Guest Post by Willis Eschenbach
Well, as often happens I started out in one direction and then I got sidetractored … I wanted to respond to Michele Casati’s claim in the comments of my last post. His claim was that if we include the Maunder Minimum in the 1600’s, it’s clear that volcanoes with a VEI greater or equal to 5 are affected by sunspots. Based on my previous analysis I figured “No way!”, but I thought I should take a look … and as is often the case, I ended up studying something entirely different.
Now, the SIDC monthly sunspot record that I used in my last analysis starts in 1700. Prior to that the only sunspot numbers available are a “reconstruction” by Hoyt and Schatten called the “Group Sunspot Number”, which is the dataset used by Michele. The Hoyt/Schatten Group sunspot data is available here. Now, as Leif Svalgaard has discussed here on WUWT, the SIDC sunspot numbers are in the process of being revised to remove an incorrect offset due to a change in the procedures in 1947. The result will be that the pre-1947 sunspot numbers will be increased by 20%. Figure 1 shows both the unrevised and revised SIDC annual average sunspot numbers, along with the annual average Group Sunspot numbers.
Several things are apparent. First, in the Group sunspot numbers (red) you can see what is called the “Maunder Minimum”, the period where there are no or few sunspots from about 1645 to about 1715 or so.
Next, although the Group sunspot numbers are a very good fit to the SIDC unrevised numbers since about 1880, prior to that the Group sunspot numbers are consistently lower, and sometimes much lower, than the SIDC unrevised numbers.
Next, the early sunspot data in the Group number dataset looks … well … odd …
Seeking to understand what made the early part of the Group sunspot number so odd, I decided to look at the most detailed underlying data. These are the individual daily observations of sunspots. When I did so, there were various strange and interesting aspects. Figure 2 shows the daily data, along with an indication of which days have missing data.
There are some quite bizarre things about this dataset. First, the amount and the location of the missing data. A number of months have no data at all, and many are missing data. Prior to 1643, and also between 1720 and 1800, about two-thirds of the data is missing (65% and 66% missing respectively). During the “Maunder Medium” period between the two light blue areas above, however, only 3% of the data is missing … three percent?
And does anyone but me find it strange that there is very little data prior to 1635 or so, but what data there is shows normal sized sunspot cycles. Then we have a period that exactly coincides with the Maunder Minimum, where we have almost no days of missing data. Finally, from about 1720 on, we again have very little data … but what data there is shows normal sized solar cycles.
Say what? Why is there great data that exactly coincides with the Maunder Minimum? Does anyone find that even vaguely unusual?
Well, I found it very unusual. So I went to take a look at the underlying records. It just kept getting stranger. The numbers of sunspot groups observed is given here on an observer-by-observer basis. Looking through the entries for peculiarosities, I got to 1632, and I found the records of J. Zahn of his observations of sunspot groups made in Nuremberg, Germany. Figure 3 shows the observations of Herr Zahn in 1632:
Figure 3 Individual observer’s record used in the calculation of the Group sunspot number. A day when no observations were made is given the value of -99, and a day with observations made but no sunspots observed is given the value of zero.
I’m sorry, but given the reality of clouds and the fact that Germany is a ways north of the Equator, I’m not believing the idea that in the year 1632 in Germany the sun could possibly be observed in enough detail to count sunspots on every single day of the year. That’s simply not on. Never happened.
And sadly, the 1632 record is far, far from an isolated example. It’s just the first one I came across. Once I looked further I found that there are no less than FORTY-FIVE such observer’s reports claiming valid observations of zero sunspots every single day of the year … and I’m absolutely not buying a single one of them, even if they’re selling at a deep discount.
And when do these bogus records occur? Well, guess what? Forty-four of the forty-five such strange yearly records occur during or just prior to the “Maunder Minimum”, with one final lonesome yearly record of all zeroes in 1810.
I would suspect that what’s happened here is that Herr Zahn used the same symbol for “no observations attempted” and “no sunspots observed”, However, that’s just a guess. More importantly, whatever the reality might be, I’d say that including those impossible records is a major reason for the claims that the Maunder Minimum is so deficient in sunspots.
The next oddity in Figure 1, once I’d wrapped my head around the claim of being able to count sunspots on every day of the year, was the fact that the early data from about 1610 to about 1720 almost all occurs in even intervals of 15 sunspots, at e.g. 15,30, 45 sunspots and so on. Then after that, there is evenly spread data from about 1720-1750.
And then, after 1720, there is a section where once again the data almost all occurs in even intervals … but in that case the intervals appear to be 24 sunspots.
I suspected that this reflected the fact that each group of sunspots is counted as a certain number of individual spots. And upon checking records of the group counts against the Group sunspot number, I find this is the case, and there’s no problem with that … but bizarrely, the number keeps changing. In 1610, each group was counted as 18 sunspots. Then for a number of succeeding years each group was counted as 15 sunspots … until around 1720 when it was changed again, and after that, one sunspot group is counted as 12 individual sunspots. Not 24 sunspots as appears to be the case from Figure 2, but 12 … odd all around.
