Guest Post by Willis Eschenbach
Dr. Nir Shaviv has kindly replied in the comments to my previous post. There, he says:
Nir Shaviv August 15, 2015 at 2:51 pm
There is very little truth about any of the points raised by Eschenbach in this article. In particular, his analysis excludes the fact that the ocean has a large heat capacity such that one expects the sea level change rate to vary in sync with the solar forcing (which it does) and not the sea level itself. This basic physics mistake is the reason he finds no correlation. If you’re interested in reading more, I tried to address his main mistakes in: http://www.sciencebits.com/reply-eschenbach
I will not answer any comments on this page, since after Eschenbach expressed his derogatory remarks I see no point.
Also, since I am traveling, I will have little time to answer comments on my blog, but I will try.
At the referenced blog page, he summarizes his arguments as follows:
Let me summarize Eschenbach’s mistakes. Some are trivially wrong, some much worse.
• Eschenbach assumed in his analysis that if the sun has a strong solar forcing, the sea level should be in phase with it. This is plain wrong. Because of the high heat capacity of the ocean system, one roughly expects the sea level change rate (and not the sea level itself) to be proportional to the solar forcing. If one looks at the slope of the sea level, it does indeed correlate nicely with solar activity.
• Given that we explained how and why we carried out the fit using a harmonic analysis, we did not deceive anyone. Writing that we did is libelous.
• The reason we used a harmonic analysis is because it makes the analysis more transparent. If one uses a solar forcing proxy (such as the cosmic ray flux), one finds a similar fit. Namely, writing that by using actual solar proxies one obtains a bad fit is simply wrong. (Again, one has to remember the heat capacity of the oceans!)
• The model has 6 and not 7 parameters. Having all of them is necessary to compare the sea level to the physical model. To ridicule us that we used many parameters is totally irrelevant and inappropriate.
• Eschenbach wrote that I haven’t heard of von Neumann’s Elephant quote. I did many years ago, and even mentioned it in a 2007 blog post on my blog. Trivially wrong, but reflects the low standards of that article.
Dr. Shaviv, thanks for your comments, and for listing your objections in such a concise manner. I will address them one at a time below, after first clarifying my main objection to your work.
My Main Objection To The Study
I wrote my previous post because I was blown away when I found out that your “solar” study has no solar data at all in it. As a result, I said that calling it a solar analysis was “deceptive”. I apologize for that without reservation, it was an incorrect claim. I forgot a very important distinction—the fact that I felt deceived doesn’t make you deceptive.
I should have said that your analysis was misleading. This is much more accurate, as it describes the effect of the analysis and not the authors’ intentions. To show that this is not an empty apology, I have gone back to my original post and removed all references to deception.
Now, I understand you don’t like me saying that your study is highly misleading. But given that there is no data of any kind regarding the sun in your study, why do you call it a study of the sun? How is that NOT a mis-statement of the facts?
Here is a precis of the section of your study describing the data used:
2. Data Sets Used
The altimetry data set used is derived from the TOPEX/Poseidon and Jason altimeter missions with the seasonal signals removed [Nerem et al., 2010] (data electronically available at http://sealevel.colorado.edu/). The data we use have the inverse barometer and glacial isostatic adjustment corrections applied, and it covers the time period between mid-1993 to early 2013. … (more etc. re sea level data)
For the El Nino–Southern Oscillation we use the NINO3.4 index [Trenberth,1997], which is based on the sea surface temperature in the middle of the Pacific (bounded by 120◦W, 170◦W, 5◦S, and 5◦N). Because this index is directly related to the oceanic temperature while the Southern Oscillation Index depends on atmospheric pressures, we expect the former to have less variations and to more directly reflect the ocean heat content … (more etc. re ENSO data)
… the end of section 2 …
I read that and I got to the end and I thought “That’s the end? … That’s it for the data sets? Where’s the solar data?”
According to Section 2, we have the sea level dataset and the ENSO dataset. This means your study is indeed about sea level and ENSO. But since it doesn’t contain any solar data, I don’t understand how you can claim it is about the sun. Where is the “solar forcing” data you are referring to in the abstract?
