Guest Post by Willis Eschenbach
[See also the new Update at the end of the post.]
I see that there is a new paper from China causing a great disturbance in the solar force … as discussed here on WUWT, the claim is that the El Nino Modoki Index, which is an index of sea surface temperatures, is significantly affected by some sunspot-related solar variable.
The first problem with their study is that the sea surface temperature (SST) “data” they have used to establish the relationship is not data as we understand it. It is not observations. It is not measurements of the actual sea surface temperature (SST). It is not stout-hearted men of oak going out and dipping up a bucket of water and inserting a thermometer.
Instead, their sea surface temperature “data” is the output of a climate model, a type called a reanalysis model. This reanalysis model is “tested” and adjusted by comparing it with the output of another climate model. That model is called the GFDL CM2.1.
So, we’re not looking at observed SST. Instead, we’re looking at the output of a couple of climate models.
This means the Chinese have found a correlation between sunspots and climate model output.
Now, having considered the OUTPUT of the climate models, would you care to guess what is used as the INPUT to the climate models?
According to one of the cited underlying documents, the inputs include variations in forcings by greenhouse gases, aerosols, and the “best available estimates of solar radiation changes”.
That means that the authors claim to have found statistically significant evidence of sunspot-related variations in the output of a climate model whose input includes sunspot-related variations … sorry, not impressed even if it were true.
However, there is a much deeper problem, which is that the claim of statistical significance is not true. Their results are not statistically significant, it’s just statistics gone bad. Let me see if I can explain the problems using mostly pictures. I’ll start by clarifying their underlying hypothesis.
Their basic claim is that the small ~11-year variations in the sun affect the sea surface temperature in some unspecified manner and by means of some unspecified solar phenomenon (TOA, solar wind, sunspots, heliomagnetism, etc.). And to their everlasting credit, and unlike far too many climate science authors, they have provided links in the paper to the datasets used in the study.
So, being a data guy, I went and got the ERSST sea surface temperature (SST) data they were using. At least when I got it I thought it was data, and I’m sure some of it is real data … but I digress. They used it, so we’ll use it.
Now, the obvious first step in this is to compare the global sea surface temperature to the sunspot record. Being a graphics-oriented guy, I calculated the correlation between each and every 1°x1° gridcell on the surface of the ocean, and the sunspot record. However, as Figure 1 shows, there is basically no correlation between the sunspots and the global average ERSST sea surface temperature (0.008).
Now, when I saw that graphic, I didn’t much believe it. At this point I’ve looked at this exact kind of map displaying dozens and dozens of different variables—rainfall, SST, atmospheric absorption, cloud reflection, correlation of albedo and temperature, the list goes on and on. As a result, I’ve grown used to the shapes and the forms of real relationships.
And Figure 1 is not much like any of the global climate-related maps I’ve seen. There’s no trace of the usual suspects like the inter-tropical convergence zone (ITCZ) or the typically bi-polar nature of the North Pacific. Instead, it’s just peculiar, too random.
Now as Figure 1 shows, there is basically zero global correlation of sea surface temperature with sunspots. So they are looking at correlation of the sunspots with the sea surface temperatures in the three El Nino Modoki boxes shown in blue and red.
According to the paper the “El Nino Modoki” index is defined as:
In this work, the El Niño Modoki Index (EMI) is defined as (Ashok, Behera, and Rao 2007)
EMI = [SSTA]C − 0.5 × [SSTA]E − 0.5 × [SSTA]W, (1)
where the square bracketed terms [SSTA]C, [SSTA]E, and [SSTA]W represent the area-averaged SST anomalies in the central Pacific region (C (10°S–10°N, 165°E–140°W)), eastern Pacific region (E (15°S–5°N, 110–70°W)), and western Pacific region (W (10°S–20°N, 125–145°E)), respectively.
The problem with Figure 1 is that those individual El Nino Modoki areas don’t particularly match up with the variations in correlation. As mentioned above, the El Nino Modoki index is the red box temperature anomaly minus half of each of the blue box anomalies. So ideally, to see the greatest correlation you’d want the blue boxes in areas of negative correlation and the red box to be in positive correlation … not happening.
