The New Sunspot Data … and Satellite Sea Levels

Guest Post by Willis Eschenbach

[UPDATE: Upon reading Dr. Shaviv’s reply to this post, I have withdrawn any mention of “deceptive” from this post. This term was over the top, as it ascribed motive to the authors. I have replaced the term with “misleading”. This is more accurate since it describes the effect of the analysis on the readers, and not the intentions of the authors. Dr. Shaviv and his co-authors have my apologies for my unwarranted accusation of bad faith.]

I see that Dr. Nir Shaviv has a blog post up regarding the recent fixing of problems in the historical sunspot record. He put up several interesting graphs and made several interesting claims, and I wanted to comment on them. To begin with, here’s an overview of his claim about the new sunspot record:

So, what do I think about it [the new sunspot data]? First, I have no idea whether the calibration is correct. They do make a good argument that the SN reconstruction is problematic. Namely, some corrections are probably necessary and there is no reason a priori to think that what they did is invalid. However, their claim about solar activity in general not varying much since the sun came out from the Maunder minimum is wrong. There are other more objective ways to reconstruct solar activity than subjective sunspot counting, and they do show us that solar activity increased over the 20th century. So at most, one can claim that solar activity has various facets, and that the maximum sunspot number is not a good indicator of all of them.

And here is his first graph, comparing the new and old sunspot data:

Figure 1. Dr. Shaviv’s first figure from his blog post, showing the old and new sunspot numbers.

His basic claim is that the changes in historical sunspot numbers don’t make a difference, and that there is still an increase in solar activity over the 20th century. Since both datasets are very similar during the 20th century, the new/old dataset choice makes no difference. However, I wouldn’t say that “solar activity increased over the 20th century”. It increased from 1900 to 1960, and decreased after that.

He then puts up the yearly aa index data, and points out that “The AA index (measured since the middle of the 19th century) clearly shows that the latter part of the 20th century was more active than the latter half of the 19th century.” Well, yes … and the sunspot data says that as well, and again this is true no matter which sunspot dataset is used. So I’m not clear how this adds to his argument.

Next, he examines the beryllium isotope 10Be record. This record is claimed to reflect solar activity. I say it is a very poor proxy for solar activity. I’ve pointed out a variety of problems with this “proxy” in my post here.  Dr. Shaviv says:

The longer 10Be data set reveals that the latter half of the 20th century was more active than any preceding time since the Maunder minimum.

Note that he’s making a brand new claim, that the latter half of the 20th century is more active than anything since 1700. Again, I must point out that both sunspot datasets, new and old, say the exact same thing. However, they differ greatly from the 10Be proxy. In addition, he is also using the 10Be data to tacitly claim a significant increase in solar strength since 1425 or so.

Figure 2. Solar activity proxies, showing concentration of the beryllium isotope 10Be (blue), as well as the sunspots (red). From Dr. Shaviv’s blog post.

So does Figure 2 show that the old sunspot number is correct? Does it show that solar activity has been increasing since 1425, or that the sun has been “particularly active in the latter half of the 20th century”? Well … no. All it shows is that 10Be is a very poor proxy for solar activity. Let me add a few annotation lines to Dr. Shaviv’s graph to illustrate one of the reasons why it’s a bad proxy.

Figure 3. Solar activity proxies as in Figure 2, with added lines connecting the 10Be data to the sunspot record.

I’ve added a horizontal red line at a 10Be concentration of about 1.1 or so. From there, I’ve dropped vertical violet lines to the sunspot data, and then horizontal blue lines over to the sunspot scale.

So … if the marvelous 10Be “solar activity proxy” has an averaged value of 1.1, does that mean that the sunspot level is zero, or twelve, or twenty-four, or thirty-six sunspots per year? I’m sorry, but using 10Be data as a “solar proxy” in that manner doesn’t pass the laugh test.

Dr. Shaviv’s final claim in his blog post is that there is a clear solar effect on the sea level. He says (emphasis mine):

The second point I wanted to write about is a recently published analysis showing that the sun has a large effect on climate, and quantifying it. … Daniel Howard, Henrik Svensmark and I looked at the satellite altimetry data. It is similar to the tide gauge records in that it measures how much heat goes into the ocean by measuring the sea level change (most of the sea level on short time scales is due to thermal expansion). Unsurprisingly, we found that the satellite altimetry showed the same solar-cycle synchronized sea level change as the tide gauge records.