Instead of solar, you’ve just put in a fitted sine wave. You have made no connection of any kind, statistical or otherwise, between this sine wave and the sun. While this converts your study from a ‘sea level as a function of ENSO’ study to a ‘sea level as a function of ENSO plus a fitted sine wave’ study, it doesn’t magically turn it into a solar study. This is particularly true since the sine wave is not related to the actual solar data by anything but a common period.
So I ask again—how can you call this a solar study? You have made no effort to statistically relate the sine wave to the actual solar forcing over the period. What gives you the right to say this is about “The Sun and ENSO”? I can understand the “ENSO” part … but how does the sun ever rise on a study which contains no solar data?
Replies to Dr. Shaviv’s Particular Objections
Having apologized to Dr. Shaviv, and having re-stated my main problem with the study, let me go through Dr. Shaviv’s objections one at a time.
Eschenbach assumed in his analysis that if the sun has a strong solar forcing, the sea level should be in phase with it. This is plain wrong. Because of the high heat capacity of the ocean system, one roughly expects the sea level change rate (and not the sea level itself) to be proportional to the solar forcing. If one looks at the slope of the sea level, it does indeed correlate nicely with solar activity.
Dr. Shaviv, looking at the change rate rather than at the sea level height is indeed what I started out believing you had done. And from an initial examination of your model formula, at first it appeared to me that you had done exactly that, viz:
I looked at that, and I thought, this looks fine. In your Equation (1), t is time in fractional years. In the text above it says that “h is the sea level height”, which means of course that ∆h is not the sea level height, but the change in sea level height discussed in your Objection 1. That is the usual meaning of the delta (∆) in the ∆h. It means the change in something. In the case of Equation (1) the delta in ∆h means the change in the sea level height h. So your formula said the change in sea level height ∆h(t) was a function of the values at time t of a sine wave plus ENSO plus the integral of ENSO plus a trend. So far, so good.
But then I tried to implement your formula, and after much confusion and head scratching I realized that no, in your notation, for some unknown reason ∆h is NOT the change in the sea level height h. Instead, you are using the notation ∆h for the sea height itself! Most peculiar.
I verified this oddity in a couple of ways. First, the fitted variable h1 in Equation (1) is the size of the annual trend in the model results. In your study you give a list of the fitted parameters which includes:
Table 1. The Model Fit Parameters
h1 3.29 ± 0.04 mm/yr
But 3.29 mm/year is absolutely not the trend in ∆h, the rate of sea level change. That is the trend in h, the sea level height itself.
Next, consider. If ∆h(t) in Equation 1 actually does represent change in sea level, and the change in sea level is increasing by 3.3 mm per year as the parameter h1 shows, twenty years after the start of the record the sea level would be rising by a six centimetres (about 2.5 inches) per year … not happening.
As a final piece of evidence that for unknown reasons you are incorrectly using ∆h for sea level height, look at Figure 1 from your study. It shows the detrended and smoothed sea level height h from the University of Colorado, and I have duplicated that result to verify that it is indeed correct … but then look at the label on the vertical “Y” axis:
You show the linearly detrended sea height h by means of the blue dots, but you have labeled it “∆h” on the Y-axis. You have also incorrectly referred to the sea height h in the caption as ∆h. Clearly this is not just a typo, it is an ongoing misunderstanding.
So in fact, despite telling me that I screwed up by comparing solar forcing to sea level height h instead of comparing it to what you call the “sea level change rate”, which is ∆h … that is exactly what you did in your analysis.
As a result, when you say that “It is quite upsetting that Eschenbach did this mistake even though it was clearly explained in our paper”, I’m sorry, but although you are correct that it was clearly explained in your paper, that’s not what you did in your paper. Look at your equation 1. You are not calculating the change in height ∆h as you think, not with a trend of 3mm per year—you are calculating the sea height h itself. In other words, you did precisely what you accuse me of doing.
Now, I discovered this while replicating your work in the course of researching for my previous post. As a result, I was left in a quandary regarding how to handle this additional and very separate issue. I didn’t want to get into all of these h versus ∆h questions in my previous post. I like my posts to have a fairly narrow focus, and just mentioning this ∆h problem would have sidetracked or entirely derailed my main point, which was that your paper has nothing to do with the sun.
