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Then I replied: “Please make a statement to that effect in comments, asking the story be withdrawn.“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)
Bart says:
May 3, 2013 at 1:20 pm
son of mulder says:
May 3, 2013 at 4:19 am
“And what was Newton’s physical explanation for the parameter ^2 in the gravitational inverse square law?”
Divergence of the force is zero – empty space is neither a source nor a sink for gravity. That leads ineluctably to a 1/r^2 dependence.
While true Bart, that isn’t very helpful to people with low level math.
More simply, the relationship of an expanding sphere’s surface area to it’s radius is inverse square.
Thus if the medium itself is frictionless to the energy (Bart’s “neither a source nor sink”) you would expect gravity to be inverse square.
And let’s not forget that Newton was wrong.
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.
Note for the few — if any — who are willing to work patiently & carefully on this to arrive at a more lucid level of awareness: I’ve done the diagnostics on this and Salvador has indeed sampled a proxy for SCD (whether accidentally or intentionally).
Sparks says:
May 3, 2013 at 10:41 am
E=MC2 was derived using Newtonian physics before Einstein was even born, by Weiss.
The thought experiment was a train with perfectly reflecting mirrors at both ends of the car, tangential to the direction of travel. It’s 30+ years since I read it so it’s a bit fuzzy, sorry.
Gerrit, Jan Pompe and I did a bit of curve fitting ourselves before he died.
What we tried to do was build a model of our climate as an LCR filter with TSR as input and temperature as output and managed to get a fair correlation. My contribution was small, though I think I suggested a transistor effect for something.
I’ll try to retrieve it for anyone who’s interested. Gmail’s great for the amount of back data you can have.
DaveE.
I’ll just throw this out there; RJ, I don’t know who you are, but you either are presenting this as a legitimate discovery or you are presenting this as bait.
It remains to be seen if the ‘alarmist’ websites point to this article as an example of the gullibility of the people who frequent this site.
Either way; the comments prove that there is a diverse base of knowledgeable people commenting on the articles presented here. And they sniffed it out pretty quick.
If you truly did believe you had found something; congratulations. You did. You learned that curve fitting is an exorcise akin to the reading of tea leaves. I believe Thomas Edison found 10,000 ways NOT to make a light bulb before he figured out how TO make one.
If you wrote this as a way to demonstrate how gullible us rubes are, over here at WUWT, then I suggest you take your findings to the ‘alarmist’ websites, and let them know that not everyone who questions the alarm bell of CAGW is an idiot or a paid shill. You might also point out to them that curve fitting is as far from science as a rain dance is from meteorology. You aren’t the first person to employ the method in climate science, and right now a lot of it passes for GCMs.
Or, you can go back and point out that it got published at all, pretend we didn’t notice the fallacy of your work, and also pretend that you aren’t part of a cult. Climate science is science. The alarmism surrounding climate science right now is not science, and a lot of that alarmism masquerades as science. Real scientists are and will be hurt by this charade. And worse; if real scientists actually do, in some future period, find something that should truly alarm the people living on this planet, it is likely that these charlatans will have cost them their credibility in advance. Instead of saving the planet, these fools could very likely doom the future of mankind.
As I said; if you truly thought you found something, congratulations, you did. If you are a baiter, congratulations, you found something as well. If you are too small to learn from it; I guess your fate was probably decided well before you ever wrote the article.
cos(a*SN) with a=148 is essentially a (bad) pseudorandom number generator. Even small changes in SN (which is measured to 1 decimal place) give large changes in cos(a*SN). So Σcos(a*SN) is a random walk, the shape of which is controlled by a.
Σb*SN^c is monotonic, it provided the trend for the wiggles in Σcos(a*SN).
This is simply a curve fitting exercise, with no physical meaning.
Any idea what John Cook says about this?
Livingston and Penn wrote a paper: “Sunspots may vanish by 2015″ that was posted on this blog. What happens to the global temperature anomaly if sunspots do vanish by 2015?
Mooloo says:
May 3, 2013 at 4:47 pm
“And let’s not forget that Newton was wrong.”
He was not wrong, he was incomplete. In a static situation with no angular momentum, the acceleration with respect to proper time is still Newton’s formula.
