolve the higher frequency peaks).

I made the assumption that the Sun spot number is a proxy for the magnitude of the process which is occurring. I redid the estimate using the magnitude squared because the autocorrelation function for the square of a Gaussian process is well known, as I related here:

Preliminary PSD analysis informs me that the solar cycle is governed by two quasi-periodic processes with periods of roughly T1 = 20 and T2 = 23.6 years.

The physical basis of the solar cycle was elucidated in the early twentieth century by George Ellery Hale and collaborators, who in 1908 showed that sunspots were strongly magnetized (this was the first detection of magnetic fields outside the Earth), and in 1919 went on to show that the magnetic polarity of sunspot pairs:

*“Hale’s observations revealed that the solar cycle is a magnetic cycle with an average duration of 22 years. However, because very nearly all manifestations of the solar cycle are insensitive to magnetic polarity, it remains common usage to speak of the “11-year solar cycle”.’*

Is always the same in a given solar hemisphere throughout a given sunspot cycle;

Is opposite across hemispheres throughout a cycle;

Reverses itself in both hemispheres from one sunspot cycle to the next.

As per Papoulis (for me, 2nd edition, page 233), if a Gaussian process with autocorrelation function R(t) is squared, the resulting autocorrelation function, which I will call Q(t), is

Q(t) = R(0)^2 + 2*R(t)^2

The PSD of this is the Fourier transform of a constant R(0)^2 plus the scaled convolution in the frequency domain of the Fourier transform of R(t) (PSD of the underlying process) with itself (i.e., multiplication in the time domain results in convolution in the frequency domain, and vice versa).

The sunspot count appears to reflect the energy of these combined processes at around 20 and 23.6 years, which necessarily has apparent periods of 0.5*T1, 0.5*T2, T1*T2/(T2+T1), and T1*T2/(T2-T1) years, or 10 years, 11.8 years, 10.8 years, and 131 years. This latter appears as a quasi-beat period in the data. I say “quasi-” because these are not rigidly defined periods of steady state sinusoids, but mean periods of random excitation of resonance phenomena.

It is pretty clear that the model for the process governing Sun spot occurrence is the correct one, even if the parameterization is somewhat statistically uncertain (and even if some parameters may be randomly or deterministically varying slowly and/or narrowly in time, as well as the precise frequency distribution of noise energy, though we really only care about that within a narrow band around the resonances).

The processes can be characterised by the following simple model:

I started with zero initial conditions, ran it for the time period indicated, and re-looped around a couple more times to make sure initial transients were settled out to get a stationary process. I implemented it in MATLAB Simulinkusing the continuous time simulation blocks exactly as in my diagram. For the random inputs, I used the Band Limited White Noise with a bandwidth of 5 years^-1 (sample time of 0.1 years). Doing this just happened to create the results shown in a couple of runs.

Here is an example of the output generated:

If I had just four random periods, I could not generally fit them in this way. I have a mapping of a 2d plane to 4d space, and the appropriate 4 parameters just happen to lie on the projected 2d submanifold described by the set of points (T1/2,T2/2,T2*T1/(T2+T1),T2*T1/(T2-T1)) which has measure zero in that 4d space.

**Measure zero means the probability of the line up of these frequency lines by chance is ZERO. There is no doubt about it. Zero. Zilch. None.**

I could devise a model for the amplitude of a sinusoidal process “z” driven by noise “e” as

xdot = -y

ydot = w^2 * x + e

z = sqrt((w*x)^2+y^2)

You could also model it directly as a phase “phi” and z using a transformation of variables so as to obtain a pair of differential equations

phidot = f1(z,phi,e)

zdot = f2(z,phi,e)

for appropriate functions f1() and f2(). The periodicity of z would be twice that of x and y, so you would tell me the frequency is 2w and I would say it was w. Both models are valid. Both are right. But, the linear model is much easier to work with.

All these numbers are preliminary, rough estimates, mind you. There are many other steps which would be needed to nail them down precisely. Once completed a Kalman Filter run backwards and forwards on the data set will properly initialize the states, and a projection forward with error bounds from the propagated covariance can easily be generated. (but, it takes time, and I have a job and a life).

Postscript:

Now, an interesting aside I noticed on another thread is:

Here’s another possibility I happened on the other day, though. Let’s suppose that the Sun’s instantaneous average temperature is dominated by the sum of a bias and two sinusoidally varying processes

Tsun = A + B*cos(w1*t + phi1) + C*cos(w2*t + phi2)

where w1 = 2*pi/T1 is the radial frequency of a process with period T1, and similarly for w2. A, B, and C are constants of proportionality. The phases phi1 and phi2 determine the relative phase of the cyclical processes.

