Guest Post by Willis Eschenbach
I came across a curious graph and claim today in a peer-reviewed scientific paper. Here’s the graph relating sunspots and the change in sea level:
And here is the claim about the graph:
Sea level change and solar activity
A stronger effect related to solar cycles is seen in Fig. 2, where the yearly averaged sunspot numbers are plotted together with the yearly change in coastal sea level (Holgate, 2007). The sea level rates are calculated from nine distributed tidal gauges with long records, which were compared with a larger set of data from 177 stations available in the last part of the century. In most of the century the sea level varied in phase with the solar activity, with the Sun leading the ocean, but in the beginning of the century they were in opposite phases, and during SC17 and 19 the sea level increased before the solar activity.
Let me see if I have this straight. At the start of the record, sunspots and sea level moved in opposite directions. Then for most of the time they were in phase. In both those cases, sunspots were leading sea level, suggesting the possibility that sunspots might affect sea level … except in opposite directions at different times. And in addition, in about 20% of the data, the sea level moved first, followed by the sunspots, suggesting the possibility that at times, the sea level might affect the number of sunspots …
Now, when I see a claim like that, after I get done laughing, I look around for some numerical measure of how similar the two series actually are. This is usually the “R2” (R squared) value, which varies from zero (no relationship) to 1 (they always move proportionately). Accompanying this R2 measure there is usually a “p-value”. The p-value measures how likely it is that we’re just seeing random variations. In other words, the p-value is the odds that the outcome has occurred by chance. A p-value of 0.05, for example, means that the odds are one in twenty that it’s a random occurrence.
So … what did the author of the paper put forwards as the R2 and p-value for this relationship?
Sad to relate, that part of the analysis seems to have slipped his mind. He doesn’t give us any guess as to how correlated the two series are, or whether we’re just looking at a random relationship.
So I thought, well, I’ll just get his data and measure the relationship myself. However, despite the journal’s policy requiring public archiving of the data necessary for replication, as is too common these days there was no public data, no code, and not even a Supplementary Online Information.
However, years of messing around with recalcitrant climate scientists has shown me that digitizing data is both fast and easy, so I simply digitized the graph of the data so I could analyze it. It’s quite accurate when done carefully.
And what did I find? Well, the R2 between sunspots and sea level is a mere 0.13, very little relationship. And even worse, the p-value of the relationship is 0.08 … sorry, no cigar. There is no statistically significant relationship between the two. In part this is because both datasets are so highly auto-correlated (~0.8 for both), and in part it’s because … well, it’s because as near as we can tell, sunspots [or whatever sunspots are a proxy for] don’t affect the sea level.
My conclusions from this, in no particular order, are:
• If this is the author’s “stronger effect related to solar cycles”, I’m not gonna worry about his weaker effect.
• This is not science in any sense of the word. There is no data. There is no code. There is no mathematical analysis of any kind, just bald assertions of a “stronger” relationship.
• Seems to me the idea that sunspots rule sea level would be pretty much scuttled by sunspot cycles 17 and 19 where the sea level moves first and sunspots follow … as well as by the phase reversal in the early data. At a minimum, you’d have to explain those large anomalies to make the case for a relationship. However, the author makes no effort to do so.
• The reviewers, as is far too often the case these days, were asleep at the switch. This study needs serious revision and buttressing to meet even the most minimal scientific standards.
• The editor bears responsibility as well, because the study is not replicable without the data as used, and the editor has not required the author to archive the data.
So … why am I bothering with a case of pseudo-science that is so easy to refute?
Because it is one of the papers in the Special Issue of the Copernicus journal, Pattern Recognition in Physics … and by no means the worst of the lot. There has been much disturbance in the farce lately regarding the journal being shut down, with many people saying that it was closed for political reasons. And perhaps that is the case.
However, if I ran Copernicus, I would have shut the journal down myself, but not for political reasons. I’d have closed it as soon as possible, for both scientific and business reasons.
I’d have shut it for scientific reasons because as we see in this example, peer-review was absent, the editorial actions were laughable, the authors reviewed each others papers, and the result was lots of handwaving and very little science.
And I’d have shut it for business reasons because Copernicus, as a publisher of scientific journals, cannot afford to become known as a place where reviewers don’t review and editors don’t edit. It would make them the laughing stock of the journal world, and being the butt of that kind of joke is something that no journal publisher can survive.
To me, it’s a huge tragedy, for two reasons. One is that I and other skeptical researchers get tarred with the same brush. The media commentary never says “a bunch of fringe pseudo-scientists” brought the journal down. No, it’s “climate skeptics” who get the blame, with no distinctions made despite the fact that we’ve falsified some of the claims of the Special Issue authors here on WUWT.