David A. Evans says:
May 3, 2013 at 5:04 pm
E = mc^2 follows directly from the postulate that the speed of light is constant in all reference frames, so it is not a curve fit. As Newtonian physics has nothing to say about the invariance of the speed of light, I do not see how it could be derived from it. But, the relationship was derived by Henri Poincare before, or at least contemporaneous with, Einstein. It is the outcome of calculating the energy using the Lorentz Transformation, so Lorentz could have derived it if he had been attuned to do so. Larmor and Fitzgerald probably could have, too.
“What we tried to do was build a model of our climate as an LCR filter with TSR as input and temperature as output and managed to get a fair correlation.”
It sounds reasonable to me. An oscillatory response driven by outside forcing akin to that provided by the progressively strengthening solar cycle is basically what the temperature series looks like to me.
E.M. Smith says
http://wattsupwiththat.com/2013/05/03/sunspot-cycle-and-the-global-temperature-change-anomaly/#comment-1296527
Henry says
I do appreciate your comment and the criticism. As I said : the biblical references were only added in because I want to reach a Christian/Judaic audience. Just ignore that.
I determined in three different ways that the beginning of warming started around 1951 and the cooling part of the cycle started around 1995. This is looking at energy-in.
Average temp. on earth will lag a bit. But, clearly you can see that the trend is negative for the past 12 years:
http://www.woodfortrees.org/plot/hadcrut4gl/from:1987/to:2014/plot/hadcrut4gl/from:2002/to:2014/trend/plot/hadcrut3gl/from:1987/to:2014/plot/hadcrut3gl/from:2002/to:2014/trend/plot/rss/from:1987/to:2013/plot/rss/from:2002/to:2013/trend/plot/hadsst2gl/from:1987/to:2014/plot/hadsst2gl/from:2002/to:2014/trend/plot/hadcrut4gl/from:1987/to:2002/trend/plot/hadcrut3gl/from:1987/to:2002/trend/plot/hadsst2gl/from:1987/to:2002/trend/plot/rss/from:1987/to:2002/trend
From the above simple compilation of linear trends in these 4 major global data sets, you can also see that before 2000 we were still warming and that after 2000 we started cooling….
Obviously this cooling will continue. We are on a 88 year cycle, so to calculate where we are is simple: 2013 – 88 = 1925.
Now I said, and I quote: “So, a natural consequence of global cooling is that at the higher latitudes it will become both cooler and drier.”
I remembered something of the 1930’s dust bowls and looked it up for you. We are not that many years away from this. Check this study:
http://www.ldeo.columbia.edu/res/div/ocp/drought/dust_storms.shtml
To quote from the above study:
“The Dust Bowl drought of the 1930s was one of the worst environmental disasters of the Twentieth Century anywhere in the world. Three million people left their farms on the Great Plains during the drought and half a million migrated to other states, almost all to the West”
end quote
That looks pretty serious to me. Now I never said things will become catastrophic as that, but due to the droughts it could become a bit challenging in the years ahead? Better to know these things beforehand? Remember, there are now so many more people looking for food than we had in the 1930’s.
As far as this post is concerned, I am disgusted that “R J Salvadore” does not even bother to show up to defend his work. I think people like that should not be allowed to post here at all. I have to conclude that he is just a phantom writer trying to confuse issues for us and trying to lead us in the wrong directions. We all know who he is, don’t we? My conclusion was that he suffers from a multi personality disorder. (in the olden days they would say:possessed by the devil. In this case we would say in dutch: he has a “plaaggeest”. (teasing spirit)
Forget about all this nonsense in this post. To fish out where we are with the sun, you only have to look at direct the measurements, like average daily data from maximum temperatures, converted to yearly average data. I have done it all for you. You can just repeat it.
http://blogs.24.com/henryp/2013/02/21/henrys-pool-tables-on-global-warmingcooling/
Henry said
you only have to look at direct the measurements, like average daily data from maximum temperatures, converted to yearly average data.
Henry says
sorry that should have been:
you only have to look at direct measurements, like daily data from maximum temperatures, converted to monthly average data, converted to yearly average data.