In addition, the overall global correlation of SST and sunspots is basically zero (correlation of 0.008). In such a situation we’d expect to find individual areas with small positive or small negative correlation … and due to the high spatial autocorrelation in ocean temperatures, we’d expect the positive and the negative gridcells to be grouped into large areas.
In other words, Figure 1 looks about like what we’d expect if there is no connection between the ~11-year solar variations and the ocean temperatures. So to determine whether the pattern is representative of some real enduring sunspot–>SST relationship that persists over time, I repeated the exercise using only the first half of the data, and then using only the last half of the data. Figures 2 shows the early data up to 1935, and Figure 3 shows the more recent half of the data.
In this earlier half of the dataset, the pattern is very different from that of the full dataset. This is a clear sign we’re not looking at a stable enduring relationship In addition, the El Nino Modoki areas are even more poorly placed than in the full dataset. There’s almost no correlation between the Index and the sunspots during this period. The red box, which was in the hot spot, is now in the cold spot.
Compare those first two with the recent half of the data.
As you might expect by now, the pattern of positive and negative correlations in this one is once again totally different from both the full dataset (Figure 1) and the early data (Figure 2). However, presumably by coincidence, the variations in correlation happen to line up well with the El Modoki areas … blue boxes where there’s negative correlation and the red box where there’s positive correlation.
So which of these time spans have the authors used? Well … none of them. Instead, they’ve picked 1890 as their starting date. Here are the correlations for the data from 1890 to the present
So now, we have a fourth different and distinct pattern of positive and negative correlation. In this case of this particular pattern, the blue and red boxes line up pretty well with the negative and positive sections of the correlation map.
And as a result, the authors of the study found a statistically significant correlation between the El Nino Modoki index and the sunspots. But only if you include a two-year lag from sunspots to El Modoki variations.
And to be fair, my own standard statistical analysis of these results says that they are indeed significant at the 95% level. The usual statistical tests give a p-value of 0.03, which is less than their significance level of 0.05.
However, that usual statistical analysis is wrong for four reasons. First, they’ve looked for results in more than one place, so they need to divide the desired p-value (0.05) by the number of places they looked. Second, they have not allowed for autocorrelation. Third, they have not allowed for the strongly cyclical nature of the sunspot data. Finally, they have not shown that the correlation they’ve demonstrated is stable over time.
Looking in lots of places – the effect of repeated trials
Consider. If you pick up ten coins, flip them all in the air, and every one comes down heads, you’d suspect that the coins were weighted. Why? Because the odds of that happening by chance are less than one in a thousand. So it would be a statistically significant occurrence, with a p-value less than 0.001.
But suppose you flipped that batch of ten coins a thousand times, and you find one flip that ends up with ten heads. Is that still significant? No, because the more trials, the more chance you have of finding something unusual. If you look in lots of places, you’re likely to find odd things … but that does NOT make them statistically significant.
As a result, when you look in more places, your criteria for significance has to become more stringent. The usual correction is called “Bonferroni’s correction”. What you do is to divide the initially required p-value (e.g 0.05) by the number of trials, and that’s the p-value you need to find for it to be significant in that many trials.
So if you look in five places for results, and you desire significance at a p-value of less than 0.05 (the usual standard in climate science), you need to find something with a p-value of less than 0.05 / 5 trials = 0.01. Not so easy.
And therein lies the first problem. We’ve already looked for significance in the whole ocean for the whole time period, and for the whole ocean for the first half and last half of the time period. No joy in any of those. So now, we’re looking at three small boxed-in areas out of the whole ocean, in a period limited to only the time since 1890 … and those three boxes represent just under eight percent of the ocean area.
How many places in time and space have we searched the ocean so far for the elusive solar signal?
Whatever the appropriate Bonferroni correction number might be for this calculation, at this point we’ve established that a “significant” correlation (p-value of 0.03) can be found if we turn our sights to a specially selected 8% of the ocean during a particular time period … you’ll forgive me if I find that less than significant.
The first problem is, no Bonferroni correction, and we’ve already looked a lot of places …
The pernicious effect of autocorrelation
Autocorrelation is a measure how much today is like yesterday. For example, the time of sunrise is constantly changing, but it never changes much. So today is a lot like yesterday in that regard. With air temperature there is less regularity than with sunrise times. But it is rare to have a sweltering hot day followed by a freezing day. So air temperature is less autocorrelated than is sunrise time.
