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Then I replied: “Please make a statement to that effect in comments, asking the story be withdrawn.“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)
Here are 3 suggestions for Janice Moore’s supposed “science giants”:
1. Show that Salvador’s method can be used to make the CO2 record (and any other record whatsoever) fit anything and everything.
2. Prove beyond all shadow of a doubt that http://img13.imageshack.us/img13/5691/911k.gif does not illustrate the 9 year asymmetry and 11 year volatility cycles underpinning the 107 year to 108 year solar activity cycle.
3. Attempt to prove that neural networks can be used to isolate the simple rules governing the phase reversals illustrated here http://img13.imageshack.us/img13/5691/911k.gif .
Unfortunately, Paul Vaughan’s communication skills are a major impediment to ability to get across his message. However, Paul is trying his best to get across a very important message about the synchronization between the cycles that he observes in the Helios-sphere and the cycles that he observes here in the Earth’s climate.
He is a deep thinker with considerable skills in interpreting and analyzing data. If you are willing to spend the time investigating what he trying to say you will be greatly rewarded. With Paul, patience is a virtue.
Mr. Paul Vaughan.
I heard you when you observed that the correlation seem to pick out a crude alias for a shifting harmonic either “brilliantly or haphazardly”. It wasn’t brilliance I can a sure you.
And I also heard you when you pointed to the data set that might explain why the correlation worked. I asked to withdraw the story because the correlation equation wasn’t stable not because I didn’t believe in the harmonic. The one cosine term in the correlation is aliasing for other harmonics. Right now I think you may have identified which ones.
Thank you!
Mr. Salvador, I’m a blue collar working man severely short on free time. To keep things simple, I hard-manage the effort I put into communications on the Pareto Principle. My aim is only to get through to a few key individuals. Your article triggered a series of revelations. The concert of decadal solar heliographic N+S, |N-S|, & N-S (where N = north & S = south) is coherent with multidecadal timescale July & August ENSO and year-round North Pacific Index (NPI). It’s remarkable how on-the-money Bob Tisdale has been with key elements of his narrative, which dovetail seamlessly. As time permits, I will share further illustrations. Some of the details will be best shared via Tallbloke’s Talkshop. I hope you will join us for discussions there.
Dr. Wilson, thanks sincerely for dropping by.
Best Regards.
Re Ian Wilson, the cosine in the formula is NOT helpful to identify the cyclicity of the SSN in time. There’s no way that formula will extract any information regarding the periodicity of the SSN just because of putting a cosine there in the way that it has been done. Any cycles that the SSN signal has will be analysed by doing the FFT of the SSN(t) itself. After you do that, you can do the FFT of T(t) and then you can see if there is any resemblance between the two, if nature has cycles in the variation of the global temperature that match similar cycles in the SSN.
Re Paul Vaughan: I’m showing you several plots using the same SSN data and the same formula, only changing parameter “a”. in each of them. As you can see they offer very different results. I certainly could keep playing with “a” until I find a fit to virtually anything.
http://www.elsideron.com/wuwt_ssn_study/Different_a_values.PNG
As you can see, I can make it show temperatures going down all the way until 1950 and then steadily rising to match current temperatures, with a=148.6. Or I can make it reach the same current temperatures but rising steadily until 1964 and then keeping pretty constant till present, with a=148. Or I can create runaway warming with a=151.5. Or I can create little variation of temperature during the whole 20th century by choosing a=147.7. Salvador happened to find a value of “a” that by pure chance made the graphic match the global temperatures real evolution. Had temperature evolution been radically different, he would also have been able to find another value of “a” to obtain the match and claim a direct relationship with the SSN, despite SSN data been the same. And although all 5 different graphics plotted with different a values have big differences with the line in green color, the only difference with it is the cosine term. The green graphic is obtained by just removing the cosine. Any differences with it are introduced by the cosine.
I hope this settles the issue of whether or not Salvador formula can be used to fit an elephant.
Henry@Nylo
My maths is not that good, but I figure you got it right.
Could I ask you for a big favor?
George E Smith did not react to my post here:
http://wattsupwiththat.com/2013/05/03/sunspot-cycle-and-the-global-temperature-change-anomaly/#comment-1298548
I wonder if I could ask you to try and do that plot for the drop in global maximum temps. in K/yr
against time….I just want to check with someone that I did it right. What would you say is the best fit for those particular 4 data? ( I proposed a sine wave with wavelength 88 years)
Mr.Vaughan, It was almost too easy. I did some preliminary analyzes of the data you suggested and I am getting results with a 3 wave form very similar to the ones in the image you posted. The R^2 is 0.77 and the change frequencies are very long in years. It’s like the signal from three skewed Gaussian distributions moving in time along a wave. A two wave model may also explain the data. I am not a solar scientist and like you I have another life, so this will take some time.
