UPDATE: The author writes:
Thank you for posting my story on Sunspots and The Global Temperature Anomaly.
I was pleasantly surprised when I saw it and the amount of constructive feedback I was given.
Your readers have pointed out a fatal flaw in my correlation.
In the interests of preventing the misuse of my flawed correlation please withdraw the story.
Then I replied: “Please make a statement to that effect in comments, asking the story be withdrawn.“
To which he replied:
After further reflection, I have concluded that the objection to the cosine function as having no physical meaning is not valid.
I have posted my response this morning and stand by my correlation.
Personally, I think the readers have it right. While interesting, this is little more than an exercise in curve fitting. – Anthony
Guest post by R.J. Salvador
I have made an 82% correlation between the sunspot cycle and the Global Temperature Anomaly. The correlation is obtained through a non linear time series summation of NASA monthly sunspot data to the NOAA monthly Global Temperature Anomaly.
This correlation is made without, averaging, filtering, or discarding any temperature or sunspot data.
Anyone familiar with using an Excel spread sheet can easily verify the correlation.
The equation, with its parameters, and the web sites for the Sunspot and Global temperature data used in the correlation are provided below for those who wish to do temperature predictions.
The correlation and the NOAA Global Mean Temperature graph are remarkably similar.
For those who like averages, the yearly average from 1880 to 2013 reported by NOAA and the yearly averages calculated by the correlation have an r^2 of 0.91.
The model for the correlation is empirical. However the model shows that the magnitude, the asymmetrical shape, the length and the oscillation of each sunspot cycle appear to be the factors controlling Global temperature changes. These factors have been identified before and here they are correlated by an equation to predict the Temperature Anomaly trend by month.
The graph below shows the behavior of the correlation to the actual anomaly during a heating (1986 to 1996) and cooling (1902 to 1913) sunspot cycles. The next photo provides some obvious conclusion about these same two Sunspot cycles. 
In the graph above the correlation predicted start temperature for these same two solar cycles has been reset to zero to make the comparison easier to see.
High sustained sunspot peak number with short cycle transitions into the next cycle correlate with temperature increases.
Low sunspot peak numbers with long cycle transitions into the next cycle correlate with temperature decreases.
Oscillations in the Sunspot number, which are chaotic, can cause increases or decreases in temperature depending where they occur in the cycle.
The correlation equation contains just two terms. The first, a temperature forcing term, is a constant times the Sunspot number for the month raised to a power. [b*SN^c]
The second term, a stochastic term, is the cosine of the Sunspot number times a constant. [cos(a*SN)] This term is used to model those random chaotic events having a cyclical association with the magnitude of the sunspot number. No doubt this is a controversial term as its frequency is very high. There is a very large degree of noise in the temperature anomaly but the term finds a pattern related to the Sunspot number.
Each term is calculated by month and added to the prior month’s calculation. The summation stores the history of previous temperature changes and this sum approximates a straight line relationship to the actual Global Temperature Anomaly by month which is correlated by the constants d and e. The resulting equation is:
Where TA= the predicted Temperature Anomaly
Cos = the cosine in radians
* = multiplication
^ = exponent operator
Σ = summation
a,b,c,d,e = constants
TA= d*[Σcos(a*SN)-Σb*SN^c]+e from month 1 to the present
The calculation starts in January of 1880.
The correlation was made using a non-linear time series least squares optimization over the entire data range from January of 1880 to February of 2013. The Proportion of variance explained (R^2) = 0.8212 (82.12%)
The Parameters for the equation are:
a= 148.425811533409
b= 0.00022670169089817989
c= 1.3299372454954419
e= -0.011857962851469542
f= -0.25878555224841393
The summations were made over 1598 data months therefore use all the digits in the constants to ensure the correlation is maintained over the data set.
The correlation can be used to predict future temperature changes and reconstruct past temperature fluctuations outside the correlated data set if monthly sunspot numbers are provided as input.