So after thinking it over, I took another tack. I decided to compare the solar forcing, not against ∆h as you said you’d done, but directly against the sea height h, just as you had actually done in your model. I figured that if it went by without comment, no harm, no foul … and if someone complained about my not using ∆h, I could give the explanation I just gave.
What I didn’t expect was that you’d be the one to bust me for it, but that’s OK. It just makes the issue clearer.
Given that we explained how and why we carried out the fit using a harmonic analysis, we did not deceive anyone. Writing that we did is libelous.
I have withdrawn the term “deceptive” entirely. However, from reading the comments on your paper at blogs like Tallbloke’s Talkshop, it seems there were many people who were misled by your work. Neither the commenters nor Tallbloke himself noticed that your paper had no solar data of any kind.
And I was certainly misled. Based on the title and the comments I’d seen on Tallbloke’s blog, I went into this expecting a study about solar forcing. Imagine my surprise when halfway through I realized I’d gotten a paper about sine waves with no solar in sight.
I started as usual by reading the title, all about solar effects on the sea level. I read the abstract, all about solar and solar cycles. Not a word about harmonic analysis. According to the abstract it was as the title said, a study of solar and ENSO components of sea level. Looked good.
So I read the introduction, more about the sun and its effects, about solar cycles and solar forcing. And again, nothing about sine waves, it was all solar, solar, solar. Onwards.
Everything was going swimmingly, until I got to the end of Section 2, Data Sets Used. I got to the end of that section and I though “Huh? What solar dataset did they use?” I thought I’d missed something so I re-read Section 2 … still nothing about solar.
Now as you point out, you did say in the later sections of the paper that “The above empirical fit assumed a harmonic solar forcing.” But you described the sine wave as a “harmonic solar component”, which it is not unless you can show it is, and you haven’t done that. You call it “harmonic solar forcing”, but there is no solar, it is 100% harmonic. You titled your paper as being about “The solar and Southern Oscillation components in the satellite altimetry data”, but there is nothing remotely solar about it. Let me repeat my example from my last post:
Suppose I’m studying the effect of gamma rays on marigold growth. And unfortunately for my lovely hypothesis, the gamma ray data is poorly correlated with the marigold growth data.
But an inspiration hits me. I notice a sine wave can be fitted to the marigold growth data quite well, and the sine wave kinda sorta looks like my gamma ray data, and even better, using the sine wave allows me to “significantly simplify the analysis” … sound familiar? It should, that is your justification for using a sine wave in place of the real solar data.
So I set aside all of my gamma ray data, and I just use the fitted sine wave in my computations. Here are the questions about my analysis of marigold growth.
Given that there is no gamma ray data of any kind in my study, and given that I have made no statistical or other connection between the sine wave and the gamma ray data, am I justified in calling the sine wave a “harmonic gamma ray component”?
Can I validly call the cycle of the sine wave the “gamma ray cycle”?
Is it legit to discuss “gamma ray forcing” without gamma ray data?
Can I title my sine-wave paper “The gamma ray components in the growth of marigolds” given the total absence of a single gamma-ray observation in the entire paper?
Or on the other hand: given that my paper has no gamma ray data of any kind in it and I have made no connection between the sine wave and the gamma rays, are all of those claims about gamma rays misleading?
I call those actions highly misleading. Their effect is to convince the reader that the sine wave data is gamma ray data. I say when someone leaves out every bit of gamma ray data in their analysis and then puts “gamma ray” in the title of their analysis, and calls a bog-simple sine wave a “harmonic gamma ray component” and talks knowingly of “gamma ray cycles” and “gamma ray forcing”, their analysis misleadingly describes a sine wave analysis as a gamma ray analysis, no matter what explanation they put into their small print.
Yes, as you say, it may well “significantly simplify the analysis”. And yes, as you explained in your objection, you “carried out the fit using a harmonic analysis”. That is 100% true. You did do a harmonic analysis.
But that is all it is, a HARMONIC analysis. It is not a “solar” analysis of any kind. The components are harmonic components, not “harmonic solar components” as you claim. You have made no connection at all between the sun and the sine. The cycles are harmonic cycles, not “solar cycles” as you assert. The calculated forcing, if it exists at all, is harmonic forcing, not “solar forcing”.
And the study is actually about “The harmonic and Southern Oscillation components in the satellite altimetry data”, not about the solar components as your actual title incorrectly states.
