Sunspots and Sea Surface Temperature

Guest Post by Willis Eschenbach

I thought I was done with sunspots … but as the well-known climate scientist Michael Corleone once remarked, “Just when I thought I was out … they pull me back in”.  In this case Marcel Crok, the well-known Dutch climate writer, asked me if I’d seen the paper from Nir Shaviv called “Using the Oceans as a Calorimeter to Quantify the Solar Radiative Forcing”, available here. Dr. Shaviv’s paper claims that both the ocean heat content and the ocean sea surface temperature (SST) vary in step with the ~11 year solar cycle. Although it’s not clear what “we” means when he uses it, he says: “We find that the total radiative forcing associated with solar cycles variations is about 5 to 7 times larger than just those associated with the TSI variations, thus implying the necessary existence of an amplification mechanism, though without pointing to which one.” Since the ocean heat content data is both spotty and incomplete, I looked to see if the much more extensive SST data actually showed signs of the claimed solar-related variation.

To start with, here’s what Shaviv2008 says about the treatment of the data:

Before deriving the global heat flux from the observed ocean heat content, it is worth while to study in more detail the different data sets we used, and in particular, to better understand their limitations. Since we wish to compare them to each other, we begin by creating comparable data sets, with the same resolution and time range. Thus, we down sample higher resolution data into one year bins and truncate all data sets to the range of 1955 to 2003.

I assume the 1955 start of their data is because the ocean heat content data starts in 1955. Their study uses the HadISST dataset, the “Ice and Sea Surface Temperature” data, so I went to the marvelous KNMI site and got that data to compare to the sunspot data. Here are the untruncated versions of the SIDC sunspot and the HadISST sea surface temperature data.

Figure 1. Sunspot numbers (upper panel) and sea surface temperatures (lower panel).

So … is there a solar component to the SST data? Well, looking at Figure 1, for starters we can say that if there is a solar component to SST, it’s pretty small. How small? Well, for that we need the math. I often start with a cross-correlation. A cross-correlation looks not only at how well correlated two datasets might be. It also shows how well correlated the two datasets are with a lag between the two. Figure 2 shows the cross-correlation between the sunspots and the SST:

Figure 2. Cross-correlation, sunspots and sea surface temperatures. Note that they are not significant at any lag, and that’s without accounting for autocorrelation.

So … I’m not seeing anything significant in the cross-correlation over full overlap of the two datasets, which is the period 1870-2013. However, they haven’t used the full dataset, only the part from 1955 to 2003. That’s only 49 years … and right then I start getting nervous. Remember, we’re looking for an 11-year cycle. So results from that particular half-century of data only represent three complete solar cycles, and that’s skinny … but in any case, here’s cross-correlation on the truncated datasets 1955-2003:

Figure 3. Cross-correlation, truncated sunspots and sea surface temperatures 1955-2003. Note that while they are larger than for the full dataset, they are still not significant at any lag, and that’s without accounting for autocorrelation.

Well, I can see how if all you looked at was the shortened datasets you might believe that there is a correlation between SST and sunspots. Figure 3 at least shows a positive correlation with no lag, one which is almost statistically significant if you ignore autocorrelation.

But remember, in the cross-correlation of the complete dataset shown back in Figure 2, the no-lag correlation is … well … zero. The apparent correlation shown in the half-century dataset disappears entirely when we look at the full 140-year dataset.

This highlights a huge recurring problem with analyzing natural datasets and looking for regular cycles. Regular cycles which are apparently real appear, last for a half century or even a century, and then disappear for a century …

Now, in Shaviv2008, the author suggests a way around this conundrum, viz:

Another way of visualizing the results, is to fold the data over the 11-year solar cycle and average. This reduces the relative contribution of sources uncorrelated with the solar activity as they will tend to average out (whether they are real or noise).

In support of this claim, he shows the following figure:

Figure 4. This shows Figure 5 from the Shaviv2008 paper. Of interest to this post is the top panel, showing the ostensible variation in the averaged cycles.