If the sunspot number is zero in a month the correlation predicts that the Global Temperature Anomaly trend will decrease at 0.0118 degree centigrade per month. If there were no sunspots for a year the temperature would decline 0.141 degrees. If there were no Sunspots for 50 years we would be entering an ice age with a 7 degree centigrade decline. While this is unlikely to happen, it may have in the past. The correlation implies that we live a precarious existence.
The correlation was used to reconstruct what the global temperature change was during the Dalton minimum in sunspot from 1793 to 1830. The correlation estimates a 0.8 degree decline over the 37 years.
Australian scientists have made a prediction of sunspots by month out to 2019. The correlation estimates a decline of 0.1 degree from 2013 to 2019 using the scientists’ data.
The Global temperature anomaly has already stopped rising since 1997.
The formation of sunspots is a chaotic event and we can not know with any certainty the exact future value for a sunspot number in any month. There are limits that can be assumed for the Sunspot number as the sunspot number appears to take a random walk around the basic beta type curve that forms a solar cycle. The cosine term in the modeling equation attempts to evaluate the chaotic nature of sunspot formation and models the temperature effect from the statistical nature of the timing of their appearance.
Some believe we are entering a Dalton type minimum. The prediction in this graph makes two assumptions.
First : the Australian prediction is valid to 2019.
Second: that from 2020 to 2045, the a replay of Dalton minimum will have the same sunspot numbers in each month as from may 1798 to may 1823. This of course won’t happen, but it gives an approximation of what the future trend of the Global Anomaly could be.
If we entered another Dalton type minimum post 2019, the present positive Global Temperature Anomaly would be completely eliminated.
See the following web page for future posts on this correlation.
http://www.facebook.com/pages/Sunspot-Global-Warming-Correlation/157381154429728
Data sources:
NASA
http://solarscience.msfc.nasa.gov/greenwch/spot_num.txt
NOAA ftp://ftp.ncdc.noaa.gov/pub/data/anomalies/monthly.land_ocean.90S.90N.df_1901-2000mean.dat
Australian Government Bureau of meteorology
http://www.ips.gov.au/Solar/1/6
Related articles
- Current solar cycle data seems to be past the peak (wattsupwiththat.com)
- Paper finds solar influence on climate has been underestimated (oneworldchronicle.com)
Finally we have proof that Man Made Global Climate Change is not only affecting Earth, but it is clearly affecting the Sun
The fact that Global Temp appears to lag Sunspot Activity helps reinforce that Ancient CO2 levels Lagged Temp. yet still were the cause of the Temp. rise.
It all makes sense now.
Why this does strike me as an example of over-fit curve fitting, I do think the insistence on a physical mechanism is one of the weaknesses of climate science and modern science in general.
Climate may be considered a Function of what we Know and what we don’t known – the Unknown. Mathematically this might be expressed as:
C = F(K,U)
Given C and K, solve for F and U.
So, if we limit ourselves to only those terms that have a known or hypothetical mechanism, we are unlikely to arrive at the correct answer. This has been very amply demonstrated by the current climate models, which have gone off the rails post 2000, and demonstrates that they are also nothing more than curve fitting.
Paul Vaughan says:
May 3, 2013 at 4:51 pm
Realize it? Paul, I can’t even understand it. “Lace an average harmonic through …”? “Crude alias of the anharmonic framework …”?? “Amplitude change temporal autocorrelation …”???
‘Fraid I’ll have to pass, my friend.
w.
ferd berple says:
May 4, 2013 at 8:17 am
Thanks, ferd. In science there is no “insistence on a physical mechanism”. As I pointed out above, such a lack is a problem but not a deal-killer. I had said:
In this case, we have a very, very strange mathematical relationship with no known physical basis. In such a case, the lack of a possible mechanism becomes a more significant issue.
w.
R A Salvador @ur momisugly May 4, 2013 at 7:31 am
The Cos(a*SN) term measures the accumulated effect of sunspot oscillations within a cycle. I believe that is why the frequency associated with this term is high. It is a sunspot change frequency. Each sunspot cycle is different not just in terms of magnitude and length but also when the sunspots appear and disappear.
This is sheer fantasy.