…

You can see in fig. 4 how much the sun and el-Niño can explain a large fraction of the sea level change over yearly to decadal time scales.

In support of this idea that the small approximately 11-year variations in the sun affects the sea level, he posts the following graph:

Figure 4. Graph quoted in Dr. Shaviv’s blog.

Figure 4 is from the paper by Howard, Svensmark, and Shaviv, The solar and Southern Oscillation components in the satellite altimetry data. Their abstract states (emphasis mine):

Abstract With satellite altimetry data accumulating over the past two decades, the mean sea level (MSL) can now be measured to unprecedented accuracy. We search for physical processes which can explain the sea level variations and find that at least 70% of the variance in the annually smoothed detrended altimetry data can be explained as the combined effect of both the solar forcing and the El Nino–Southern Oscillation (ENSO).  

So to be clear, they are talking about studying how solar forcing and ENSO affect sea level. According to their abstract, they model the sea level, using solar forcing and ENSO as their independent variables, to get the purple line in Figure 4 above. And to be fair, Figure 4 shows a pretty good match between model (purple line) and data (blue dots).

Now, in order to get their model results (lovely purple line) to match the sea level data (blue dots), would you care to know how which solar dataset the authors actually used? Because after the big buildup about the sun, and about solar forcing, I was certainly curious which dataset they would choose. Would they look at TSI, total solar irradiance? Of, since Svensmark is a proponent of solar-modulated cosmic rays affecting the climate, would they use the neutron count dataset that measures cosmic rays? Or would it be something else, solar wind or something  … the paper gives the answer.

…

…

…

No solar data. Period.

Not one bit of solar data was used in their study. No aa index data. No TSI (total solar irradiation) data either. No trace of the sunspot data. Not a sign of the cosmic ray information. Nothing about the solar wind. No sign of heliomagnetic information. Rude truth is, no solar data of any kind were harmed in the creation of their model … because no solar data of any kind were used.

Instead, what you see is a seven-tunable-parameter model (purple line), using solely El Nino 3.4 data as the only observational input, that has been fitted to the sea level data (blue dots in Figure 4 above). No solar data was involved at all.

Well, of course when I found that out, I had to go see why they didn’t use the solar data. After all, we have reasonable TSI data and good sunspot data for the period.

Figure 5. Sunspot data (black, at bottom, scale on right)  and satellite TSI (total solar irradiance) data (color) from a succession of satellites. SOURCE

I started by doing what the authors did. I used the detrended Colorado sea level data and the Trenberth El Nino 3.4 data. I’ll call the El Nino 3.4 Index the “ENI” for simplicity.

Next I standardized the datasets, which means I transformed them by subtracting out the mean (average) and dividing by the standard deviation. This gives both datasets a mean of zero and a standard deviation of one. I often do this to get an idea of how well related a couple of datasets might be, when they are in different units. Note that this standardization procedure does not include any tunable parameters. Here’s the result:

Figure 6. A comparison of the standardized detrended monthly Colorado satellite sea level (red) and the monthly El Nino 3.4 data (black)

As you can see, there is a reasonably good overall correlation between the El Nino 3.4 Index (“ENI”, black) and the detrended sea level (black). Now, what we want to determine is whether the solar variation is a possible explanation for the difference between the ENI and the sea level. To do that we need to look at the “residuals”, which means the part if the sea level data that is NOT explained by the ENI. The procedure is to use the ENI values to calculate the expected corresponding sea level values. Then we subtract those fitted sea level values from the actual sea level values, and what is left are the “residuals”. These residuals are the variations in sea level which are not related to the ENI. The residuals are what we hope is explained by solar fluctuations. Here is a graph of the residuals over the period after we subtract out the El Nino 3.4 variations:

Figure 7. Residual sea level after removal of the El Nino variations.

Now, when the authors saw that, they must have been very happy. That sure looks a whole lot like a solar-related variation to me. So what’s not to like?

Well, as also unfortunately happens at times with my own ideas, a beautiful theory founders on a hidden reef of data. Let me overlay the actual solar variations on top of the residual sea level shown in the figure above. I’m showing both the sunspots and the TSI, so you can see how the sunspots are an excellent proxy for TSI.

