Michele Casati: Correlation between solar activity and Arctic ice extent

In Suggestions, Michele has drawn attention to a correlation found by two contributors to the Daltons Minima website in Italy he runs. The following translation is from Google, and is easy to follow. While I think that performing a Pearson correlation between 4th order polynomials is… an interesting technique, 😉  I do think they are onto something here – Note how the Arctic Dipole goes positive at all the solar minima they examine. Bravo Richard and Zambo!

THE NORTH POLE IS MELT AND THE FAULT IS ONLY ……. (PART III)
by Richard and Zambo

In the appointment earlier we learned about this new scheme circulatory, characterized by a dipolar structure and therefore known as pattern Artctic Dipole. This is measured by an index that corresponds to the pressure gradient between the boreal Siberian (centered on the Kara Sea) and the area Canadian-Greenland (DA index.) In short, when there is a strong episode DA +, circulation on the pole (in general on the whole northern hemisphere), undergoes a radical change, with a strong acceleration of the southerly winds of Pacific origin and an increase in northerly winds on the Atlantic-European. This fact leads to a dramatic increase in heat fluxes peaceful directly on the pole, resulting in acceleration of the melting rate of the summer Arctic sea ice. Finally, we have seen the results of experimental studies (PIOMA model in the first place), in which unequivocally demonstrate that the orientation and magnitude of the DA + pattern is the key to understanding and predicting the decline of sea ice in the Arctic basin.

In the third and final part of this paper we try to identify the phenomena that govern the evolution and intensity of the DA pattern, and consequently of Arctic sea ice in summer.
For this purpose, we start by considerations of purely intuitive, based on the following image that shows the progress of the DA index from 1980 to present:

Looking at this graph, in fact, there is one thing that leaps to the eye: the more fundamental change of movement on the pole there was from 2005-2006. This prompts us to think that the phenomenon that regulates the DA pattern (and thus the movement on the pole) has undergone a significant change just from that period. Now, of all the (few) phenomena that can force heavily hemispheric-scale atmospheric circulation (and thus polar), there is one in particular that has suffered a heavy distortion in the reporting period: solar activity. This factor might assume that the main actor in “comedy” is the sun. Now let’s see if we can find evidence to support the hypothesis dictated by intuition.
First of all, again referring to the same graph, we can observe that the upward trend of the DA is started, slowly and gradually, starting from the second half of the 90s. If we now look at the recent history of the sun, we find that an initial drop in activity has been recorded right in the same period, due to a solar cycle (cycle 23) subdued compared to previous:

Other evidence in favor of our thesis are derived from scientific research worldwide. Fact, many studies are conducted by the most authoritative research showing that the low solar activity is able to make, even in the short term, significant changes in circulation patterns most important . Specifically, it was shown that on several occasions the low solar activity brings the dominant figure baric to assume abnormal positions can greatly enhance exchanges between meridians mid and high latitudes. example has been widely observed that, when the sun remains low levels of activity tends to significantly increase the frequency of episodes of major-NAO pattern. Now, for those who have not yet understood, the NAO-pattern is closely correlated with the pattern DA +.
To sum up, the official science has correlated on several occasions with success, the low solar activity with the most famous pattern in favor of boosting trade between the meridians mid and high latitudes (AO-NAO-etc ..). The fact that we have not yet made explicit reference (at least to our knowledge) to link low solar activity-pattern DA +, may lie simply in the fact that precisely the pattern DA +, has been identified only recently (but do not exclude other reasons …..).
On the contrary, although it is proven the ability of anthropogenic emissions (greenhouse gases) to alter global temperatures, there are no relevant studies that have found the cause-effect relationship between greenhouse gas emissions and trends of the most important atmospheric pattern (pattern as AO , NAO, etc. ..). Only the chlorofluorocarbons (CFCs) can influence the movement polar because of their effectiveness in the depletion of stratospheric ozone. In this case, however, it comes to a strengthening of the Polar Vortex (it is therefore the opposite effect). Finally, at this point, assuming by contradiction that there is a weak correlation between the amount of greenhouse gas emissions and “type” of movement on the pole, to justify the overturning circulation between 2004 and 2007, it must be admitted that in ‘ arc of this triennium pollutant emissions are increased by several orders of magnitude.
Until now, therefore, all the “clues” lead one to think that it is precisely the solar activity to drive the evolution of the DA pattern (and therefore of the Arctic sea ice). However, there is still the overwhelming evidence, to eliminate any doubt. While waiting for the “official science” get to provide it, we decided to play in advance. Here we show the results of research we have conducted on precisely the presumed relationship between solar activity and DA pattern.