Now, I’ve used this technique myself. However, if I were to do it, I wouldn’t do it the way he has. He has aligned the solar minimum at time t=0, and then averaged the data for the 11 years after that. If I were doing it, I think I’d align them at the peak, and then take the averages for say six years on either side of the peak.

But in any case, rather than do it my way, I figured I’d see if I could emulate his results. Unfortunately, I ran into some issues right away when I started to do the actual calculations. Here’s the first issue:

Figure 5. The data used in Shaviv2008 to show the putative sunspot-SST relationship.

I’m sure you can see the problem. Because the dataset is so short (n = 49 years), there are only four solar minima—1964, 1976, 1986, and 1996. And since the truncated data ends in 2003, that means that we only have three complete solar cycles during the period.

This leads directly to a second problem, which is the size of the uncertainty of the results of the “folded” data. With only three full cycles to analyze, the uncertainty gets quite large. Here are the three folded datasets, along with the mean and the 95% confidence interval on the mean.

Figure 6. Sea surface temperatures from three full solar cycles, “folded” over the 11-year solar cycle as described in Shaviv2008

Now, when I’m looking for a repetitive cycle, I look at the 95% confidence interval of the mean. If the 95%CI includes the zero line, it means the variation is not significant. The problem in Figure 6, of course, is the fact that there are only three cycles in the dataset. As a result, the 95%CI goes “from the floor to the ceiling”, as the saying goes, and the results are not significant in the slightest.

So why does the Shaviv2008 result shown in Figure 4 look so convincing? Well … it’s because he’s only showing one standard error as the uncertainty in his results, when what is relevant is the 95%CI. If he showed the 95%CI, it would be obvious that the results are not significant.

However, none of that matters. Why not? Well, because the claimed effect disappears when we use the full SST and sunspot datasets. Their common period goes from 1870 through 2013, so there are many more cycles to average. Figure 7 shows the same type of “folded” analysis, except this time for the full period 1870-2013:

Figure 7. Sea surface temperatures from all solar cycles from 1870-2013, “folded” over the 11-year solar cycle as described in Shaviv2008

Here, we see the same thing that was revealed by the cross-correlation. The apparent cycle that seemed to be present in the most recent half-century of the data, the apparent cycle that is shown in Shaviv2008, that cycle disappears entirely when we look at the full dataset. And despite having a much narrower 95%CI because we have more data, once again there is no statistically significant departure from zero. At no time do we see anything unexplainable or unusual at all

And so once again, I find that the claims of a connection between the sun and climate evaporate when they are examined closely.

Let me be clear about what I am saying and not saying here. I am NOT saying that the sun doesn’t affect the climate.

What I am saying is that I still haven’t found any convincing sign of the ~11-year sunspot cycle in any climate dataset, nor has anyone pointed out such a dataset. And without that, it’s very hard to believe that even smaller secular variations in solar strength can have a significant effect on the climate.

So, for what I hope will be the final time, let me put out the challenge once again. Where is the climate dataset that shows the ~11-year sunspot/magnetism/cosmic rays/solar wind cycle? Shaviv echoes many others when he claims that there is some unknown amplification mechanism that makes the effects “about 5 to 7 times larger than just those associated with the TSI variations” … however, I’m not seeing it. So where can we find this mystery ~11-year cycle?

Please use whatever kind of analysis you prefer to demonstrate the putative 11-year cycle—”folded” analysis as above, cross-correlation, wavelet analysis, whatever.

Regards,

w.

My Usual Request: If you disagree with someone, myself included, please QUOTE THE EXACT WORDS YOU DISAGREE WITH. This prevents many flavors of misunderstanding, and lets us all see just what it is that you think is incorrect.

Subject: This post is about the quest for the 11-year solar cycle. It is not about your pet theory about 19.8 year Jupiter/Saturn synoptic cycles. If you wish to write about them, this is not the place. Take it to Tallbloke’s Talkshop, they enjoy discussing those kinds of cycles. Here, I’m looking for the 11-year sunspot cycles in weather data, so let me ask you kindly to restrict your comments to subjects involving those cycles.

Data and Code: I’ve put the sunspot and HadISST annual data online, along with the R computer code, in a single zipped folder called “Shaviv Folder.zip“