Ocean temperatures, however, are very highly autocorrelated, because the thermal mass of the water means that today is very much like yesterday. And this is a problem for statistics, because autocorrelation increases the uncertainty. How much? Well, in the case of highly autocorrelated datasets, the answer is, a shocking amount.
For example. The El Nino Modoki/sunspot correlation has a p-value of 0.03. But adjusted for autocorrelation (using the method of Koutsoyiannis, see note at end) the p-value goes up to 0.37, a long, long ways from significant.
So the second problem is, no adjustment for autocorrelation.
Statistics of a cyclical signal
There are special problems and special procedures needed when looking at correlations with a signal with a strong varying-length, varying-amplitude cycle … like say sunspots. Again let me explain this with pictures. First, here is the cross-correlation of the post-1890 El Nino Modoki and the sunspots. It shows how well the Index and the sunspots correlate at a variety of lags. In it you can see the best correlation at a two-year lag (El Nino Modoki Index responding two years after the sunspots) that the authors discuss.
So Figure 5 looks convincing, it looks like it represents a real correlation … as far as it goes. And again according to standard statistics it is supposed to be significant. But is it? Let’s expand the boundaries of our same analysis out to say thirty years …
I’m sure that you can see the problems. First off, there’s a better correlation at 13 years than at two years. And there’s a strong negative correlation out eighteen years … warming sun now means cooling eighteen years from now? Say what?
The difficulty is two-fold. First, if there are a couple of bumps or dips of any kind in the data, doing a cross-correlation with a cyclical signal like sunspots will give you alternating correlations as seen above. Second, the result is likely to appear significant at the peaks, without actually being significant.
Let me demonstrate this problem with pseudo-data. Here are nine instances of pseudodata modeled on the actual El Nino Modoki Index, along with the actual El Nino Modoki Index itself.
And here’s what you get when you run a cross-correlation of that selection of pseudodata with the highly cyclical sunspot data:
Not a pretty picture … as you can see, the results of the pseudodata are indistinguishable from those of the real data. We know the pseudodata has no connection with the sun but it still gives strong correlations that appear to be significant. So the third problem is that have not considered the effect of the cyclical nature of the sunspot data.
Duration Over Time
Natural climate-related datasets are maddeningly tantalizing because they appear to contain stable natural cycles, but the dang things have an ugly habit of suddenly appearing and disappearing without warning. After some period where there is no correlation, a correlation with say sunspots will suddenly pop up, and it will last and last, sometimes for as long as five full sunspot cycles … and then it will just vanish. Gone. Perhaps it will be replaced by a cycle with some other longer or shorter period, perhaps not, perhaps we’ll just get random noise for a while before another cycle pops up.
This is visible in the examination of the maps of the early (Figure 2) and late (Figure 3) halves of the data. In each one there are things that seem to be strong, significant correlations. And since each half is eighty years long, you’d sure think that over that time the random fluctuations would have evened out …
Fuggeddaboutit. The two halves of the one single dataset are widely different, the differences have not averaged out. The observational climate datasets tend to be self-similar at all scales. Daily data is no less chaotic and full of appearing and disappearing cycles than is monthly data, which has as many apparent but evanescent cycles as does yearly data, which in turn is no less chaotic than a century or a millennium. At all time scales, apparently real and regular cycles appear and disappear at unpredictable times.
Now, are there long-term, enduring relationships in there? Definitely … but you cannot assume you are looking at such a stable relationship, as the examination of this dataset shows. Even averaged over eighty years the relationships are not stable. Their fourth problem is, they provide no verification of the stability of the purported relationship.
Conclusions:
The paper claims that a climate model that is fed solar variations will reflect those variations in its output. However, whether or not that is the case, the paper has four much more serious issues with their statistical analysis:
• They have not used the Bonferroni correction to adjust for the number of places that they have looked at in order to come up with the 8% of the ocean’s surface that they find “significant”.
• They have not allowed for autocorrelation in their calculations of claimed significance.
• They have not considered the effect of the strongly cyclical nature of the sunspot data on the calculation of significance.