The study came about almost by accident when, looking at the values ​​assumed in the last 54 years (from 1959 onwards) index DA, we found a possible link with the trend taken by solar activity during this period. So this is a study for statistical aims to assess a potential correlation between the performance of solar activity and the trends of the DA pattern in the reference period (such as value representative of the solar reference was made to the Sunspot Number)
To assess the overall trends of the two phenomena (DA pattern and solar activity), use was made of the methods of polynomial interpolation. Specifically have been used functions interpolating polynomial of the same order (fourth-order polynomials). The following shows the graphs representing the results of the interpolation process:

DA-PATTERN TREND

SOLAR ACTIVITY TREND

Note the perfect correspondence between the red line representing the trend of the DA pattern) and the green line, which instead expresses the trend of solar activity. Obviously, since the two functions are in antiphase (when one increases the other decreases and vice versa), in order to better visualize correspondence, the graph relative to solar activity has been overturned. [Turned upside down]
Although the only visual analysis between the two interpolating give results more comforting that, in order to obtain a certain proof and irrefutable is necessary to proceed with a more refined study, based on the methods of statistical inference. In the present case, to determine the degree of correlation between the two quantities, we proceeded by calculating, for the park available data (reference period), the covariance and thus the index of Pearson correlation.
Briefly, the index of Pearson correlation (or Bravais-Pearson) is used to assess the degree of correlation between two random variables and their consequent relationship of cause and effect, if it is not a spurious correlation (this is not our case). Specifically, given two random variables x and y, the index of Pearson is defined as the ratio between their covariance and the product of standard deviations of two variables:

The index of Pearson can take values ​​between -1 and 1. Of course, negative values ​​indicate an inverse correlation (as in our case), while positive values ​​are obtained by direct correlations. In addition, both values ​​represent extremes of perfect relationships between the variables, while the value 0 is obtained in the absence of relationship. Obviously, in practical cases are not obtained never precisely the extremal values ​​and the value 0. In general, when values ​​are obtained low (close to zero) the correlation is weak, while for values ​​above 0.7 the correlation begins to become strong. Finally, for values ​​greater than 0.9 the correlation is very strong to become perfect when it exceeds the threshold of 0.95 (obviously the exact same is true for negative values ​​of the index).
Now, without too circled around, performing calculations on the data in our park, it turned out one value of the Pearson correlation, which left us pretty much blown away: we’re talking about a value close to -0.97. In other words, we analytically found a perfect correlation between the performance of solar activity and DA pattern.

If you have some ‘of familiarity in the discipline statistics knows that the Pearson correlation coefficient does not measure the intensity of any relationship, but a special relationship: we’re talking about the type of correlation desired by scientists, that the linear relationship between two variables. In other words, when values ​​are obtained very high index of Pearson (as in our case), it means that there is a strong linear relationship between the two variables. At this point, some of the positive feedback and by using the least squares method, we calculated the equation of the line that expresses the link between solar activity and DA index.
In this case, for simplicity of calculation, we performed the study of regular intervals of predetermined width (at the conceptual level it makes no difference):

As can be seen, each time interval of reference is roughly from a maximum of solar cycle to the maximum of the next cycle. For each of the intervals were calculated the average values ​​of the sunspot number and the index FROM:

Not surprisingly, it is found that the experimental points (in the table) are arranged along a straight line:

Using the method of least squares was deduced the analytical equation of the said straight line:
y = ax + b
where:
a = -8.22
b = 38.86

It can be concluded that:

1) the Arctic dipole pattern (DA) is the key to understand and predict the decline of sea ice in the Arctic basin;

2) the average performance of solar activity is perfectly correlated with the performance of the DA pattern, implying that the two phenomena there is a close relation of cause and effect;
3) the relationship is linear;

4) because as I said, from the average of the DA pattern depends on the trend of the summer Arctic sea ice extent, it is concluded that solar activity plays a key role in the modulation of the Arctic sea ice;

5) the present study does not in any way the influence of anthropogenic global warming in the process of melting of Arctic ice, what has been clearly demonstrated is that solar activity, modulating heavily atmospheric circulation on the pole, plays a primary role in the evolution of the extent of Arctic sea ice (with reference to the summer), for the same reasons, it is absolutely undeniable that the collapse of solar activity (Cycle 24) has contributed heavily to the curtailment of Arctic sea ice over the last few 7-8 years.

Finally, in this paper the DA pattern has been used to explain the anomalous trend in Arctic sea ice. However, as mentioned above, the change in this index corresponds to a change of general circulation in both boreal winter and summer, with considerable emphasis on trade meridians and subsequent cooling of the mid-latitudes. Therefore, in the near future, so do predict climate change that will affect the European continent, it will be fundamental understanding of the mechanisms associated with this type of movement as well as its (some) links to solar activity.

Richard and Zambo