So no, Dr. Shaviv, it is far from enough to claim in the small print as you did that you are using “harmonic solar forcing”. It is harmonic forcing, pure and simple, nothing solar about it.
When your title and your abstract both claim the study is about the sun and solar forcing and solar cycles, a statement halfway through the study that your solar component is actually “harmonic solar forcing” just muddies the waters. Your study is no more about the sun and solar forcing and solar cycles than my analysis above with no gamma ray data is about gamma rays and gamma ray forcing and gamma ray cycles …
The reason we used a harmonic analysis is because it makes the analysis more transparent. If one uses a solar forcing proxy (such as the cosmic ray flux), one finds a similar fit. Namely, writing that by using actual solar proxies one obtains a bad fit is simply wrong. (Again, one has to remember the heat capacity of the oceans!)
I’m sure using a sine wave simplifies the computations, and makes the analysis more transparent. My issue is that it also makes the analysis an “ENSO and sine wave” analysis, not an “ENSO and sun” analysis as you seem to think.
And yes, I suspect you can get a “similar fit” with sunspots, or with any of a dozen other datasets, whether solar datasets or any of a number of kinds. That’s the beauty of fitting cycles with lots of tuned parameters as you are doing. You can get a “similar fit” lots of ways, particularly since “similar fit” doesn’t mean “better fit”. For example, I can show a “similar fit” between historical 20th century sea levels and the cost of US postage stamps. But that doesn’t turn a harmonic analysis into a postage stamp analysis.
And I do remember the heat capacity of the oceans. See my reply to Objection One above …
The model has 6 and not 7 parameters. Having all of them is necessary to compare the sea level to the physical model. To ridicule us that we used many parameters is totally irrelevant and inappropriate.
Six or seven, either is too many. Consider: exactly your same argument might have been made by Freeman Dyson to Fermi, and he had only four parameters. The four parameters were certainly “necessary” to Dyson’s model, just like the six parameters are assuredly “necessary” to your model … so what? It’s still a six-parameter fitted model. And not just any fitted model. It is a sine-wave-containing model fitted to a dataset that is not even two full sine-wave cycles in length. If you couldn’t fit the sea level under those conditions, I’d be shocked.
I’d be especially shocked if you couldn’t get a good match because contrary to good modeling practice you have included outcome information among your independent variables in the form of ENSO. Let me explain exactly how this has happened.
The ENSO measure you’ve used is the temperature of a large expanse of the Pacific Ocean. Because water expands at a known rate as it warms, ocean temperature can be used to calculate ocean height, and vice versa. We know the expansion coefficient of sea water, so if the ocean is heated by a certain amount, to calculate the resulting thermal change in sea level height ∆h we simply multiply the change in temperature by the coefficient of expansion. And of course, the reverse is true—if the sea level height goes up because of temperature, we can calculate the corresponding change in temperature necessary to produce that rise in sea level by dividing the sea level change by the coefficient of expansion.
The important point to note is that change in global ocean temperature is calculable as a function of change in sea level. Now, let’s see what this means in terms of ENSO.
If we divide the areas of the ocean into areas A1 … An with temperatures T1 … Tn, we can state the temperature/sea level relationship as h ≈ Coef.of.Expansion * mean(T1, T2, T3, T4 … Tn). In English, the global sea level is a function inter alia of the average ocean temperature.
Now, you’ve taken the temperature of a part of the ocean, the ENSO3.4 area. Let’s call that temperature T1. You’ve fitted T1 as a global ocean temperature proxy to the sea height h, and subtracted out the fitted values.
Now, lets imagine that instead of just using the temperature of the ENSO 3.4 area T1, you also use the temperatures of three other areas T2, T3, and T4 … since you now have more data about the ocean temperature, your estimate of the global ocean temperature will be more accurate, and as a result your calculated value of the sea level height h will be better as well.
But how can this be, that your model gets more and more accurate? Take it to the logical conclusion. If you included the temperature of every ocean area T1 to Tn as part of your “independent” variables, you’d be able to model the temperature dependent sea height h exactly … but that is only because you are directly including information about the dependent variable “h” in the so-called “independent” variables. So it’s no surprise at all that you can model the sea level so well—you have badly contaminated your sole “independent” variable with outcome information. As noted above, the relationship works both ways, which means that global ocean temperature change is a function of sea level change … which in turn means we can calculate your “independent” variable ENSO as a function of sea level. And that means your “independent” variable is a function of the dependent variable.
