Guest Post by Willis Eschenbach

In a previous thread here on WUWT, a commenter said that the sunspot-related variations in solar output were shown by Labitzke et al. to affect the stratospheric temperature over the North Pole, viz:

Karin Labitzke cracked that nut. She was the first one to find a correlation between not one but two atmospheric parameters and solar activity. After almost 40 years her findings are still solid, and thanks to her we know that the strength of the polar vortex depends on solar activity modulated by the quasi-biennial oscillation.

And when I went and got the data from the Freie Universität Berlin, I was able to replicate their result. Here’s the relationship Dr. Labitzke et al. found between sunspots and polar stratospheric temperatures:

So … what’s not to like? To lay the groundwork for the answer to that question, let me refer folks to my previous post, Sea Level and Effective N, which discusses the Bonferroni Correction and long-term persistence (LTP).

The Bonferroni Correction is needed when you’ve looked in more than one place or looked more than one time for something unusual. 

For example. Suppose we throw three dice at once and all three of them come up showing fours … that’s a bit suspicious, right? Might even be enough to make you say the dice were loaded. The chance of three 4’s in a single throw of three dice is only about five in a thousand.

But suppose you throw your three dice say a hundred times. Would it be strange or unusual to find three 4’s in one of the throws among them?  Well … no. Actually, with that many tries, you have about a 40% chance of getting three 4’s in there somewhere.

In other words, if you look in enough places or you look enough times, you’ll find all kinds of unusual things happening purely by random chance.

Now in climate science, for something to be considered statistically significant, the odds of it happening by random chance alone have to be less than five in a hundred. Or to put it in the terms commonly used, what is called the “p-value” needs to be less than five hundredths, which is usually written as “p-value < 0.05”.

HOWEVER, and it’s a big however, when you look in more than one place, for something to be significant it needs to have a lower p-value. The Bonferroni Correction says you need to divide the desired p-value (0.05) by the number of places that you’ve looked. So for example, if you look in ten places for some given effect, for the effect to be significant it would have to have a p-value less than 0 05 divided by ten, because ten is the number of places you’ve looked. This means it would have to have a p-value of 0.005 or less to be statistically significant.

So … how many places were examined? To answer that, let me be more specific about what was actually found.

The chart above shows their finding … which is that if you look at the temperature in February, at one of seven different possible sampled levels of the stratosphere, over the North Pole, compared to the January sunspots lagged by one month, during the approximately half of the time when the equatorial stratospheric winds are going west rather than east, the p-value is 0.002.

How many different places have they looked for a relationship? Well, they’ve chosen the temperature of one of twelve months, in one of seven atmospheric levels, with one of three sunspot lag possibilities (0, 1, or 2 months lag), and one of two equatorial stratospheric wind conditions.

That gives 504 different combinations. Heck, even if we leave out the seven levels, that’s still 72 different combinations. So at a very conservative estimate, we’d need to find something with a p-value of 0.05 divided by 72, which is 0.0007 … and the p-value of her finding is about three times that. Not significant.

And this doesn’t even account for the spatial sub-selection. They’re looking just at temperatures over the North Pole, and the area north of the Arctic Circle is only 4% of the planet … which would make the Bonferroni Correction even larger.

That’s the first problem, a very large Bonferroni Correction. The second problem, as I discussed in my post linked to above, is that we have to account for long-term persistence (LTP). After accounting for LTP, the p-value of what is shown in Figure 1 above rises to 0.09 … which is not statistically significant, even without considering the Bonferroni Correction.

To summarize:

• As Labitzke et al. found, February temperatures at 22 kilometres altitude over the North Pole during the time when the equatorial stratospheric winds are blowing to the west are indeed correlated with January sunspots lagged one month.

• The nominal p-value without accounting for LTP or Bonferroni is 0.002, which appears significant.

• However, when you account just for LTP, the p-value rises to 0.09, which is not significant.

• And when you use the Bonferroni Correction to account just for looking in a host of locations and conditions, you’d need a p-value less than about 0.0007 to be statistically significant.

• So accounting for either the LTP or the Bonferroni Correction is enough, all by itself, to establish that the claimed correlation is not statistically significant … and when we account for both LTP and Bonferroni, we see that the results are far, far from being statistically significant.

Unfortunately, the kind of slipshod statistical calculation reflected in the study is far too common in the climate debate, on both sides of the aisle …

ADDENDUM: I was lying in bed last night after writing this and I thought “Wait … what??” Here’s the idea that made me wonder—if you were going to look for some solar-related effect in February, where is the last place on Earth you’d expect to find it?

Yep, you’re right … the last place you’d expect to find a solar effect in February would be the North Polar region, where in February there is absolutely no sun at all … doesn’t make it impossible. Just less probable.

Finally, does this mean that the small sunspot-related solar variations have no effect on the earth? Not at all. As a ham radio operator myself (H44WE), I know for example that sunspots affect the electrical qualities of the ionosphere.

What I have NOT found is any evidence that the small sunspot-related solar variations having any effect down here at the surface. Doesn’t mean it doesn’t exist … just that despite extensive searching I have not found any such evidence.

My best regards to all,

w.

PS—As usual, I request that when you comment, you quote the exact words you are referring to, so that we can all be clear about just who and what you are discussing.