Let us assume that Sun Spot numbers are proportional to the magnitude of the cyclical part:

Sspot ~ | B*cos(w1*t + phi1) + C*cos(w2*t + phi2) |

The square of this process is

Sspot^2 = (B*cos(w1*t + phi1))^2 + (C*cos(w2*t + phi2))^2 +

2*B*C*cos(w1*t + phi1)*cos(w2*t + phi2)

or, using trig identities

Sspot^2 = (B^2+C^2)/2 + (B^2/2)*cos(2*(w1*t+phi1)) + (C^2/2)*cos(2*(w2*t+phi2)) +

B*C*( cos((w1+w2)*t+phi1+phi2) + cos((w1-w2)*t+phi1-phi2) )

Thus, we have frequencies of 2*w1, 2*w2, w1+w2, and w1-w2, which is to say, periods of T1/2, T2/2, T1*T2/(T2+T1), T1*T2/(T2-T1). Spectral analysis shows that this is essentially what we have, with T1 = ~20 years, and T2 = ~23.6 years. This begets periods in the Sun Spot data of T1/2 = 10 years, T2/2 = 11.8 years, T1*T2/(T2+T1) = 10.8 years, and T1*T2/(T2-T1) = 131 years.

Now, radiative heat transfer goes as temperature to the fourth power, so Earth temperatures should be modulated at all the combinations above taken one step further, and including the bias offset of temperature not reflected in the Sun Spot data. So, we have frequencies of 4*w1, 4*w2, 2*(w1+w2), 2*(w1-w2), 3*w1+w2, w1-w2, 3*w1-w2, w1+w2, w1+3*w2, -w1+3*w2, 2*w1, 2*w2, all modulo sign. The periods are then T1/4, T2/4, 0.5*T1*T2/(T2+T1), 0.5*T1*T2/(T2-T1), T1*T2/(3*T2+T1), T1*T2/(T2-T1), T1*T2/(3*T2-T1), T1*T2/(T2+T1), T1*T2/(T2+3*T1), T1*T2/(3*T1-T2), T1/2, T2/2, T1, and T2. These work out to 5, 5.9, 5.4, 65.6, 5.2, 131, 9.3, 10.8, 5.6, 13, 10, 11.8, 20, and 23.6 years. Some of these may cancel each other out depending on the phases and amplitudes. And, some may be attenuated or amplified by the Earth’s actual thermal response, particularly the shorter period (higher frequency) ones ought to tend to be attenuated.

Most of these periods appear to describe the locations of major and minor peaks in the 20th century HADCRUT data within the resolution of the PSD. In particular, there is the ~65 year one, and what may be an average of the 20 and 23.6 year ones, which would resolve into two peaks with more data.

Thus, it is possible that the entire shooting match is the result of just two guns at 20 and 23.6 years, but more extensive analysis is needed.

========================================================================

How about it solar physics institutions? Don’t you think it would be worth negotiating a contract with Bart to continue this promising work so we can get a potentially useful prediction rather than the Hathaway ‘prediction’ which changes monthly?

Preliminary PSD analysis informs me that the solar cycle is governed by two quasi-periodic processes with periods of roughly T1 = 20 and T2 = 23.6 years.That is base of my formula with 19.859 & 2×11.862 years, i.e. Jupiter /Saturn synodic and 2x Jupiter sidereal periods: http://www.vukcevic.talktalk.net/NFC7.htm

btw.

Just put this on WUWT

Drs. Svalgaard & Eschenbach

Here is 4 centuries long data file.

http://www.vukcevic.talktalk.net/4C-data.txt

To resolve the dilemma of a natural ~60 year component ‘operating’ in the geo-sphere could you please do independently spectral analysis and provide links to the output data in numerical (and graphic, if you whish to do so) form.

Anyone here willing to do the same would be welcome.

Hi Vuk,

Bart does acknowledge your J-S formulation here, after Leif mentioned it.

http://wattsupwiththat.com/2011/06/02/earth-itself-is-telling-us-there%e2%80%99s-nothing-to-worry-about-in-doubled-or-even-quadrupled-atmospheric-co2/#comment-684833

“Vukcevic’s formula is the right form, but suffers from the assumption of steady state sinusoidal oscillation. This is a modal oscillation driven by a random input. I see time constants of most likely somewhere between 80 and 100 years, based on the width of the lobes. Nailing down the model is the greater part of the Kalman Filter effort.”