And when I say “badly contaminated”, I mean “terminally”. You are using the ENSO information at time t in Equation (1) (identified as S3.4(t)) to calculate the sea level height at time t. But ENSO temperature is composed entirely of outcome information, that is to say the ENSO information is a function of and can be calculated from the sea level data you are trying to model.
The problem is that this information coming from looking at the outcome before calculating your results is meaningless in terms of actual modeling. This is because the only thing that information about the outcome can tell us is that the outcome looks like the outcome … not useful at all. It’s like saying “I can forecast todays average temperature with very good accuracy … as long as I know the temperatures at 3 pm and 3 am” … not impressive, right? It is unimpressive because you are using information about the outcome to predict the outcome. Bad model, no cookies. Same thing with ENSO and sea level.
This means that in your model you have three things:
1. Useless ENSO information which is a function of the outcome to be modeled, but dang, it looks so good.
2. A sine wave with no connection to reality, but which reminds you of the sun, and
3. A linear trend.
Since there is no solar data, and the ENSO temperature is contaminated with outcome information, that leaves your study containing no independent observational variables of any kind …
There is another related problem with your model. When you measure the ENSO 3.4 ocean temperature, that ocean temperature is created, modified, and maintained by the sun. As a result, the ENSO data already contains the solar signal including any possible effects of the tiny ~ 11-year variations. Again, imagine that we know all of the ocean temperatures T1 … Tn. Inter alia, that temperature determines the sea level … and every bit of the solar signal is present in the temperature, including tiny solar variations. This means that when you use the ENSO data to remove part of the signal, you are removing part of the solar signal as well …
Curiously, in your case that doesn’t matter much because as you point out yours is NOT an ENSO/solar analysis, it’s actually an ENSO/sine wave analysis that you are merely calling a solar analysis …
But that in itself makes the analysis strange, because now you have both solar data mixed in with the ENSO data, which is contaminated from snooping the outcome, plus the sine wave data acting as a clumsy proxy for the solar data … messy.
So those are my objections to your model itself. You have used a six-parameter tuned model which takes as input ENSO and a sine wave. You have fit this model to a sea level dataset barely one-and-a-half sine wave cycles in length. Your one “independent” variable is not independent, it is contaminated with outcome information. And you have picked independent variables that are not independent of each other, because the solar signal is present in the ENSO data.
Like I said above about your strange use of ∆h in place of h, I let all of this go without comment in my last post because I was so shocked that you would say your study is about the sun, and I didn’t want to distract people with a bunch of other issues. But since you brought it up … your model fails not just because it is a multi-parameter tuned fit. It fails for those other reasons I just listed.
Eschenbach wrote that I haven’t heard of von Neumann’s Elephant quote. I did many years ago, and even mentioned it in a 2007 blog post on my blog. Trivially wrong, but reflects the low standards of that article.
You are correct, Dr. Shaviv, my apologies. What I wrote was:
Have these folks never heard the story of Von Neumann’s elephant? Obviously not … so I attach it for their edification.
My bad. I didn’t even consider the possibility that you could have heard that critical cautionary tale and then gone ahead and designed that model. My apologies, I was wrong to say you hadn’t read it, bad assumptions on my part.
I should have said that if you’d read it, that unfortunately you hadn’t taken it to heart. Freeman Dyson didn’t tell that story just to be passing the time. Model fitting, particularly to a short dataset, is both very easy and very meaningless, as you have just proven once again. Let me repeat the quote from Enrico Fermi regarding how to do calculations, as his words apply directly to your analysis:
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 self-consistent mathematical formalism. You have neither.
Dr. Shaviv, I understand that I upset you by saying that your work was “deceptive”, and I have apologized to you for that. Let me say instead that your work strongly tends to mislead the reader into thinking you are talking about the sun.
I think it is accurate to say that describing a study which contains no gamma ray data as a “gamma ray study” that is using a “harmonic gamma ray component” and “gamma ray cycles” to calculate “gamma ray forcing” is highly misleading. Similarly, I think that entitling a study containing no gamma ray data “The gamma ray and ENSO components of satellite sea levels” is misleading … and they are misleading even if in the small print you hedge your claims by saying you are using “harmonic gamma ray components”.