For a particular month, Cos(a*SN) is the added contribution from the sunspot number for that month. Have you bothered to see what those values look like? Note that the sunspot numbers are all single decimal values. As an example, suppose we calculate the values from the Cos term for the values of SN from 50.0 to 51.0 (or pick any other range – the effect is the same) :
50.0 0.66093757
50.1 -0.99986134
50.2 0.63558111
50.3 0.17570427
50.4 -0.86341658
50.5 0.94388669
50.6 -0.36051987
50.7 -0.47640113
50.8 0.97826849
50.9 -0.79211814
51.0 0.04886991
Don’t you find it somewhat amazing just how sensitive these values are to miniscule changes in the SSNs as they oscillate up and down like a yo-yo? Do you honestly believe that this is the result of when “the sunspots appear and disappear”? What kind of magic is involved in the connection of the “sunspot change frequency” and this super-sensitive oscillation?
Change the value of a by adding or subtracting 0.1 from it. Do the values predicted by your equation look much different from the current ones? All of this should indicate to you that the inclusion of the Cos term is simple not realistic.
ferd berple (May 4, 2013 at 8:17 am) wrote:
“So, if we limit ourselves to only those terms that have a known or hypothetical mechanism, we are unlikely to arrive at the correct answer.”
So you understand why they resort to online stalking, harassment, & abuse to limit discussion to authoritatively alleged knowns. It’s becoming clear that the heavy hand of the law is needed to ensure civility, as we are dealing with extremists who believe their ends justify online means that would not need to be tolerated in person. Here in Canada, after some recent high profile internet-bullying-related suicides, the federal government now finds itself at the center of a sociopolitical context that’s critically ripe to expedite the introduction of laws to ensure the type of online civility that we’ve always demanded legally in person.
_______
R J Salvador (May 4, 2013 at 7:31 am) wrote:
“Let me address some of the objections […] The main one is that the correlation has no physical significance. I disagree.”
I’ve done extensive diagnostics on your work Salvador and I concur: the correlation has physical significance.
R J Salvador (May 4, 2013 at 7:31 am) wrote:
“The Cos(a*SN) term […] Each sunspot cycle is different not just in terms of magnitude and length but also when the sunspots appear and disappear.”
I find it curious that so many have knee-jerk-reacted that this term is “random noise”. It leaves me speculating about what false assumptions they must be making about the mathematical properties of the input series. I can only conclude that while they may have done diagnostics, they have not done so carefully. Possibly they’re ignoring quasicyclic volatility and falsely extrapolating the convergence rate of temporally-global asymptotics to the lower timescales. There are other possibilities.
Careful preliminary diagnostics suggest that with deeper understanding your method could be extended to hindcast the details of ENSO. I personally would not use the approach for forecasting at this stage, but I do not object to your freedom to make forecasts.
Jeez, if we keep this up much longer I might just defect to the other side!
If I had the time and inclination I suspect that, by playing ‘the numbers’, I could easily link the DJ or the FTSE 100 to Sun Spots. I’m not seeing a mechanism here beyond a lot of free parameters to play with.
OK Paul, I’m completely lost.
Paul Vaughan says: @ur momisugly May 4, 2013 at 11:36 am
“So you understand why they resort to online stalking, harassment, & abuse to limit discussion to authoritatively alleged knowns.”
What are you going on about? Criticizing grandiose claims is abuse? Stick to the topic at hand. You claim you have done “extensive diagnostics” on this material. So show what you have done to justify saying “the correlation has physical significance.” I’d like to learn how that can be done.
” Possibly they’re ignoring quasicyclic volatility and falsely extrapolating the convergence rate of temporally-global asymptotics to the lower timescales. There are other possibilities.”
Huh???? I understand what all of the words mean individually, but I’ll be damned if I can make rational sense of them all occupying places in the same sentence. Never mind the “other possibilities” – I’d just like some indication of what you are trying to convey with this ridiculous jargon.
Meanwhile, why don’t you address the point that I made above about how consecutive changes of magnitude 0.1 in the sunspot number not only produce massive changes in their “explanatory” effect, but also reverse the sign of that effect each time. I guess that when you are dealing with temporally-global asymptotics this sort of thing happens all the time… 😉
son of mulder says:
May 4, 2013 at 4:35 am
“That’s not a physical explaination, purely an assumption that the mysterious gravity diminishes as a sphere’s area increases with r as R^2.”