Re: Dr. Svalgaard
Data on his charts
http://www.leif.org/research/TSI-SORCE-Latest.png
http://www.leif.org/research/TSI-SORCE-2008-now.png
use to get updated daily with no more than day or two delay
It looks that the last updates was for 10th of April (jugging by F10.7 flux)
There is also a paper
http://www.leif.org/research/Synoptic-Observations.ppt dated 27 April
I hope that Dr. S. is well, his absence from the solar threads is very much missed.
five parameter and an arbitrary choice of mathematical functions…
Sorry to say it demonstrate nothing. And you knew from the beginning that a crude sunspot number has followed global mean temperature in the past…
But you can do several test..first truncate the data find out new parameters and see predictions
Try to do the same analysis using something different from sunspot number…and so on…
Or wait 20 years to see if predictions are still valid!!
some other did the same job it with fourier analysis, the principle is the same..if there is no physics it is just fitting curves..somethings you can always do if you use enough parameters.
vukcevic:
At May 4, 2013 at 1:35 am you say
I write to draw attention to your “hope”.
A few days ago I made a WUWT post which noted his absence, said he is a valued member of the ‘WUWT community’ and asked if anybody knew he is OK. Nobody has responded.
I again ask if anybody can confirm that Lief Svalgaard is alright.
The lack of news is becoming concerning to you, to me, and feel sure to many others in the ‘WUWT community’.
Richard
I did a much cruder version of this correlation in 1987 when I was working in ag chemical research. I got a similar correlation coefficient. I found that the correlation improved dramatically when the sunspot count was correlated with the temperature three years later, my reasoning being that any effect would be reflected after one atmospheric mixing. That sound reasonable?
henry@richard, vukcevic
come on you guys.
You honestly had not figured out yet that R.J. Salvadore is Dr. S?
He is a real Jeckyl and Hyde,
so he is hiding
“Bart says:
May 3, 2013 at 1:20 pm
Divergence of the force is zero – empty space is neither a source nor a sink for gravity. That leads ineluctably to a 1/r^2 dependence.”
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.
It does not physically explain how the force is transferred instantaneously from one mass to another, so it’s no different in principle to what R.J. Salvador is doing ie see a pattern but not know the possible physical mechanism. But it is quite reasonable to create a scientific hypothesis in this way, test it and move on as appropriate.
Henry
No sane person working in any kind of science would quote parameters withs ao many decimal places
a= 148.425811533409
b= 0.00022670169089817989
c= 1.3299372454954419
e= -0.011857962851469542
f= -0.25878555224841393
unless it is a send-up.
E=MC2 is just curve fitting!
…speaks ignorance so abysmal that it would take a very long rope to even reach down to offer you a leg up.
Indeed, understanding the difference between an amazingly well-founded, empirically supported theory and “just curve fitting” is precisely what the debate is about. Nylo, I agree with everything you are saying (again). I have to admit that I am a bit surprised that they were able to find a way of scaling the integral of a cosine of what amounts to a cosine squared to fit anything at all (especially with a large multiplier) but I’ll take your word for it. Either way, the term is clearly totally bullshit.
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. Build a neural net. At least then your basis is generalized nonlinear function approximator capable of resolving nontrivial multivariate correlations.
Anything else is kid’s stuff. Henry P fits a second order polynomial to predict the future. This paper fits a bizarre, meaningless function with meaningless parameters. Neural nets yield meaningless fits in the specific sense that the weights cannot be connected back to anything causal, but damn! They can actually sometimes manage some pretty damn good predictions of highly multivariate, nonlinear probability distributions in predictive models. The only way one can — sometimes — beat them (and the other related Bayesian methods) is with a really, really solid, physically motivated model fit/trained by an expert statistician.
Of course, building a predictive NN requires following rigorous rules. One has to regulate the power of the (potentially vastly overcomplete) representation by limiting the number of hidden layer neurons to the minimum that can capture the data without overtraining. One has to split available input data in to training and trial, to verify that the trained net has at least some plausible predictive power on data outside the training set. And in the end, one is still susceptible to black swan syndrome and/or omitted variable syndrome (and to simple errors or noise in the building process).