I’ve posted this on Willis E’s Pseudocycles thread:

Willis, the strong sixty year modulation in the barycentre data is in the z axis. The Sun is tilted wrt the plane of invariance and so when the conjunction between Jupiter and Saturn takes place near the nodes of the solar equatorial plane and the plane of invariance there is less ‘pull’ on the Solar core in the up or down direction. Because the three conjunctions over the sixty year period take place almost exactly 240 degrees apart (the precession period is 934 years for a 120 degree displacement), the power of this effect will be modulated over 934/2=467 year period (because there are two nodes), but since there seems to be a ~934 year analog in Earth’s climate, (MWP-LIA-Now) it seems likely that another factor comes into play, such as the orientation of the conjunctions to the bowshock of the heliosphere (Vuk’s idea) or the orientation wrt the galactic centre.

The 467 year period is near a cyclic frequency we found to be important in this study:

https://tallbloke.wordpress.com/2011/02/21/tallbloke-and-tim-channon-a-cycles-analysis-approach-to-predicting-solar-activity/

———————

I forgot to mention that the modulating effect of U & N makes the 60 year J-S wave hard to spot though, and it leads me to think the E/M coupling of the J, S, and E magnetospheres with the Sun may turn out be important, more kudos to Vuk there if so.

Also, the 467 year period is roughly twice the 238 year period Tim C found in the proxy data. This isn’t far from the de Vries cycle at 207.5 years either… Some proxy recalibration effort might be helped with these nudges.

What kind of energy phenomenon does drive these?

Nuclear fusion mostly.

tallbloke says:

July 31, 2011 at 4:27 pm

“Vukcevic’s formula is the right form, but suffers from the assumption of steady state sinusoidal oscillation. This is a modal oscillation driven by a random input.”This is actually an assumption I made. In a large sense, it is true, because even planetary orbits can be considered modal oscillations of the Solar System. However, locally, it is possible that the process could be externally driven with a time varying input. I was assuming here I had identified locally driven modes of the Sun itself.

It does not matter, really, as far as prediction is concerned. It can be modeled equivalently in any case. An optimal filter acting on the data using a lightly damped sinusoidal model will act as a bandpass filter for the mode in question no matter how you formulate it – all roads will lead to Rome.

I keep trying to make the point, but it doesn’t seem to get through to my audience. The underlying causes are interesting, but understanding them is not really necessary to formulate a predictive model. Understanding the exact process can help formulate a better filter/predictor, but it’s likely to be a 2nd order improvement.

Hi Bart and welcome to the talkshop.

If I understood correctly (!) you said that there was no room for doubt that the ~20 and ~23.6 year periods you found are the basic periods which explain the other periods observed.

Leif has countered with his 10.81 and 121.9 year ‘toy model’.

Can you explain in layman’s terms why we can legitimately prefer one pair of periods over the other in terms of your technique, and if possible in terms which refer to underlying physics.

Perhaps a bit of expansion on how the bottom panel of figure 1 is constructed would help.

Thanks for dropping by over here.

Thanks for your graciousness, TB. It’s actually possible to have equivalent models which give the same results, as I described where you posted above in the analogous equivalence between modeling a randomly forced sinusoid in polar or in rectangular coordinates. To my way of thinking, the simplest should be preferred.

What really has “Zero. Zilch. None.” probability is that the model of the process cannot be simplified to the way I have described it. The model is constrained such that this may be done. Any valid model must satisfy this constraint, and be capable of being decomposed in this manner.

The “scaled HRP autoconvolution” line in the bottom plot of Figure 1 is simply the convolution of the second plot with itself, scaled approximately to match the PSD of the SSN^2 data. If you had a process with autocorrelation R(t) and it had a PSD of the HRP, then a portion of the PSD of the square of the process would be proportional to the HRP PSD convolved with itself. Theoretically, the other portion is a spike at the origin but, due to the finite length of data available for estimation, it will manifest as a low frequency function proportional to the magnitude of the autocorrelation window.

As I explained at the WUWT thread, I will be away for a week or more. I’ll check back when I can and see if there are any other questions or comments for which I can provide constructive inputs.

