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Then I replied: “Please make a statement to that effect in comments, asking the story be withdrawn.“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)
This also shows that the sun doesn’t repond to volcanoes. Which I guess is no surprise.
Why is there any noise in the predicted paths? I would expect a perfect curve, unless someone has added random noise to an expected SN for 2032.
You can’t tax sunspots.
This looks like a nice example of curve fitting and bad science. FIVE empirically adjusted parameters without any physical explanation to them? I’m particularly baffled by the cosine, if a~148 and you expect the angle in radians! What the hell is that? A minuscule change in parameter a would lead to entirely different results, No surprise that you need give it with a precision of 12 decimal positions. Same for the others. This is not science, it is a joke.
Interesting. The sunspot numbers will affect other solar outputs like magnetic strength. All solar outputs will affect climate on our planet.
A better correlation than a trace gas vital for life.
R.J. Salvador: For future presentations, if you smooth the global surface temperature data with a 5-year (or 61-month) running mean filter, you can minimize the ENSO-related wiggles. This would help to show the agreement between your sunspot model and observations.
Regards
It was the sun wot won it.
What result do you get if you use the first half of the data to estimate all your parameters and the second half as a control?
To see if your reconstruction has any merit, I compared it to BEST, which extends longer back in time, and also other well known long temperature series (e.g. CET, Prague) – and it looks like your reconstruction fails terribly. For instance, both BEST and CET have a peak near 1830 where you have the lowest values.
Please have a look at the advice of Thomas: Try curve-fitting on half of your temperature series and see if your estimated time series for the other half looks anything like the real temperature data.
Data fitting is one thing. Let’s see how the model performs going forward, in competition with other models.
Kurt in Switzerland
This means that a month with a SN of 76 contributes approximately +0.00626C to TA (warming), whereas if the SN=77, it contributes -0.01C (cooling), and if it is SN=78 it contributes +0.01C (warming)…
It varies wildly even in the sign of the contribution without any logical explanation, and does this even for the smallest variations of SN possible. This blog post should be retracted.
Now link those charts to changes in global cloudiness, the latitudinal positions of the climate zones and the degree of zonality / meridionality of the jets.
I would be surprised if there were not to be a clear correlation.
The big disadvantage of this technique is that it does not require a multimillion dollar computer. It will put the climate modelers out of business. This technique also has the problem of not being able to predict the future as the sunspot cycles are not very predictable.
If this models holds up for the next 20 or 30 years, there is still a lot of science required to explain why?
“Nylo says:
May 3, 2013 at 3:52 am
….parameters without any physical explanation to them”
And what was Newton’s physical explanation for the parameter ^2 in the gravitational inverse square law? If he’d been able to generalise to the n-body problem beginning with n=3 in the lab he’d have been laughed at for curve fitting.
“A minuscule change in parameter a would lead to entirely different results, No surprise that you need give it with a precision of 12 decimal positions. Same for the others.”
Sounds like chaotic behaviour to me. All you can do is curve fit since there is no known physical mechanism for predicting sun spots in the hypothesis. Similarly any pretense that climate models will work is itself “not science, it is a joke” if they contain or don’t account for any unknown physical mechanisms like say aerosols, clouds, cosmic rays, solar variations etc.
If the curve fitting shows good correlation over the next 100 years then the author may be onto something.
However I won’t be holding my breath.
steveta_uk says:
May 3, 2013 at 3:43 am
Why is there any noise in the predicted paths? I would expect a perfect curve, unless someone has added random noise to an expected SN for 2032.
Because of the absurd cosine in the formula. It creates that seemingly random noise even if you consider a perfectly smoothed curve in the prediction of the SN. The cosine varies wildly for tiny changes in SN.
Curve fitting is interesting, but curve fitting that requires lots of decimal places to fit data which has only a couple of places of significance is suspect from the word go.
A good model would get the correlation without lots of digits, e.g. Willis’ tropical thunderstorm analyses are classic. The raw data, correctly presented, shows the salient information without lots of curve fitting necessary.