Here is the physical explanation:
A) there are no gravitational sources or sinks in the intervening free space
B) the solution is non-trivial (non-zero)
C) the solution is spherically symmetric
D) the interaction goes to zero at infinite radius
Those four physical requirements uniquely, mathematically dictate a 1/r^2 relationship.
“It does not physically explain how the force is transferred instantaneously from one mass to another…”
Neither does Coulomb’s Law. But, it is still useful in electrostatics. Newton’s Law is a sort of gravito-statics. It is still used overwhelmingly in spaceflight and other applications involving low relative speeds and weak gravitational attractions. And, this has nothing to do with whether the 1/r^2 relationship is a curve fit or not. It isn’t.
rgbatduke says:
May 4, 2013 at 5:43 am
“There are, sadly, a few people who love to fit curves to data and then pretend that the result has extrapolative predictive power. If you’re going to play this game, you might as well not screw around with crippled bases.”
There is often at least some justification, and long record of success, for choosing a low order polynomial base (Taylor’s theorem). Ordinarily, if the function is periodic, there is justification for choosing a harmonic base (Fourier’s theorem). The problem here is that a base which is harmonic in time would be reasonable, but one which is harmonic in SN? What in the world does that physically represent?
David A. Evans says:
May 3, 2013 at 5:04 pm
It’s too bad not many people know what to make of David’s LCR model. The use of a linearized, 2nd order response to model the dominant behavior of a physical process when subjected to an input has a long, long pedigree and record of success. David, I would encourage you to share your model parameters and results. By tweaking the gain and initial states, I bet you can get a really good fit.
“Bart says:
May 4, 2013 at 1:17 pm
Here is the physical explanation:
A) there are no gravitational sources or sinks in the intervening free space
B) the solution is non-trivial (non-zero)
C) the solution is spherically symmetric
D) the interaction goes to zero at infinite radius
Those four physical requirements uniquely, mathematically dictate a 1/r^2 relationship.”
The same is true for 1/r^3 as regards B,C,D and A is an assumption. Newton had no idea as to whether A was true or not. If he’d observed distant galaxies he’s have been somewhat perplexed as to why they don’t fly apart given his law.
“Neither does Coulomb’s Law. But, it is still useful in electrostatics.”
Precisely, you are making my whole point in this one statement. What R.J. Salvador is saying is an observation, formulated as a hypothesis, without a physical basis that through experimentation (long term observation) may be shown to be an accurate model of the future temperature record.
@ur momisugly RomanM (May 4, 2013 at 1:07 pm)
Multidecadal climate waves perfectly match multidecadal heliosphere waves:
http://tallbloke.files.wordpress.com/2013/03/scd_sst_q.png
Since you appear strongly resistant to this observation, I cannot justify further engagement with you at this time.
Sincerely
You show a graph illustrating something – who knows what – but which does not in any way provide support to the equation shown in the post. You have not addressed any of the questions that I posed to you. How you can use the adjective “further” for engagements is beyond me.
And I was, oh so hoping, that you could teach me how to show that Salvaddor’s correlation had physical significance. I am inconsolably bereft!
son of mulder says:
May 4, 2013 at 2:19 pm
“Newton had no idea as to whether A was true or not.”
That would require Newton to have been an idiot. Since Newton was verifiably not an idiot, the statement is disproved, QED.
When you are looking for the cause of an observed attraction between two masses, which is proportional to the masses involved, it necessarily follows that where there is no mass, there is no such interaction.
The View from the Back of the Class…
I (as you are likely well aware!) am not well-versed in science. In case you’d like to hear how you all came off to one person sitting in this part of your audience (there are LOTS of us listening in), here’s the poop:
1) Mr. Vaughan is not firing on all four cylinders.