The other reason it’s a tragedy is that they were offered an unparalleled opportunity, the control of special issue of a reputable journal. I would give much to have the chance that they had. And they simply threw that away with nepotistic reviewing, inept editorship, wildly overblown claims, and a wholesale lack of science.
It’s a tragedy because you can be sure that if I, or many other skeptical researchers, got the chance to shape such a special issue, we wouldn’t give the publisher any reason to be unhappy with the quality of the peer-review, the strength of the editorship, or the scientific quality of the papers. The Copernicus folks might not like the conclusions, but they would be well researched, cited, and supported, with all data and code made public.
Ah, well … sic transit gloria monday, it’s already tuesday, and the struggle continues …
w.
PS—Based on … well, I’m not exactly sure what he’s basing it on, but the author says in the abstract:
The recent global warming may be interpreted as a rising branch of a millennium cycle, identified in ice cores and sediments and also recorded in history. This cycle peaks in the second half of this century, and then a 500 yr cooling trend will start.
Glad that’s settled. I was concerned about the next half millennium … you see what I mean about the absence of science in the Special Edition.
PPS—The usual request. I can defend my own words. I can’t defend your interpretation of my words. If you disagree with something I or anyone has written, please quote the exact words that you object to, and then tell us your objections. It prevents a host of misunderstandings, and it makes it clear just what you think is wrong, and why.
rgbatduke says:
January 22, 2014 at 1:32 pm
As if …
Following Nicola Scafetta’s suggestion above, I looked at the two sea level datasets used by Nir Shaviv and by Solheim, viz:
Now, following your excellent suggestion, here’s the further comparison of Solheim sea level data with the Church and White dataset you referenced, which is available here:
Oh, my goodness! You put your finger on that one, Robert. This is hilarious. When we use the C&W data, which is somewhat of an industry standard, that’s what we get.
And since this is a science site, the R2 value of the relationship between the Church and White sea level data, and the data used by Solheim, is 0.004 … and the p-value is 0.40.
Finally, this makes it perfectly clear that as you suggest, Robert, “If you plotted sunspot numbers against the actual coarse grained first derivative of SLR, I don’t think there would be any correlation at all.”
Nicola and Tallbloke, are you following this? Your comments would be … well, likely inflammatory but interesting. In any case, any paper making the claims Solheim makes should have dealt with this glaring problem.
w.
Here is the true relationship between sunspots (I’ve used the NASA values) and sea level changes (Church and White values):
The R2 between the two is 0.009, and the p-value is 0.26 …
In other words, the Solheim paper discussed in the head post got the fate it deserved when the journal was shut down …
w.
Willis Eschenbach says:
January 23, 2014 at 10:54 am
Here is the true relationship between sunspots (I’ve used the NASA values) and sea level changes (Church and White values)
It looks like the solheim values are just a smoothed version of C&W, perhaps with a 5-year window. What happens if you smooth C&W and compare with Solheim?
Mike Rossander says:
January 22, 2014 at 1:50 pm
Mike, usually I would do that, but in this case to emphasize my point about poor science in the Special Issue, I’m gonna say no, and refer you to the author. Why should I do the author’s work for him?
In this debate, many people including the authors think that not publishing data is some minor thing. Lots of folks, including Jo Nova, tell me that I should just email the author. So I regret to say, I’m gonna just pass their excellent advice on to you …
w.
Ian Schumacher says:
January 22, 2014 at 1:52 pm
Looking at the graphs above, I’d say you should believe me … false correlations are a dime a dozen in climate science.
In addition, you say:
Since the R^2 value is the square of the correlation, your statement has no meaning.
w.
Greg Goodman says:
January 22, 2014 at 1:56 pm
Ummm … I think that’s his point …
w.
One last comment (I shouldn’t even take the time as I’ve got deadlines rapidly approaching). The paper at the top only uses 9 specific coastal sites that appear to be correlated with sunspots (although there are many more sites to choose from, IIRC, tide data is available from most the major harbors around the world on hundred year timescales is it not?) This exposes the paper to the criticism of cherrypicking/data dredging. In the figure caption they indicate that they only included nine of 177 that were available. Really? Why THESE nine? Could it be because when these nine were averaged, it looked like there was a correlation, where when all 177 were averaged, there was nothing?
So sorry, Willis, your R^2 and in particular your p-values are incorrectly computed. You have to use:
http://en.wikipedia.org/wiki/Bonferroni_inequalities
(or a Bonferroni correction) to assess the p-value, lest you fall into the trap of believing that green jelly beans cause cancer. Choosing 9 out of 177, I can confidently state that one must adjust even the p-values you obtain to nothingness. If one looks at all possible groupings of the tide gauge data and chooses a finite set that happens to exhibit a (comparatively poor) correlation, you have to take into account all of the rejected permutations that had even less. Otherwise we’ll be able to prove that ESP is real, that prayer works, pretty much anything we like. In fact, this is sort of like what the warmists do when they point to a bad storm and go “look, must be due to global warming”.