Figure 8. Residual sea level as in Figure 7 (black), overlaid with the sunspot (blue) and TSI (red) data. This is the new sunspot data, but for this period the new and old data are nearly identical.

I’m sure you can see the problem the authors faced with using actual solar data … the TSI/sunspot records (red/blue) start out well correlated, with both bottoming out in about 1996. But then, the TSI/sunpots inconveniently peak around 2001 and bottom out around 2008-2009. Meanwhile, sea level peaks at around 2006, about five years after the TSI/sunspots, and doesn’t bottom out until 2011 … no bueno for their lovely theory.

So, just what is a poor scientist supposed to do in such a case? Sadly, what Dr. Shaviv and the other authors decided to do was to just add a simple sine wave to the model and claim that it is the “solar term”. Here’s their graph of their so-called “harmonic solar component” …

Figure 9. The “harmonic solar component” used in their model

And here’s how it fits into the previous figure …

Figure 10. As in Figure 8, but overlaid with their “harmonic solar component” (black/yellow). For clarity I have not shown the underlying TSI/sunspot data, only the gaussian averages (red/blue).

How lovely! You see that a sine wave (black/yellow line) is a pretty good fit to the sea level over the period. The only problem is that despite the authors calling it the “harmonic solar component”, there is nothing “solar” about a sine wave at all. Zero. Nada. It has nothing to do with the sun. Instead, it is merely a 12.6 year sinusoidal cycle that has been fitted to match the sea level data.

And why have they chosen a 12.6 year cycle? The study says:

Last, we take P = 12.6 years, which is the duration of the last solar cycle.

However, I note that the actual length of the last solar cycle was 12.4 years (trough-trough, from the data shown above). I also note that the best fit of the simple sine wave to the residual sea level data gives a “harmonic solar component” with a period of 12.61 years. It is possible that is a coincidence.

Conclusions? In no particular order …

• The 10Be beryllium isotope truly sucks as a solar proxy when used as it was in their study.

• Climate science is in a horrible state when you can pass off a bog-simple 12.6 year sine wave as a “harmonic solar component”. The journal, the peer reviewers, and the authors all share responsibility for this highly misleading study. The study is not about “The solar and Southern Oscillation components in the satellite altimetry data” as the title claims. Iit’s not about solar anything. Instead, it is about fitting a sine wave to sea level data. That is false advertising, not science of any sort.

• Finally, a seven-parameter model? Have these folks never heard the story of Von Neumann’s elephant? Obviously not … so I attach it for their edification. In any case, they have the following parameters in their model:

The intercept parameter, which adjusts the model results vertically

The trend parameter, which sets the trend of the model results

Three sine wave parameters (amplitude, phase, and period) for their grandly-named “harmonic solar component”

The ENI index parameter, setting the effect of the ENI

The ENI index integral parameter, as they’ve used both the ENI and the integral of the ENI in the model

Seriously? Seven tunable parameters? Von Neumann weeps …

In any case, summer is here, the day is warm … I’m going walking in the solar forcing.

Best to all,

w.

The Usual: If you disagree with someone, please quote the exact words that they used that you disagree with. I’m tired of being accused of things I never said. Quote the words you object to so we can all understand what you are getting at.

[UPDATE]: In the comments, Brandon Shollenberger says correctly, albeit quite unpleasantly, that I was remiss in not discussing the authors’ stated reason for using a fitted sine wave in place of the real solar data, so let me remedy that oversight. They say:

The above empirical fit assumed a harmonic solar forcing. Although it is only an approximation, it significantly simplifies the analysis. By describing the radiative forcing anomaly as a complex number: ΔFsolar(t) = ΔFsolar exp(−iωt), each component of the sea level can then be described with a complex amplitude. The phase will then describe a lag or lead relative to the solar forcing.

Let me begin by saying that if the real solar data had fit the sea level record, if the actual solar observations had provided strong and unequivocal support for their hypothesis that tiny variations in the sun affect the sea level, they would have used the real data without a qualm or a question. And rightly so, I’d do the same myself, as would you or anyone. Finding such clear evidence of solar influence would be the jewel in the crown, it would be the final piece to the puzzle that folks have searched for over centuries.

But the fact is, as the graphs above clearly show, the solar data does NOT match up with the sea level residuals, not in any sense. And it also doesn’t match up with the sine wave, so their claim that the sine wave is an “approximation” of the solar data doesn’t hold water either.