To wit:
Paul Vaughan says:
May 3, 2013 at 4:51 pm
“My best guess at where critics are going fatally wrong with their “random” noise assumptions:
Failure to recognize that amplitude change temporal autocorrelation must necessarily shift phase with solar cycle deceleration (SCD). Such a failure would lead to a further failure to recognize the potential to lace an average harmonic through the manifold and (either brilliantly or haphazardly, depending on whether it was conscious or not) yank out a crude alias of the shifting anharmonic framework that gets considerably sharpened up (in central limit) by integration.
I wouldn’t expect that anyone here would realize the preceding.” [End Vaughan]
[Willis E.’s response in part]
“Realize it? Paul, I can’t even understand it.”
COMMENT: Oh, I understand. Perfectly. Vaughan is full of it. Vaughan, your crazy verbal gymnastics were TRANSPARENTLY nonsense; you couldn’t even fool a non-science major, much less the science giants above. You were a fool to try.
****************************************************************************
2) While I started the thread being quite impressed at Mr. Salvador’s hard work and the apparently plausible correlation between solar events and Earth’s temperature, by the middle, I was nearly convinced and, by the end, convinced that for Mr. S. it is, sadly, BACK TO THE DRAWING BOARD.
@ur momisugly Mr. Salvador
Do keep trying (IF you are not a poseur) — those wonderful mathematicians, engineers, physicists, etc…, above would, I think, be glad to help you — several have already given some excellent advice.
!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!
WELL DONE, all you science giants! I could understand just enough to convince me that you soundly won the argument. BRAVO! BRAVO! BRAVISSIMO!
!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!!*!*!*!*!*!*!*!*!*!*!*!*!*!
FYI: I would have been convinced more readily and quickly if Nylo’s attitude had not been so arrogantly contemptuous. While he was the main refuter, I was still wanting Salvador to win; yeah, my emotions were clouding my thinking a bit at that point, but, THAT IS REALITY when attempting to persuade. Not that what us non-scientists think determines the truth of the debate, but, we do have a battle to win, a big part of which is showing the public that the AGW Cult is wrong. “Pleasant words promote instruction” is about far more than merely being civil. It is a fact about the human brain’s ability to listen and learn.
Dear Anthony,
I know you are awfully busy, but, I sure hope you will do as someone above suggested and PUT A DISCLAIMER or a NOTICE of some sort indicating the nearly unanimous rejection of the WUWT scientists of the above article.
Perhaps, something like: PLEASE NOTE: MANY SKEPTIC SCIENTISTS DISAGREE WITH THE FOLLOWING ARTICLE (see comments in thread below).
Thanks again for letting non-scientists enjoy your wonderful site!
And CONGRATULATIONS on your THIRD Weblog Award!!! Simply the best!
Janice
Multidecadal climate waves perfectly match multidecadal heliosphere waves:
http://tallbloke.files.wordpress.com/2013/03/scd_sst_q.png
Watching how upset this makes people is quite informative.
In an article carried here last year I compared BEST and CET . Cet is recognised by many scientists as being a reasonable (but not perfect) proxy for NH temperaturres and to a lesser extent global temperatures.
http://wattsupwiththat.com/2012/08/14/little-ice-age-thermometers-historic-variations-in-temperatures-part-3-best-confirms-extended-period-of-warming/
.
It must be remembered that even in the cold years of the LIA there were some very warm periods so not sure how that squares with a below power sun. It could well be that if all the elements that would create a cold year, or sequence of years, were in position that sunspot numbers might then have some impact.
I’m not convinced by the article. There is possibly some correlatrion between sunspot numbers and temperatures but equally, looking at the same evidence, you could claim the opposite. I remain open to persuasion either way
tonyb
Willis Eschenbach says:
May 4, 2013 at 10:39 am
In this case, we have a very, very strange mathematical relationship with no known physical basis. In such a case, the lack of a possible mechanism becomes a more significant issue.
=======
If the relationship can predict future temperatures given future sunspot numbers, it has value. If not, the value is questionable at best. The formula itself does not inspire confidence, but that doesn’t mean it is wrong, but suggests that it probably is.
The close fit bothers me most of all, because the temperature signal includes noise, which the model should be unable to fit. Too good to be true comes to mind.