Your insight seems to be dead on. Kudos to you!!
Regards,
R J Salvador
The Real issue…
I advise sensible, sober parties to duly appreciate and understand nature:
http://img268.imageshack.us/img268/8272/sjev911.png
http://tallbloke.files.wordpress.com/2013/03/scd_sst_q.png
_______
Mr. Salvador,
Tallbloke runs a clean, pleasant shop. He appreciates and understands the value of free thinking, ambiance, & good harmony. I do hope you will consider joining us for cordial, comfortably-paced discussions at The Talkshop in the weeks & months ahead.
http://tallbloke.wordpress.com/
Thanks again for your stimulating contribution.
Henry said previously
http://wattsupwiththat.com/2013/05/03/sunspot-cycle-and-the-global-temperature-change-anomaly/#comment-1298548
the silence is deafening
Anyway,
could I ask anyone here, if you think what I say below is correct or incorrect:
I would think that sun spots, as they appear dark on the sun, are cooler areas. So less sunspots means more activity of the sun in the high peak area (<0.5 um)
so I say:
less sunspots, equals more E-UV, equals more ozone/ peroxides/ nitrous oxides lying TOA, equals more back radiation to space, equals less energy (F-UV) going into the oceans, equals global cooling, eventually.
I am right, right?
@ur momisugly HenryP
I suggest you see the cautionary note I’ve volunteered in appendix E here to help correct widespread misconceptions of solar-ozone phase relations.
Sensible, sober parties wishing to become more deeply & fully aware of the exact nature of Nylo’s fundamentally severe & strictly intractable misunderstanding &/or misrepresentation of Salvador’s relationship are directed here:
Donner, R.; & Thiel, M. (2007). Scale-resolved phase coherence analysis of hemispheric sunspot activity: a new look at the north-south asymmetry. Astronomy & Astrophysics 475, L33-L36. doi: 10.1051/0004-6361:20078672.
http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/abs/2007/45/aa8672-07/aa8672-07.html
Patient, careful explorers: A trivial adjustment of wavelet parameters (substantially widen the support span without changing resolution, grain, & extent) will precisely stabilize Donner & Thiel’s phase estimates.
Regards
Henry@Paul
I think you did not get it. Trenberth’s missing energy is in the peroxides and nitric oxides TOA that he simply forgot (there are no data!!!)
To put all your terrible geometric maths into words, is quite simple:
There is a window TOA that gets opened and shut every so often. Once it gets closed a bit, on a type of sine wave scale, ca. 44 years, progressively getting closed, the differential T between the equator and the poles increases, causing more condensation at lower latitudes and less at higher latitudes. As the temperature differential between the poles and equator grows larger due to the cooling from the top, very likely something will also change on earth. Predictably, there would be a small (?) shift of cloud formation more towards the equator, on average. At the equator insolation is 684 W/m2 whereas on average it is 342 W/m2. So, if there are more clouds in and around the equator, this will amplify the cooling effect due to less direct natural insolation of earth (clouds deflect a lot of radiation). Furthermore, assuming equal amounts of water vapour available in the air, less clouds and precipitation will be available for spreading to higher latitudes. So, a natural consequence of global cooling is that at the higher latitudes it will become both cooler and drier.
As the people in Anchorage (Alaska) have noted,
http://www.adn.com/2012/07/13/2541345/its-the-coldest-july-on-record.html
the cold weather in 2012 was so bad there that they did not get much of any harvests. And it seems NOBODY is telling the farmers there that it is not going to get any better.
The mechanism that is in place, actually prevents runaway global warming and without it, I suspect, there would be little or no weather (rain!!)
That what opens and closes the window is most probably caused by the alignment of planets as they circle around the sun. Their weight somehow seems to affect the inside of the sun..
If true, that means that if one of our planets were not there ( or if it is put out of orbit) life as we know it, would (will) not exist. It is part of creation. We have an awesome God.
Paul Vaughan…… see you at TallBloke.
@ur momisugly HenryP (May 10, 2013 at 7:44 am)
I’m more than content to leave detailed narrative development to you & others, but occasionally (certainly not always since usually I don’t have time) I may let you know if your story mismatches observations. (For example, for the past century at least you have to say 54 years, not 44 years (even though I cannot with the short record available prove it’s not 44 years in long run central limit) due to the way the 9 year asymmetry phase-flipped (via ephemeral 13.5 year wave) when 11 year solar activity was weak and SCD was high (perhaps has something to do with sufficient power being available for resonant entrainment to be maintained and equivalently wobbles being “free” to temporarily phase drift when power falls below some threshold). Good luck trying to build a narrative on that which impatient people can follow —– the numbers & pictures on the other hand make it dead simple for anyone patient & thorough enough to look with sufficient care (see 1897.5 & 2005.5 — and be aware that I simplified the labeling on this [ http://img268.imageshack.us/img268/8272/sjev911.png ] graph, in part to save time & in part to make sure people would have to do the calculations themselves to see which curves are negatives and which are rotated a 1/4 cycle inside the constraining envelopes (where rates &/or threshold-crossings, rather than min & max are key).) I too am concerned about the farmers in Alaska. May God bless you Henry — and once again: I deeply appreciate your due appreciation of nature.