As a result, we can start with the certain knowledge that they have left out the main explanation for why they didn’t use the solar data—because it didn’t fit the sea level residual for beans. They’ve put a sine wave in their instead and called it a “harmonic solar component”. I call that highly misleading.

However, there is another, larger reason that describing the sine wave “solar” anything is misleading, which is that it “begs the question”. This oft-misused expression means that the speaker assumes what they are trying to demonstrate—in this case, they assume that the cause is the sun, and go forwards with that unproven, untested, and unlikely assumption. They have assumed that the solar variations are the missing link in explaining sea level variations, but that solar-sealevel connection is exactly what the authors are trying to prove! Circular logic at its finest.

So they can’t assume that connection, they have to demonstrate it … and unfortunately, the solar data doesn’t support it.

Let me try to clarify this by example. Suppose I’m studying the effect of gamma rays on marigold growth. And unfortunately for my lovely hypothesis, the gamma ray data is uncorrelated with the marigold growth data.

But I notice a sine wave can be fitted to the marigold growth data quite well, and the sine wave kinda sorta looks a bit like my gamma ray data, and even better, using the sine wave allows me to “significantly simplify the analysis” … sound familiar? So I throw away all of my gamma ray data, and I just use the sine wave in my analysis.

Here’s the question. Given that there is no gamma ray data of any kind in my study, am I justified in calling the sine wave a “harmonic gamma ray component”, and calling the cycle of the sine wave the “gamma ray cycle”? Or is that misleading?

I say it is misleading as hell, because it leads the reader to believe that gamma rays and the “gamma ray cycle” are indeed the cause of variations in marigold growth, when in fact my gamma ray study showed the opposite, little correlation. Here’s the bottom line. Once I pull out the gamma ray data and replace it with a sine wave, I no longer have a gamma ray model. I have a sine wave model. My sine wave model can only tell me if there is an apparent sine wave component to the marigold growth. It can’t tell me anything about gamma rays because there are none in my model.

Note that the same thing is happening in their paper. Despite the fact that the solar cycle is clearly NOT correlated with the sea level data, and despite the fact that there isn’t one scrap of solar data in their study, they call a simple sine wave a “harmonic solar component”, they ascribe causality to “the Sun”, they call what their model shows “solar forcing”, and they talk at length of “solar cycles” in an effort to persuade the reader that they’ve demonstrated their case about the sun causing sea level variations … when in fact, the data shows the opposite, little correlation. Here’s the bottom line. Once they pull out the solar data and replace it with a sine wave, they no longer have a solar model. They have a sine wave model. Their sine wave model can only only tell us if there is an apparent sine wave component to the sea level. It can’t tell us anything about solar variations because there are none in their model.

And that’s why their paper is misleading. Here’s the simple version. If you have to use a sine wave because the solar data doesn’t fit, you can’t claim it is a “harmonic solar component” when that is what you are trying to prove … even if it ”significantly simplifies the analysis”. It may indeed let you simplify the analysis, or it may not, but that doesn’t magically make it a “harmonic solar component”. It’s a fitted sine wave, and claiming otherwise is misleading.

Finally, the authors never seem to have considered the effect of their replacement of actual data with a sine wave. While it is true that you can do analyses using a sine wave that you can’t do using the real data, because the real data doesn’t look like a sine wave … doesn’t it seem to you that the results of said analyses are likely to apply only to the world of the sine wave, and not to the world of the real data?

Freeman Dyson tells the story of Von Neumann’s elephant (emphasis mine)

We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering.We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.

When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our newborn baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice. “There are two ways of doing calculations in theoretical physics”, he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and selfconsistent mathematical formalism. You have neither.” I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a selfconsistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us.With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.”

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?”

I thought for a moment about our cut-off procedures and said, “Four.”

He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

With that, the conversation was over. I thanked Fermi for his time and trouble,and sadly took the next bus back to Ithaca to tell the bad news to the students. Because it was important for the students to have their names on a published paper, we did not abandon our calculations immediately. We finished them and wrote a long paper that was duly published in the Physical Review with all our names on it. Then we dispersed to find other lines of work. I escaped to Berkeley, California, to start a new career in condensed-matter physics.