However, curve fitting itself does not bother me in the least, because it clearly has predictive powers. Leaning machine, such as neural networks are a form of curve fitting. Likely human intelligence develops by way of a similar process. The problem is in arriving at the correct curve. Often a very large number of curves will match the data, but relatively few will have predictive power. Intelligence is then the measure of the ability of machine or organism to select the best curve from all possibilities.
As you have correctly noted, one way to eliminate the “incorrect” curves is to test the model by hiding some of the data and training the model on the part not hidden. If the model can predict what is hidden, this is strong evidence that the model has predictive ability. As you increase the size of the training data, the model can eliminate more and more of the sub-optimum curves from the set of all possible curves, arriving eventually at those curves that have predictive ability.
Almost certainly that is how we learn. Our brains guess at a “curve” to solve the problem that fits the available data. We receive feedback from our environment to tell us if the guess is any good. Based on this feedback we adjust the curve to try and improve the fit – to try and better predict what feedback we will get next. Over time we then learn to select the correct curve to deliver the feedback we desire. This reinforces this curve in preference to less effective curves.
In the case of climate data it may well turn out that no curve will be discovered that will have predictive power, because the missing piece of the puzzle is part of the “unknown”. That at present we lack the ability to predict climate because we lack the tools that are capable of such a prediction, in much the same way that we lack tools that would allow us to travel to other stars or other galaxies. Maybe some day, but not today.
the cosine term in the formula appear at a glance to give the curve “wiggle” at a frequency similar to the temperature data, which to the eye at least will make the fit “look better”. Whether it actually improves the fit could simply be coincidental.
tonyb says:
May 5, 2013 at 12:09 am
…..
Hi Tony
As Dr. S. ‘use’ to insist TSI is more or less constant.
Henry P thinks Salvador is Dr.S.
Since Salvador = Saviour in Spanish, ossibly Dr.S trying to be Saviour of science from the pseudo-science, and if so I congratulate him. Reading comments on this thread I found by far the most amusing since I came to WUWT.
Back to the CET, I think the CET is inexorably linked to ratio of cold and warm currents around Iceland, where lot of heat is released to the atmosphere
http://www.vukcevic.talktalk.net/CB.htm
this moves polar jet stream around, so you can very nice and winter next to the freezing cold one, e.g. middle of Maunder minimum
CET winterstonyb says:
May 5, 2013 at 12:09 am
1683: 3.8 C
1684: -1.2C Laki volcano erupted
1685: +2.7
1686: +6.3C
……
1963: -0.3
2010: +2.4
There you go, not much of Maunder cooling in the early 1860’s.
🙂
Correction:
in the early 1680’s
My post turned ‘gobbledygook’ (so what’s new?)
So here it is again
tonyb says:
May 5, 2013 at 12:09 am
…..
Hi Tony
As Dr. S. ‘use’ to insist TSI is more or less constant.
Henry P thinks Salvador is Dr.S.
Since Salvador = Saviour in Spanish, possibly Dr.S trying to be Saviour of science from the pseudo-science, and if so I congratulate him. Reading comments on this thread I found by far the most amusing since I came to WUWT.
Back to the CET, I think the CET is inexorably linked to ratio of cold and warm currents around Iceland, where lot of heat is released to the atmosphere
http://www.vukcevic.talktalk.net/CB.htm
this moves polar jet stream around, so you can very nice and winter next to the freezing cold one, e.g. middle of Maunder minimum
CET winters
1683: 3.8 C
1684: -1.2C Laki volcano erupted
1685: +2.7
1686: +6.3C
……
1963: -0.3
2010: +2.4
There you go, not much of Maunder cooling in the early 1680’s.
🙂
Conclusion of this thread:
Not one of the self-appointed thought police on this thread have successfully challenged our freedom to think independently. There’s plenty of evidence on the record now that they’re intent on ignoring and denying aspects of nature that they neither appreciate nor understand:
Multidecadal climate waves perfectly match multidecadal heliosphere waves:
http://tallbloke.files.wordpress.com/2013/03/scd_sst_q.png