Thanks Paul. I do appreciate your last comment.\ God bless you for that.
As I said, my data set for incoming energy suggests a 88 years wave, split half between warming and cooling. If you think it could be a different time, tell me and I will check my data for that wave length?
What earth does with incoming energy + what Earth produces itself (e.g. volcanic activity) is a different matter, which makes exact prediction a bit difficult, because there could be some lag either way.
However, whichever way you look at things, global cooling has started and it will not stop until ca. 2040.
To check where we are: 2013-88= 1925.
We are about 7 years (give or take a few years) away from the Dust Bowl drought 1932-1939
i.e. we have
7 FAT years left and 7 LEAN years coming
Note the change in the direction of wind mentioned in Gen. 41 vs. 23 & 27 to east. It seems a change in the direction of wind was also been mentioned in the annals on the Dust Bowl drought….. …
Henry, the Dust Bowl Drought has been a strong motivator of my explorations. I probably never would have developed the strong interest I have in solar-terrestrial relations were it not for ~1920-1940 patterns in local precipitation records — see here:
Solar-Terrestrial Resonance, Climate Shifts, & the Chandler Wobble Phase Reversal
While doing my M.Sc. thesis I noticed those patterns and found a clear multivariate framework of 11 year & 6.4 year statistical summaries. I looked to the mainstream climate science literature for an explanation, found nothing substantive, and so began the tedious task of taking personal responsibility for investigating further despite having insufficient time & resources.
This landmark paper provided a crucial puzzle piece:
Le Mouël, J.-L.; Blanter, E.; Shnirman, M.; & Courtillot, V. (2010). Solar forcing of the semi-annual variation of length-of-day. Geophysical Research Letters 37, L15307. doi:10.1029/2010GL043185.
With that piece of information, several barriers dissolved. I became more lucidly aware of exactly which statistical properties of natural data were varying on the 11 & 12.8 year frameworks and exactly what (ENSO) was causing conventional methods to overlook the framework:
Solar-Terrestrial Volatility Weaves
Jean Dickey of NASA JPL had already been there:
Dickey, J.O.; & Keppenne, C.L. (1997). Interannual length-of-day variations and the ENSO phenomenon: insights via singular spectral analysis.
http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/22759/1/97-1286.pdf
My respect for Jean is deep. She doesn’t say all she knows.
Recently I noticed this coherence:
http://tallbloke.wordpress.com/2013/04/18/paul-vaughan-comparing-jupiter-earth-venus-alignment-cycles-with-variation-in-the-solar-rotation-period/
An earlier comment by Ulric Lyons had caused me to consider that these hierarchically-nested patterns are generalizable & extensible. (Some of the details are best left for future discussions at The Talkshop.)
So what caused the Chandler wobble phase reversal and the Dust Bowl?
I’ll share some new graphs to provoke better awareness of the importance of Mursula & Zieger (2001):
http://img267.imageshack.us/img267/8476/rrankcmz.png
http://img829.imageshack.us/img829/2836/volcano911.png
volcanic indices in italics
Cy = Chandler wobble y phase
SOST = southern ocean surface temperature
ISW = integral of solar wind
To within round-off error, there’s also this possibility of long-run coherence on the 6.4 year framework, so the responsible thing to do is report it:
~60 Year Cycle of ~27 Day Terracentric Solar Rotation
That’s enough for today.
Please join us at Tallbloke’s where I will go into much more detail in the weeks & months ahead.
Best Regards
Henry@Paul
I find the no. of parameters that you bring in confusing.
I only looked at maxima because I think, eventually, it, alone, determines incoming energy!.
Including my own results, I find 4 sources indicating 1950 or 1951 was the start of warming (increasing maxima) and 1995 was the start of cooling.(decreasing maximum temps.)
http://blogs.24.com/henryp/2013/04/29/the-climate-is-changing/
William Arnold missed the 1995 date by only 5 years
(he predicted 1990 for maximum flooding of the Nile)
On that scale I predict the start of the droughts similar to 1932-1939 (.>40 degrees latitude) to start somewhere from 2019-2024