• They have assumed that the signal they found is stable over time, where in fact it is very different in the early and late parts of the same dataset.
The effect of any single one of these statistical errors is enough to invalidate their results. The combined effect of all four errors is … well, words fail me.
Here’s the odd part. Look, I’m no statistician. As with all of my scientific knowledge, I’m entirely self-taught. I never took one single class in statistics. What are the odds of that?
My question is, if a self-tutored man like myself knows about the Bonferroni correction and the need to adjust for autocorrelation … what’s up with these PhD folks all across the climate landscape who apparently never heard of those concepts?
Final Reflections
Many folks seem to misunderstand my position in all of this. I started out a firm believer in the “It’s The Sun” mantra. I thought the sunspot cycle truly did affect wheat prices as Herschel had speculated in the 1700’s. I thought that there were a number of climate phenomena that were affected by something related to the sunspot cycle. I didn’t know whether that “something” was the solar wind, or the changes in total solar insolation, or changes in the far UV, or variations in the heliomagnetic field, but I sincerely believed that there was a clear sun/climate connection related in some manner to the sunspot cycle. I thought that all I had to do to verify that solar connection was look up in the daytime.
And as a result, I thought it would be a piece of cake to find solid scientific evidence to back up what I took to be a fact—that the small ~ 11-year variations in the sun’s output would leave their mark somewhere on the earth’s climate. I had no doubt that was true.
But then I encountered something strange. None of the studies I found had any more solidity than does the Chinese study I just analyzed above. Almost all of them had some or all of the same four huge problems with the statistics exhibited above—no Bonferroni, no correction for autocorrelation, no allowance for strong cycles in the sunspots data, and no investigation of the long-term stability of the claimed relationship.
So I looked and looked, and found nothing. To try to winnow through the literally hundreds of sunspot-related claims, I asked people who thought they had a solid scientific study establishing the connection between the ~ 11-year solar variations and some surface climate variable to send me two links—one link to the study, and a second link, to the actual data used in the study.
Many, perhaps most folks couldn’t seem to grasp the “two links” concept of the request. But it’s essential to have a link to the data as well. I was able to do the above analysis only because I had access to the data that they used. Without that link to the dat there is nothing to analyze. So for people who sent in one link, it went straight to the circular file …
But even when I got two links to some piece or other of research that I was assured was the best, their claims melted like snowflakes in the Sahara when examined closely. Like this study above, it wasn’t just small flaws. It was huge problems, and often the very same four problems I listed above
And as a result, as an honest man I have to say that despite looking for something that I started out truly and completely believing existed, and despite examining a long string of solar-related studies, to date I have not found convincing evidence of such a connection between the ~11-year solar cycles and the climate here at the surface where we live. Now, if the facts change I’ll change my mind, but as it stands I haven’t yet found the requisite evidence.
We had condensing fog last night. When I woke up the deck was soaked and the ground wet. Cold and overcast all day. Where is global warming when I need it?
My best to all,
w.
Please: If you disagree with someone, have the courtesy to quote the exact words you disagree with. This gives all of us clarity on the exact nature of your objection.
Autocorrelation: My discussion of the Koutsoyiannis method for calculating effective N is here.
[Update]: For those of you who still think that the correlation of sunspots with the El Nino Modoki Index is significant, after reading the comments I realized that there was a simple test I could apply. This was to compare the El Nino Modoki Index, not with the sunspots, but with the time-reversed sunspots. I just swapped the full sunspot record end for end, and then I compared that reversed record to the individual gridcells as in Figures 1 to 3.
As you can see, despite the “sunspot” data in the Figure above being meaningless because it is time-reversed, the correlations are very similar to those of the actual sunspots.
Which of course means that their results are as meaningless as those from time-reversed sunspots …
High-Altitude Effects: As an erstwhile ham radio operator (H44WE), I’m well aware that the sunspot cycle affects long-range radio transmission (DXing) by messing with the beautifully named “Heaviside Layer” … what I can’t find is any solid evidence of any corresponding 11-year variation down here on the ground where we live. And yes, I do know that Heaviside is someone’s name, but I still think it’s a great name.
Further Reading: As I said above, I’ve investigated a lot of these claims. Here is a list in chronological order of my previous posts on the subject …
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