Above figure is the least important. I hope it will become clear the red trace is solar magnetics, the sun flips fairly regularly and so does the magnetic field coupled to earth. Evidence earth sees these magnetics is shown…
This is a poster from the AGU Fall Meeting (December 2012, San Francisco, USA), shown by Mikhail V. Vokhmyanin and Dmitri I. Ponyavin from Saint Petersburg State University, Russia. They are describing extending a reconstruction of the solar magnetic field further back into the 19th century to 1844 using terrestrial field measurement data from Helsinki observatory.
In other words from earth surface measurements. Optical solar is a red herring. TSI (Total Solar Irradiance) is neither accurate nor the whole energy story.
Minimal analysis of Hadcrut 4 global
Note: in all these plots example data is Hadcrut 4 global monthly, Y axis assume change in C, not shown for visual simplification. This article is dealing in concepts.
|Figure 1||Figure 2|
Figure 1, published Hadcrut 4 global temperature estimate, figure 2 with an approximation using a least squares fit minimal Fourier decomposition as a function generator.
Fourier decomposition into four components, fixed offset and three pure sines (if Figure 4 looks wrong, is an optical illusion, data provided if you want to check)
|Figure 3||Figure 4|
|Figure 5||Figure 6|
|Now recompose the decomposition, literally a point by point sum of the components.
See Figure 2, same trace.
This is a computer optimised least squares fit to the dataset.
Figure 8 is included but is unlikely to mean anything to general readers but I will try and explain.
Sunspot data, optical change on the sun is visually in ~11 year periods but in fact the underlying solar change is magnetic, by eye a polarity change of sunspots is invisible, can’t be negative light.
The magnetic cycle runs at half the speed, ~22 years. Decoding an encoded “signal”, in this case restoring the upside down sunspot periods can be done by a polarity switch, flip the data upset down or not. (=SIGN(ref to delayed) * data)
Here I am using the ~21 year signal automatically extracted from Hadcrut 4 data [A] as the switch, flipping at the zero crossing of the sine wave, but with a delay, is close to quadrature if that means anything to you.
If this is chance it is astounding it makes a good job of a difficult to do task. Curiously there seems a change 1850 … 1880 where the dataset mismatches the model.
Much more detail investigation is needed.
A). software turnkey, no human override, but to be fair I wrote the code which is stable general usage so you’ll have to trust me there is no cheating. The only guidance was choosing how many decomposition factors, gens=3, the rest is dataset driven.
Cross check for sanity
The Hadcrut 4 monthly data has been low pass filtered at about 17 years. This compares well with the model showing there is no large component which has been omitted. Slight flattening at the ends of the filtered data is present and caused by end correction failing, not serious.
The obvious mismatch 1850 to 1860 is just that, a mismatch, model failure, however, the temperature data back then is very uncertain, curiously also what the sun was doing, circa 1870 is frequently mentioned in both the news and literature over magnetic storms. The infamous Carrington flare was 1859.
As a further check
Figure 10 is a windowed chirp z transform of data.
Residual is spectra after model subtraction.
Filtered shows the effect of the low pass, the accepted by the filter is the plotted.
Fourier model contains the causal of the difference between the blue and red traces, blue trace is about 10x larger signal. The filter has rejected the fast “noise” to the left and accepted everything below the red trace, shown Figure 10.
Model and filtered, r2 = 0.99
More realistically, between the model and original dataset r2 = 0.73, more appropriate but meaning little to general readers RMSD = 0.15 a measure of least squares fit.
There are 1955 data points.
Reported sine periods are approximately 478y, 65y and 21y. See .
These parameters are far more accurately determined than can be done using DFT (Discrete Fourier Transform) even with interpolation, in part because of binning limits. (time resolution is limited by discrete data, values have to be put into “bins” and length of dataset, is ambiguous)
I cannot figure out how to put a figure on the match with solar.
It is reasonable to assume the periodic data is about higher dimensionality in the data as is common with natural data, unless there are definite causals.
Caution is also needed over dataset errors which I suspect are considerable given known severe sampling errors and the usage of simplistic statistical math to attempt automatic correction of known bad data)
Of the numbers only 21y has known candidate causals but the merit of fit is difficult to decide.
- Saros cycle, lunar, 18.6y
- dominant solar system gravitational ~19.5y
- solar magnetic cycle, irregular around 21y
The last is the most likely candidate with both solar and solar/terrestrial linkage. An actual mechanism is unknown regardless of various hypothesis.
A notional 60 year cycle is often reported and does seem to endure to a degree in long history. I am aware of no definite causal (eg. dispute the ephemeris related as aliasing), however this work suggests the two are linked, 3:1 periodic relationship and near 1:1 phase relationship, where 21y has a good phase relationship with solar data.
Circa 500y makes little sense, are reported but without a definite causal. Given the length of data long period factors are dubious. Perhaps notably there is no obvious curve matching human activity, no higher order deviation.
Figure 11 is a detail showing how two model terms add to produce the “no warming” from 2000 to date, in fact a curve. Given the tight data match the following can be done.
Figure 11, removing the long term leaves this curious construct of two terms.
Particularly interesting is the frequency relationship, very close to 3:1 (3.02), stranger still the phase relationship as though the two are tied together.
In nature odd harmonics are unusual, symmetric effects.
A narrow image visually reveals this is indeed a very strange effect for a real dataset which ought to be high H noise.
I find this shocking. The long period does not so relate but is also likely to be wrong. If there was 3 x 65 that would be in the DeVries region or solar repeat, goodness knows.
Worrying is that if the above is true it would have been long seen and clear in many datasets. It isn’t. At the Talkshop some do consider magnetics a likely link, eg. vukcevic, such as yesterday http://tallbloke.wordpress.com/2013/01/23/ex-nasa-scientists-the-science-is-clearly-not-settled/comment-page-1/#comment-41732
Decomposition wrong? No. If anyone knows otherwise please speak up. Also, independent confirmation I have not made mistakes would be nice.
Now I have to take the heat for sticking my neck out.
Figure number 9 onwards corrected (reported by Tallbloke).
First file is source for most plots. Second file has been split off and is live for investigation of solar linkage (source for Figure 8).
Everything is in there but no filter software or dataset analysis software. Spreadsheet is used for convenient and portable post processing.
2. Underlying data http://www.metoffice.gov.uk/hadobs/hadcrut4/
3. Hurst exponent considerably different from 0.5 http://iahs.info/hsj/470/hysj_47_04_0573.pdf
Posted by Tim Channon