So its worse that we thought. So to speak.
rgb
Greg Goodman says:
January 22, 2014 at 1:56 pm
Greg Goodman says:
January 22, 2014 at 2:03 pm
Here are the Jevrejeva annual sea level changes plotted against sunspots …
You sure that you want to use that dataset? …
w.
J Martin says:
January 22, 2014 at 2:19 pm
Good question. Probably yes, just to watch the chips fly. However, I’d have insisted that my name and reviews be posted as part of the deal.
However, I fear that the editors and authors were not looking for my kind of reviews … hard as it may be to believe, I’ve been known to be blunt and direct in the past …
w.
Mike Rossander says:
January 22, 2014 at 1:50 pm
You ask, if we selectively weed out and ignore the data that doesn’t agree with our hypothesis, will the correlation get better and make our hypothesis look stronger?
I don’t think you’ve considered all the ramifications of what you are asking, Mike.
w.
Ian Schumacher says:
January 22, 2014 at 2:40 pm
First, no, sunspots are not “highly correlated” with sea level rise. That’s an artifact of poor data selection. See above et seq.
Second, while there are good examples of what you are talking about, cigarette smoking isn’t one. The R^2 between smoking and lung cancer is actually quite high. See here for an in-depth analysis.
w.
Willis Eschenbach says:
January 23, 2014 at 11:23 am
You ask, if we selectively weed out and ignore the data that doesn’t agree with our hypothesis, will the correlation get better and make our hypothesis look stronger?
some people actually do this. They call it Bayesian estimation. Here is an example:
“The regression slope was found to be somewhat different if Least Median Squares (LMS) or Bayesian Least Squares (BLS) were used [Lockwood et al., 2006a, and references therein], but the procedures converged on very similar regression lines if outliers were progressively removed. Hence we here use OLS but the largest outliers were removed until the regression converged on a stable line” from ‘Reconstruction of Geomagnetic Activity and Near-Earth Interplanetary Conditions over the Past 167 Years: 1. A New Geomagnetic Data Composite, M. Lockwood et al. [Ann. Geophys. 2013]’.
Paul Westhaver says:
January 22, 2014 at 8:56 pm
Yes, I know your pattern recognition is very convincing. It is a common problem with all humans—we often see patterns that are not there, very convincing patterns.
That’s why we invented math, Paul, in part so we didn’t have to depend on our pattern recognition skills.
w.
Paul Westhaver:
I am replying to your post addressed to me at January 23, 2014 at 10:15 am. For convenience of others, this is a link to it
http://wattsupwiththat.com/2014/01/21/sunspots-and-sea-level/#comment-1546575
It begins by saying
Well, everybody knows what is to follow when a message begins saying, With respect”, and your post does not disappoint.
There is some confirmation of your view in my post at at January 23, 2014 at 2:49 am
http://wattsupwiththat.com/2014/01/21/sunspots-and-sea-level/#comment-1546134
I said there
So, I said, “you say you “see a pattern”. Yes, you do.”
That is the ONLY confirmation of what you said that I have provided.
But the apparent “pattern” which you see is spurious for the reasons I explained.
You have persistently ignored my explanation and now say
Rubbish!
I wrote
Your “position” is that you ignore all that.
And you have the gall to say to me
I summarised the “investigation and analysis” which you refuse to consider because it refutes what you want to be true.
And you assert that I should ignore the results of that “investigation and analysis” because it does not agree with the view of “an 8 year old child”!!!
Richard
lsvalgaard says:
January 23, 2014 at 10:59 am
Not all that good … R2 = 0.12.
Remember that Solheim is using just 9 tidal stations …
w.
Dr. S.
Here it is Aurora and aurora data alone
http://www.vukcevic.talktalk.net/OldLadysHalo.htm
vukcevic says:
January 23, 2014 at 1:39 pm
Here it is Aurora and aurora data alone
You claimed that aurorae and ‘magnetic’ oscillations of the Earth itself were related. Show that. Aurorae and solar wind magnetic field are causally related but that is not what you claim. Pseudo-science piled on higher just makes it worse.
Willis, thanks for correcting my error.
What I am claiming it is that geomagnetic storms are modulated by small changes in the Earth’s magnetic field (generated by differential rotation within the liquid core).
You have to be patient, another university professor and a prominent scientist will have the first sight of entire endeavour.