Building good predictive models is not a game for the amateur. Seriously. Given a choice between ordinary physics and high end statistics, it isn’t clear which one is more difficult. Statistical mechanics is one of the most difficult subjects in the world, and climate science is technically, arguably, THE most difficult subdiscipline of statistical mechanics. So give this sort of thing a rest, is my advice. Post hoc ergo propter hoc is a logical fallacy in the first place, and what value it has is easily abused.
rgb
rgb says
Henry P fits a second order polynomial to predict the future.
Henry says
No I did not.
I refer to the 4 results for the speed of the drop in daily maximum temperatures (average, global) on the bottom of the first table here:
http://blogs.24.com/henryp/2013/02/21/henrys-pool-tables-on-global-warmingcooling/
When you set the speed of warming/cooling out against time, indeed, the binomial for the drop in the speed of daily maximum temperatures, had a correlation of 0.997
For any statistician that is a dream come true (on his random sample)
But I figured in the end that would drop us into an ice age quite quickly…..
That shows you: even with very high correlation you are still not save with a curve fit of 99.7% correlation…apparently….
In the end I found that a sine wave would also be a good fit and if you put the wavelength at around 88 years, the fit looks reasonably good, though I did not do a correlation. (don’t know how to to do that if Excel does not know that either)
http://blogs.24.com/henryp/2012/10/02/best-sine-wave-fit-for-the-drop-in-global-maximum-temperatures/
Anyway, either way, I also used two other methods to determine the dates of ca. 1951 and 1995 as turning points on my a-c wave. Which is making me confident in estimating that the next turning point (from cooling to warming) will be around 2040, give or take a few years (of my error)
” vukcevic says:
May 4, 2013 at 4:47 am
Henry
No sane person working in any kind of science would quote parameters withs ao many decimal places”
What about the fine structure constant 7.2973525698(24)×10−3 ?
http://en.wikipedia.org/wiki/Fine-structure_constant
Thanks for the comments. Let me address some of the objections being made to the correlation.
The main one is that the correlation has no physical significance. I disagree. The correlation’s two terms each measure a different physical phenomena and its accumulated effect on temperature over time.
The b*SN^C term measures the accumulated effect of the total solar cycle over time. It has been proposed by others that this involves cloud formation through a mechanism involving blocking cosmic rays.
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. The mechanism that ties it to a temperature change on earth I suspect is also related to a cloud forming mechanism. Some have suggested that this term is just an alias for a more complex set of curves. That maybe true. I chose to stay with the simplest equation that matched the data.
Some have suggested that the equation is only valid after a number of summations. The least squares test is evaluated over the 1598 summation equations of the data points. The equation is as valid or invalid for the first data point in January of 1880 as the last data point in February of 2013.
And I apologize for the typo in listing the parameters. ( e is d and f is e)
I think quite to the opposite of some here. I think the post by RJ Salvador is intended to prove to the Alarmists that this site is not full of a bunch of dunces who just jump on anything that goes against CAGW.
As illustrated by the responses, the WUWT community does not just accept any old thing that comes down the pipe. The WUWT community is as likely to tear apart reports that agree with their position that CO2 is not the culprit, as they are at tearing apart the crap that is passed off as science that claims CO2 is the driver of climate change.
All well and good but what I’d like to see is someone predict the next Heinrich Event which will probably kick us firmly into the next glaciation. My guess is 4000 years.
vukcevic says
No sane person working in any kind of science would quote parameters with so many decimal places
henry @vukcevic,
I am not saying he is insane. I do think he got very tired at beating us down until now, (recently?) he must have come to a conversion (to now being a full blown skeptic).
Perhaps he has now realized that we are going to cool down in the next 3 decades and that no amount of carbon dioxide in the air will stop that from happening. But, now, he does not want to come out of the closet, yet, so to speak. He is too afraid.. He is is feeling guilt…. He needs our help. Let us quote him this verse from the bible:
When I kept things to myself,
I felt weak deep inside me. I moaned all day long.
My strength was gone as in the summer heat
Then I confessed my sins to you
I did not hide my guilt
I said: I will confess my sins to the Lord
And you forgave my guilt.