But wait … there’s more. Here’s the same data in Figure 1, but this time showing the annual Group sunspot numbers (red) and the annual SIDC sunspot numbers.
Now, take a look at the first three sunspot cycles just after 1700 … as you can see, the Group sunspot numbers greatly underestimate the apparent size of the actual cycle. How did this happen?
Well, it’s a curious answer that can be understood by an early year of the data, 1614. In 1614, the annual average is given as 121 sunspots. This can be seen in the red line above in Figure 4.
But when you look at the data for 1614, care to guess how many days of data there are for the entire year?
Well … um … er … not to put too fine a point on it, but there is exactly one day of the year  that has data.
One day’s worth of data , and the sunspot count for that day? Well … 121 sunspots.
Now, to me, that’s bull goose loony. Including a yearly average when there is only one day’s data for the whole year? Sorry, but that’s meaningless.
But wait, it gets stranger. According to the daily data, there’s exactly one day’s worth of data in 1610, with a value of 72 sunspots. That day is in December. But according to the monthly data files, there are TWO months with data in 1610. December  has an average of 72 from the one data point, but the monthly data for February also has an average, in this case zero. So the average for the year is the average of two months, which is 36, and which can be seen as the first data point in the red line in Figure 3 above …
That’s not all. In many years, despite there being no daily data of any kind, we still have both monthly and yearly averages. Here’s a graphic that shows the difference.
You can see the data for 1610 I discussed above, one day’s observation of 72 sunspots and the annual average of 36 sunspots. But the hole keeps getting deeper and deeper. Look, for example, at 1636. According to the daily data, there’s not one single observation for the whole year. But according to the monthly data, EVERY SINGLE MONTH has an average of zero sunspots. And the same is true for 1637, 1641, 1744, 1745, and 1747 as well. In each case there are no observations in the daily data, but there are 12 months of zeros in the monthly data. And this is backed up by the raw observer data files. There are no observers at all listed for  and , no observers and no data … but despite that the monthly and yearly averages claim zero.
A final math note. Rather than average all of the days in the year, their “yearly average” is actual an average of the monthly averages. In some cases this leads to strange results. For example, in some years there are a dozen or so observations in a single month, and only one observation during the entire rest of the year. Obviously, an average of the monthly averages will give a very different answer than averaging the individual data.
I gotta say … these numerous shenanigans with the data make me very suspicious about the whole Group Sunspot Number dataset. When I find entire years where there isn’t a single daily observation, but despite a total lack of data the monthly averages for that year are all zero and the yearly average is also zero … well, that makes me wonder about the entire idea that the “Maunder Minimum” is as extreme as is depicted by the Group Sunspot numbers.
In any case, as I said, I started out to look at Michele’s claim about eruptions in the Maunder and I got blind-slided off the path by the oddities of the Group sunspot number. I couldn’t use either the daily or the monthly Group sunspot numbers to compare with the eruptions, because a number of them didn’t have any sunspot data for either the day or the month. So I used the annual average Group sunspot number to compare to the eruptions. I didn’t splice the Group dataset like Michele did, I dislike spliced datasets, so I figured I’d see things as if the Group dataset were real. To start with, Figure 6 shows the dates of the eruptions overlaid by the daily Group sunspot number …
Looking at just the vertical red lines showing the eruption dates, you can see the “clumpiness” of nature that I’ve remarked on before. However, there doesn’t seem to be any obvious correlation between sunspots and eruptions. So I turned to the histograms showing the distribution of the annual Group sunspot numbers on the dates of the eruptions, and I compared that eruption distribution to the distribution of all of the Group sunspot numbers over the entire period. Figure 7 shows that relationship:
Figure 7. Comparison of the distributions of the sunspot level during the eruptions (gold) and the distribution of all of the Group sunspot levels. Numbers at the top of the gold bins show the count of eruptions in each bin.
Now, Michele’s claim was that most of the eruptions occurred during periods of low Group sunspot numbers … and he’s right. Of the 37 eruptions, about seventy percent of them occur when Group sunspot number is below forty.
But the part he didn’t take into account was that most of the Group sunspot record is made up of periods of low Group sunspot numbers. And of course, with a small dataset of only 37 eruptions, the 98% confidence intervals are very wide. As a result, none of the results are even slightly significant.
So no, I’m afraid that the Group sunspot number, as terrible as it is, still doesn’t show any relationship between sunspots and big eruptions …
Conclusions? Well … my main conclusion is that whenever you see the word “sunspots” in a scientific study, hold tight to your wallet and check the datasets very, very closely. There may indeed have been a Maunder Minimum … but the Group sunspot number dataset is so bad that we can’t conclude anything from it regarding the Maunder or anything else.
My best wishes to everyone,
AS ALWAYS: If you disagree with someone, please quote the exact words you disagree with, so that we can all understand what you are objecting to.