…a low frequency function proportional to the magnitude of the

Fourier Transformof the autocorrelation window.Thanks again Bart. We may have worked out the alphabet soup and had a good head scratch by the time you’re back. 🙂

Have a good trip.

@Tallbloke:

Nuclear fusion mostly…My bet is on an electric current 🙂A polarizing theory!

;p

here’s an interesting link found through E.M. Smith’s “Chiefio” blog

http://thesurfaceofthesun.com/

[Edit] Interesting, maybe. Relevant to this thread, no.Glossary of terms:

PSD Power Spectral Density

http://en.wikipedia.org/wiki/Spectral_density

HRP hypothetical resonance PSD

Autoconvolution:

http://www.ask.com/wiki/Convolution_theorem

Autocorrelation: is the cross-correlation of a signal with itself. Informally, it is the similarity between observations as a function of the time separation between them. It is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal which has been buried under noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

http://en.wikipedia.org/wiki/Autocorrelation

Bart says:

July 31, 2011 at 6:46 pm

“I keep trying to make the point, but it doesn’t seem to get through to my audience. The underlying causes are interesting, but understanding them is not really necessary to formulate a predictive model.”

Exactly. Newton does a very good job of predicting gravity without the foggiest notion of understanding the process, or even the fundamentals such as the propagation speed.

The value of science comes from its ability to predict the outcome of some event in the future, so we can invest our limited time and resources to maximum benefit. The better science is able to predict, the more likely we are to benefit.

In contrast, theories that rely on “understanding” the process are often rapidly outdated as our level of understanding increases. If you seek truth, religion is more likely to provide an answer to the infinite, because all scientific explanations of an infinite universe are at some level flawed.

Without good predictions you need to invests in all eventualities at the same time. Since there are an infinite number of possibilities but only limited resources, this course of action is doomed to failure.

To use an analogy, consider the guerrilla warfare tactic. By attacking your enemy randomly without warning over a large area, you force your enemy to spread their defenses to the point at which they can be overwhelmed by a much smaller force. In effect Nature wages just such a guerrilla campaign, as we rarely know where disaster will strike next.

The value of science comes in being able to predict the actions of Nature to the point where we can best defend with our limited resources, and counter for maximum gain.

Very well put Ferd.

fred;

“all scientific explanations of an infinite universe are at some level flawed.”

Same for a finite universe. There’s always a potential for improving a scientific “account” of what’s going on or might go on.

Ferd;

Sorry for “fredding” you. My perception of your name was flawed.

8-\

Yes, very nice, ferd.

Hey Bart,

I thought I had a few more days to put my list of dumb questions together before you came back. 🙂

Here’s one:

Svalgaard says the ‘power’ of his ~121 year peak is higher than the 10, 10.8 and 11.8 year peaks. I wondered if that was because with it being (131 years as you have it) the beat frequency of the 10 and 11.8 year periods there was some kind of phase addition and canceling involved?

TB – take your time. I’m back, but will take time to decompress.

To get a feel for this, reexamine the equation for pure sinusoids given above:

Sspot^2 = (B^2+C^2)/2 + (B^2/2)*cos(2*(w1*t+phi1)) + (C^2/2)*cos(2*(w2*t+phi2)) +

B*C*( cos((w1+w2)*t+phi1+phi2) + cos((w1-w2)*t+phi1-phi2) )

The ~131 or ~121 year or whatever (the lowest frequency one – precise evaluation requires more in-depth analysis than I have put into it, +/- 10% is probably a reasonably expected uncertainty at this time) cycle is proportional to B*C, as is the ~10.8 year one. So, these should be comparable in power. They will be greater than the other two if B*C > B^2/2 (i.e., C > B/2) and B*C > C^2/2 (B > C/2).

If you look in my PSD plot above derived from the “HRP” (green line), you will see that the ~131 year peak is slightly higher than the 10.8 year one. But, the peak is not the whole story, something I don’t think Leif understands. In a PSD, the physically meaningful quantity is the area under the curve in the vicinity of the peak. So, the ~131 year peak is slightly taller, but also slightly narrower, than the 10.8 year one. The power in both is essentially equal.

The blue line, taken from the actual data, has resolution problems because the data record is only 167 years long, just enough to include a cycle and some change for the ~131 year process so, even if I take steps to remove the dc component ((B^2+C^2)/2 in the above expansion), it appears to have lower power than it should (though it is there). But, as I say, that is almost surely merely a resolution issue. The simulations demonstrate that the behavior of the actual data and the model are comparable over the relevant time period. A better PSD estimator (e.g., using a maximum entropy estimator) likely would resolve the low frequency peak better, and if I had the time, I would probably move next in that direction, as well as employing other estimation techniques to resolve frequencies to a higher level of precision.