Good try, but a little more science and a little less numeracy.
Espen says: “For instance, both BEST and CET have a peak near 1830 where you have the lowest values.”
While I’m not agreeing with or disagreeing with the model presented by R.J. Salvador, your comment presents two datasets that do not represent global temperatures. In 1830, BEST covers part of Northern Hemisphere land surface air temperatures:
http://oi41.tinypic.com/v773fd.jpg
However, there is the problem of the real 1998 warm peak NOT being higher than the 1938 peak. The current higher 1998 peak is due to bias in the data from UHI, rurual and high altitude site dropout in the 1990s, and unfounded adjustments to the data, accentuating warming. The correlation would still be good with the solar has matching warm peaks and such but the actual temps would be lower. Good job, but I do not like the temp data to pretend that we are warmer now than in the 1930s.
An interesting approach, I fear it might be susceptible to the ‘von Neumann’s elephant’ syndrome diagnosis.
An interesting approach, I fear it might be susceptible to the ‘von Neumann’s elephant’ syndrome diagnosis.
The Parameters for the equation are:
a= 148.425811533409
b= 0.00022670169089817989
c= 1.3299372454954419
e= -0.011857962851469542
f= -0.25878555224841393
R.J. Salvador
Thanks for your interesting correlation.
How well does your method do in taking half the data and hindcasting/forecasting the other half of the series?
e.g. compare with Nicola Scafetta 2012.. See Scafetta’s graph of his predictions since 2000 vs IPCC (bottom page).
May I recommend comparing temperatures with the integral of the solar cycle. See David Stockwell’s solar accumulative theory at Niche Modeling. Note especially the phase lag between temperature and solar forcing.
I look forward to your further developments.
Where does the parameter “f” fit in. you give a value, but it does not appear in your specification.
A few years ago, I too modeled the earth’s land temperature as a function of “sunspots”. I made a very simple physical model that involved earth “heat capacity”, radiation, etc. It had no adjustable parameters that were not physically based. I used raw temperature data from a couple sites that had constant thermometer measurements over the last couple hundred years or more and were less likely to be in “heat islands”.
Result, temperature over the last 250 years tracked sunspots — with an offset. It was as though sunspots up-and-down was like a fire on a gas stove being raised and lowered beneath a pot of water — the temperature of the water had “inertia”.
I did not hypothesize a “mechanism”. Rather, I tentatively-concluded “some natural process moving in concert with sunspot number” seemed to be “strongly influencing” the Earth’s temperature cycles.
Just a way of saying, I agree with the subject post — in principle.
Since then, there have been many articles on WUWT proposing mechanisms.
My results suggest that by 2040 we will be back to where we were in 1950,
http://blogs.24.com/henryp/2013/04/29/the-climate-is-changing/#comments
more or less..
It is of course possible that certain factors, like an incidental extraordinary large shift of cloud formation more towards the equator simultaneous with an extraordinary coverage of large areas with snow, mostly NH, at the end of the cooling period, could trap us, amplifying the cooling due to a particularly low amount of insolation. In 1940/1 there was a particular large amount of snow in Europe.
However, I am counting on mankind using its ingenuity to be able to reverse that trap, should such a situation occur (usually what would happen is that there would be no spring or summer)
btw
can I ask you all here a big favor? Could anyone of you please have a look at the above quoted log?
I want to use this as a communication to all (specifically) religious (e.g Christian & Judaic) media
(which is why I added some biblical references – never mind those, I just added that in as an aside)
but I would prefer to first hear all WUWT opinions about it.
It would be much appreciated if I could have your (honest) opinion about it.
Thanks!
Amazing breakthrough in climatology! How did the world science community miss that one? Handy that the sunspots co-operate with one of our basic tenets of faith; the ‘warming’ of the planet is a mirage based on malplaced weather stations, dodgy averaging over wide open spaces and sloppy science.