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Then I replied: “Please make a statement to that effect in comments, asking the story be withdrawn.“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:
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.
Australian Government Bureau of meteorology
- Current solar cycle data seems to be past the peak (wattsupwiththat.com)
- Paper finds solar influence on climate has been underestimated (oneworldchronicle.com)