…B*C > B^2/2 (i.e., C > B/2) and B*C > C^2/2

(B > C/2)🙂[edit] Corrected, thanks.Hi Bart,

No need to reinvent the wheel, Schwentek and Elling did the max entropy study back in 1984

http://esoads.eso.org/abs/1984SoPh…93..403S

Click on the ‘GET’ button rather than the blue PDF link.

I did the hunting and gathering. Over to you to decide whether they used the right recipe. 🙂

[…] Hemispheric sunspot lead/lag, …Tenuc on Juno will improve our knowledg…tallbloke on Bart: Modeling the historical …Bart on Bart: Modeling the historical …Bart on Bart: Modeling the historical […]

“No need to reinvent the wheel…”Yes, well, trying as I may not to sound insufferably pompous… I have my own methods which produce exceedingly round wheels 😉

I was just tossing off MEM as an example of alternative methods.

Excellent, how are they with Keplerian egg shapes 🙂

One thing which is puzzling me is the (near) equivalence of the result Schwentek and Elling get via Kepler and Copernicus and your result from the T1*T2/(T1+T2) equation.

Can you guide me through that?

[…] of the peaks near the solar cycle length we found when Bart made a MEM spectral analysis of sunspot numbers matches the half period of the Jupiter-Saturn conjunction cycle – 9.93 […]

[…] calculated. Additionally, the harmonic periods associated with the Power Spectral Density (PSD) study made of the sunspot number by talkshop contributor ‘Bart’ and used in the subsequent posting on Jupiter and […]

Bart lists all the permutations in his postscript eg

T1*T2/(T2-T1) T1*T2/(T2+T1)… T1,T2

“Now, radiative heat transfer goes as temperature to the fourth power, so Earth temperatures should be modulated at all the combinations above taken one step further…So, we have frequencies of 4*w1, 4*w2, 2*(w1+w2), 2*(w1-w2), 3*w1+w2, w1-w2, 3*w1-w2, w1+w2, w1+3*w2, -w1+3*w2, 2*w1, 2*w2, all modulo sign.”

Based on trig identities, this is similar the point I was making a couple of days ago about how T(t) and dT/dt can interact to produce frequency doubling and higher harmonics.

” These work out to 5, 5.9, 5.4, 65.6, 5.2, 131, 9.3, 10.8, 5.6, 13, 10, 11.8, 20, and 23.6 years.”

These need working out and adjusting for the hypothesis that the base frequencies are the planetary ones, but this would seem the obvious answer to the origin of the circa 13 year periodicities I was finding in SST.

Indian 13.11

Nino3.4 13.12

Nino1 13.42

N Atl Trop. 12.928

S Pac ex-trop 13,12

S Atl Trop 12.46

S Atl ex-trop : no.

chirp analysis of sqrt(SSN) :

28.5

21.592

19.212

19.922

12.73

11.786

11.038

10.008

9.466

9.241 cf 9.3 , something causing a doublet splitting ?

p2=5.718

pc=5.455

p1=5.263 # trip?

print -1/(1/pc-1/p1), 1/(1/pc-1/p2)

# 149.529505208333 118.599581749049 average =134a

cf Barts 5.2 5.4 5.6 , allowing of uncertainties in the analysis and taking the average of the implied long term result comes close to Bart’s 131.

Bart noted at some point but I’ve lost the quote that he found his method worked better it he did not take the square of SSN , as would be usual in his method.

This goes in the same sense as Ray Tome’s observation that the noise pattern between min and max of SSN looks like it is a dataset that would respond better to spectral analysis if we took the sqrt.

It seems SSN is a proxy of the square of the underlying physical property causing sun spots and is why I did the chip on sqrt(SSN).

ie Bart did not need to square SSN because it already is the square.

http://tinypic.com/view.php?pic=xudsy&s=6

Strong 5.42 year cycle in Arctic ice cover.

Looks like I need to chirp that too.

p1=4.014

pc=5.37

p2=8.055

print -1/(1/pc-1/p1), 1/(1/pc-1/p2)

15.8961504424779 16.11

very quickly, not uncert est.