You ascertain it is just a ‘pile of pseudoscience’, I guess you are being polite. For most of my practical engineering carrier,I dealt with data and signals, so science or pseudoscience aspect doesn’t bother me a single iota, but for the benefit of your serenity let it stay as pseudoscience. It is my bedtime; see you at another thread at another time. Keep well.
I hope I’m not being provocative, but your statements about correlation make no sense to me.
What does an autocorrelation function of ~0.8 actually mean?
How does this effect the “R^2” value?
I realise that I am being incredibly stupid but I can quite easily envisage signals that has an “aurtocorrelation” of 0.999 and an R^2 of 0.000. Alternatively I can envisage a signal that has an ” autocorrelation of 0.000 (ideally) yet can have an autocorellation of 1.0.
I realise that I cannot match your brilliance, but I would be very interested in your explanation.
P.S.: I see you have discovered “Mathematica”.. God help us all! I would point out that this is a symbolic language for mathematical manipulation – it is not a substitute for understanding (or hard work)
vukcevic says:
January 23, 2014 at 3:20 pm
What I am claiming it is that geomagnetic storms are modulated by small changes in the Earth’s magnetic field (generated by differential rotation within the liquid core).
You used to claim just the opposite: that the field in the core is modulated by geomagnetic storms, i.e. causality going the other way.
Now, on very long time scales [centuries] the intensity of geomagnetic storms is modulated by the strength of the geomagnetic dipole, as the latter determines the stand-off distance of the solar wind above the surface of the Earth and hence determines the size of the magnetosphere. The tilt of the Earth’s dipole against the solar wind direction introduces daily and seasonal variations [up to 30%] of the size of magnetic activity [and thus also of geomagnetic storms] as the solar wind sees a varying strength of the Earth’s magnetic field at the ‘sub-solar’ point as the Earth wobbles. This effect accounts for the well-known semiannual and UT-variation of geomagnetic activity http://www.leif.org/research/Semiannual-Comment.pdf but I don’t think this is what you have in mind as those variations average out over a year.
RC Saumarez says:
January 23, 2014 at 3:43 pm
What does an autocorrelation function of ~0.8 actually mean?
How does this affect the “R^2″ value?
A high autocorrelation means two adjacent data points are almost the same [and so are not independent] so that when you think you have 1000 data points you may only have [say] 50 points. this affects the p-value making you believe that the correlation is more significant than it really is. A good example is the sunspot number: in a solar cycle there are 4000 days and thus 4000 daily values of the sunspot number, but since a high sunspot number on a given day is always followed by a high number the next day, the number of independent data points for a whole cycle is only about 25, not 4000.
@Lsvalgaard
Why not consider the correlation between a sine wave and cosine wave?
Alternatively, why not consider the corellation between a random sequence and a time shifted random sequence?
RC Saumarez says:
January 23, 2014 at 4:26 pm
Why not consider the correlation between a sine wave and cosine wave?
Alternatively, why not consider the corellation between a random sequence and a time shifted random sequence?
Yes, why not? Demonstrate your eloquence by elaborating on this as you feel the need for…
RC Saumarez says:
January 23, 2014 at 3:43 pm
It means that if the dataset is duplicated, and then lagged by 1 timestep, the correlation of the dataset with the lagged version of itself is 0.8.
I have no idea about your brilliance, you’re a better judge than I. Setting that aside, autocorrelation doesn’t affect the R2 value at all. What it affects is the p-value. This is because autcorrelated datasets (also called “red noise”) tend to “wander” much more than “white noise” datasets. As a result, if we are trying say to determine if a trend is a random occurrence (p-value), autocorrelated datasets are much more likely to contain random trends, and to move in cycle-like swings. Note that these are not real cycles … but they can certainly resemble them.
To put it another way, if we see a big swing in what appears to be a white noise dataset, there’s a good chance that there is some underlying phenomenon at work. A similar swing in a highly autocorrelated dataset, on the other hand, could much more easily be just random chance.
“Discovered”?? Listen, you snide little twit. I’ve owned and driven a copy of Mathematica since Steven Wolfram came out with Version 1.0 in 1988, so I’ve used it for a quarter century now. Over that time I’ve created programs in Mathematica to provide the code to run the plasma cutters that cut out all the steel plates for the construction of four 40 metre ships, along with dozens of other real-world, “failure is not an option” type of practical tasks, plus a variety of more theoretical uses. I can program Mathematica in three languages, while you were likely unaware that there is more than one way to program it. And yes, Virginia, I also know that it also does symbolic manipulation, and I’m good at that as well. Come back when you can say the same.
I don’t advise you try your tongue on me, RC, or you’ll get a tongue-lashing. I’m willing to move on past this insult of yours, but if you’d like to continue the conversation …
w.