I also want to emphasize that your model is NOT as you have described it. It is NOT a model that calculates ∆h, the change in sea height as you have claimed. It is a model that directly calculates h, the sea level height … so you’ve busted me very emphatically for doing exactly what you did.
Moving on, you say you don’t want to discuss these matters here on WUWT because you have received “derogatory remarks” … if I followed that curious guideline, I’d never be able to comment on a host of sites, including both your site and this one. On this site, I take “derogatory remarks” that are much worse than being called “deceptive” on a daily basis … so what? I just man up and march on. On your site, you’ve busted me, in a derogatory manner, for doing exactly what you did in your study. Again, so what? That kind of thing happens all the time, and it doesn’t stop me from commenting here, there, or on any of the other web sites where I regularly take many, many more derogatory remarks than you’ve ever gotten from me.
I’ve responded to you here on WUWT, for a couple reasons. Fiirst, you didn’t enable the comments on your reply to my analysis, so neither I nor anyone else can comment there. This means you’ve refused to discuss it here, and you’ve entirely choked off comments there … I’m getting the feeling that WUWT is not actually the problem …
Additionally, I responded here because here both of us can use graphics in the discussion. It’s hard to discuss complex relationships without graphs.
Finally, you close your post by saying:
I should also add another point which is directed primarily to Anthony Watts. The Wattsupwiththat website used to keep very high standards. It also served as a very important outlet where discussions about various climate views, including those which do not conform to the dogmatic mainstream could be heard. However, the low standards borne from Eschenbach’s article, both in science and in style should be avoided. Anthony Watts should not expose himself to libelous type of writing, which is exactly what Eschenbach has done. Writing false statements is one thing, it is Eschenbach’s right for free speech, but writing that my colleagues and have “deceived” as well as other derogatory remarks that intend to tarnish our scientific integrity has no place in any scientific discussion.
Let me say in passing that I enjoy watching how everyone loves WUWT and thinks it is great until it is their own work being discussed … and then they jump up and down and complain how the WUWT standards have slipped from the good old days. Rarely fails. I note that Dr. Shaviv has never to my knowledge complained about the standards of WUWT when other peoples’ work was on the table …
Dr. Shaviv, I have apologized to you for calling you and the other authors “deceptive”. That was uncalled-for. However, people have indeed been misled by your study, a quick cruise around the web is enough to confirm that. In essence, you’ve claimed gamma rays and gamma ray cycles and gamma ray forcing where there is not a single gamma ray to be found. That is misleading.
Do I “intend to tarnish your scientific integrity”? Well, in a single paper you’ve claimed that a harmonic study is a solar study, you’ve included outcome information in your one “independent” variable and thus left yourself with no independent variables in your model, you’ve confused ∆h and h while accusing me of not understanding the difference, and you’ve used enough tunable parameters to make an elephant deliver obscene gestures with his proboscis … and you think I’m the one tarnishing your reputation?
Yes, I could have been nicer and more polite about what I’ve said, wrapped it all up in sugar, used all kinds of waffle words to muffle the impact of what I am saying. But I’ve had it up to here with bogus solar studies. I have tried to look at each one as they are brought to my attention, which I am regularly abused for doing. To date they’ve all been pathetic, all potatoes and no meat. Not as bad as your study, though—for some odd reason, almost every solar study except yours actually uses, you know … solar data … go figure.
So when I saw the title of your study, it sounded quite interesting. However, when I took the trouble to download your study and then to work my way through to the middle, I must confess I lost it when I realized I’d been a sucker, that it was not a solar study in any sense of the word. Instead, in your words, it was merely a “harmonic analysis”.
When I found that out, I fear I lost the plot, I waxed wroth and I said not one but a plethora of bad words. And while I left out the plethoretceteras in writing my post about your analysis, I know that some of my language in my post was still intemperate and unwarranted, and I apologize for that.
My best wishes to you,
A Fervent Plea: misunderstanding is the bane of the web. To reduce misunderstanding, if you disagree with what someone has said, please quote the exact words you disagree with. That way we can all be crystal clear about both who and what you are talking about.