5.37 modulated by 16

Close to Bart’s 5.4 getting, a bit far from the 5.45 if found in SSN but both were quick and dirty. Worth a closer look.

The 5.4/5.45 numbers are close to half a solar cycle. The data is for recent decades where cycles have been in that range, and the Australian BoM states the most common cycle length is around 10.5 years.

Yes, I’d made the obvious link to half a Hale cycle. Going back to what I said about T(t) and dT/dt that could point to a negative feedback in dT/dt. Lack of evidence of Hale itself seems odd though.

I’ve commented elsewhere that the return to oscillation around zero dT/dt despite current warmth also directly indicates a dominant negative feedback.

Oldbrew: The 5.4/5.45 numbers are close to half a solar cycle. The data is for recent decades where cycles have been in that range, and the Australian BoM states the most common cycle length is around 10.5 years.

Yes, I’va already mentioned we need to be aware of the solar cycle lengths during the period of the terrestrial data we are studying.

The solar cycle length clusters around 10.38 and 11.86 years in length, as Timo Niroma showed us before he passed on.

TB:”Yes, I’va already mentioned we need to be aware of the solar cycle lengths during the period of the terrestrial data we are studying.”

If you’re just simply cycle spotting , yes.

However, if you manage to correctly characterise the surface solar behaviour , as it appears Bart is very close to doing, the smaller frequencies with the correct phase will cancel where they need to cancel and should produce patterns that can be detected in any sub-period.

I think this is important. There will be significant frequencies in Barts’ auto-convolution that are not obvious in a spectrogram of a limited sub-period.

Just which of these periods particular components of the earth system respond to ( either by resonance or possibly by negative feedbacks taking them out) means cycle spotting in sub-sets may miss key driver-responses.

I have noted elsewhere that the problem with trying to attribute temperature variations to SSN is that it goes out of phase on the century scale. There is at least one major player that’s going in and out of phase on that time-scale.

I wish I had the tools to reproduce Bart’s results.

I wish I had the tools to reproduce Bart’s results.

… well perhaps I have. In fact this is very close to what I’ve already done.

Just a lash up here, will take a proper look later. Have to do some life getting the way stuff, first.

Underlines what I’ve been saying all along. There is a strong SSN signal in SST but it is being confounded by something circa 9 years that is actually a bit stronger.

I’ll check working later and have a more detailed look.

“I have noted elsewhere that the problem with trying to attribute temperature variations to SSN is that it goes out of phase on the century scale. ”

Not if you understand the way solar variation interacts with the hysteresis of the ocean it doesn’t. You need to integrate the sunspot number departing fro the long term average which matches the equilibrium value at which the ocean neither gains nor loses heat. Then in combination with a couple of other params, you can get this:

Yes, the baseline SSN seems a reasonable proposition. I commented elsewhere on TS about that. IIRC when I was looking at sqrt(SSN) a quick look was suggesting 3.6 was neutral which matches very well with your figure of 40 SSN.

However, using SST to predict SST is not particularly useful. Since SOI is a pacific index , in essence what you are doing here is saying hadSST3 is detrended Atlantic plus detrended Pacific and retrending it with a CO2 factor.

Since most of the CO2-like long term tendency in hasSST3 comes form Hadley “bias corrections” anyway that is of dubious value.

I would hope that we can come up with something a bit less self-recursive to explain the SST record.

What I posted above was a bit of a hack. I’ll have a more serious look at this later.

Soi is pressure not sst. AMO is sst but detrended. I agree that co2 might be nixed by hadley adjustment removal. 🙂

“AMO is sst but detrended. ” That is explicitly recognised my last comment. But why would anyone who is not a climate scientist expect there to be a “trend” to be there to be removed by “detrending”.

It remains self-referential to try to explain SST , at least in part, by using a sub-set of SST. I think we can do better.

Bart’s SSN treatment is impressive, it’s given me some ideas. I need some time to work on it.

I’ve been working on autocorrelation and FFT for a while now, this is essentially the same thing as what he did.

This 9 year thing seems to stand out a mile, which ever way I look at it and indications so far are that this is separate from solar. Could be wrong but I doubt it.

Neither do I go a bundle on the orthodox view that everything that is not CO2 is “internal variability”.

Now off to prove this is in a way that will stand up to my own exacting standards.

Greg: AMO has been trending up since the end of the LIA according to drop-stone data. I use the detrended set because the trend is accounted for in my SSN cumulative method. I have also found a good fit with a plain old 64yr sine wave.

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