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“
Konrad, I would imagine that intrinsic factors play a much larger role in UV variation in the oceans than solar affects. Solar affects are likely to be buried in the noise. UV at Earth’s surface is VERY noisy and is even noisier at depth in the oceans. I seriously doubt a mathematically measurable affect, and certainly not one that would show up in SST measures, which are themselves highly variable and under-sampled. I also doubt your quoted heating calculation. See the following:
Ultraviolet B (UV-B) radiation reaches different depths in ocean water depending on water chemistry, the density of phytoplankton, and the presence of sediment and other particulates. The map above indicates the average depth UV-B penetrates into ocean water. At the depth indicated, only 10 percent of the UV-B radiation that was present at the water’s surface remains. The rest was absorbed or scattered back towards the ocean surface.
http://earthobservatory.nasa.gov/Features/UVB/uvb_radiation3.php
milodonharlani says:
June 11, 2014 at 1:57 pm
Indeed, milodon, and thanks for pulling me back for that last bit of fun. I was amazed when I finally read that study in detail just how abysmally bad it was …
w.
milodonharlani says:
June 11, 2014 at 11:47 am
I guess my point wasn’t clear, usually that’s my fault. The issue is not whether the models are “better or worse”. The issue is that they are all linear, in that their outputs are nothing but lagged linear transforms of the forcing.
As a result, we can almost guarantee that if there is solar forcing in the model inputs, it will appear in the outputs. And this simple fact means that climate models are absolutely useless in determining whether the solar variations have any affect on the climate … because by and large, the models will say yes.
But unfortunately, this is means absolutely nothing about the real world. It just means that the models are boringly and robotically linear.
w.
By definition, the sample cross-correlation function is, at each lag m, the
average covariance product x(n)*y(n+m), normalized by the product of the
sample RMS-values of x and y. The latter do not distinguish between
signal, interferring components in other frequency bands, and noise; their
variances simply add together. Thus when narrow-band signals such as SSN
are cross-correlated with a wide-band signal such as SST, only the fraction
of total variance of the wide-band signal in the narrow frequency range of the former can contribute systematically to the cross-correlation.
While ~80% of SSN variance is confined to spectral bands ~11yrs in period,
only ~20% of surface temperature variance is found there, with multidecadal
oscillations accounting typically for more than half. That’s why the
cross-correlation is down by a factor of ~4 from what it would be if
temperature variations were likewise narrow-band and coherent. It is sheer folly to conclude on the basis of confidence intervals appropriate only to
TIME-INVARIANT quantities that the LAGGING relationship between SST and SSN,
plainly evident in the sample ccf in Figure 3, is statistically
insignificant.
1sky1 posted a very good comment June 11, 2014 at 5:24 pm.
Thanks for a carefully formulated remark.
This signal processing engineer would have arrived at the same conclusion – that if you put a high frequency signal (11 year period) into a low-pass filter (general thermal inertia of ocean) you don’t want to brag about what comes through the noise, particularly as magnified by an “analysis filter”.
Pamela Gray says:
June 11, 2014 at 2:23 pm
———————————
Pamela,
my reference was to UV-A not UV-B which is highly effected by ozone (which is in no way effected by CFCs).
http://www.biblioteca.uma.es/bbldoc/tesisuma/1663844x.pdf
– has some empirical measurements of UV penetration into the oceans.
Of interest was figure 3.(d), this shows UV-A still having a power of ~10 w/m2 at 50m, which is well below the thermocline.
I believe that UV the heating below the thermocline should be measurable with current instruments. All I am pointing out is that this will be one of the “many plugs” Jack Eddy mentioned with regard to solar influence on climate, however the record length of current instruments is too short to quantify effect on global climate variation. Sadly this is what wills calls an “excuse” as to why I cannot show 11 year cycles I clearly claimed would not be visible in SST records above the thermocline.
But then I am still wondering what Willis’ “excuse” is for holding the lukewarmer line. After all he lost the “does DWLWIR heat the oceans” argument to a roll of microwave-safe cling wrap way back in 2011..;-)
Pamela Gray says:
June 11, 2014 at 2:23 pm
——————————–
But what if we were to forget pointlessly stabbing the 11 year straw man?
http://tallbloke.wordpress.com/2011/02/13/roger-andrews-the-solar-sst-relationship/comment-page-1/
Back in 2011 it was claimed –
“But we still don’t have a causative mechanism”
Well, UV-A heating below the diurnal thermocline is a very plausible mechanism that also accounts for lag.
Here are my latest results for the change in the speed of minimum temperatures (27 weather stations NH + 27 weather stations SH, balanced to zero latitude and 70/30 spread @sea/inland)
last 40 years (from 1974) +0.004 degree C/ yr
last 34 years (from 1980) +0.007 degree C/ yr
last 24 years (from 1990) +0.004 degree C/ yr
last 14 years (from 2000) -0.009 degree C/ yr
nobody able to work out a cycle time from these results?
konrad says
Well, UV-A heating below the diurnal thermocline is a very plausible mechanism that also accounts for lag.
henry says
did you figure out already what the next 44 – 46 years of this graph looks like?
http://ice-period.com/wp-content/uploads/2013/03/sun2013.png
@Konrad Hartmann
there is some variation within TSI, mainly to do with the UV (C). It appears (to me) that as the solar polar fields are weakening, more energetic particles are able to escape from the sun to form more ozone, peroxides and nitrogenous oxides at the TOA.
In turn, these substances deflect more sunlight to space when there is more of it. So, ironically, when the sun is brighter, earth will get cooler. This is a defense system that earth has in place to protect us from harmful UV (C).
Konrad, using your link, I see that photosynthetically active radiation (visible light range 400-700nm) has far more W/m2 than UVa (315-400nm) at the same ocean depth. In terms of heating capacity, the longer the wavelength, the more energy it carries for the purpose of heating. Thus, any temperature variation of the sort scientists have measured would be from visible light and would bury any temperature variation from UVa. Therefore, UVa cannot be the source of short or long term measurable temperature trends in the oceans. If anything, it would be from variation in visible light the moment it breaks the ocean surface skin combined with absorption in the water column, leaving left over heat to drive trends
Pamela Gray says:
June 12, 2014 at 11:20 am
UVa was the source of many spurious temperature reconstructions when Mann degraded its faculty.
(I know that allegedly he who would pun would pick a pocket, but couldn’t resist.)
period.
Bernie Hutchins says:
June 11, 2014 at 9:17 pm
Sadly, it’s a typical 1sky1 comment. Big on claiming how much he knows, full of opinions, and totally lacking in any kind of citation, worked examples, quotations, or facts.
Since you have given us absolutely no evidence that the ocean is a “low-pass filter” for temperature, and since the ocean responds to solar variations on a daily and an annual basis, and many folks claim that it responds on an 80-100 year basis, it doesn’t take a signal processing engineer to know that a low-pass filter wouldn’t do anything at all like you claim. Instead, a low-pass filter would also cut out the annual and daily cycles. You do understand what “low-pass” means, right?
Of course, you don’t provide any more facts, citations, worked examples, or evidence than 1sky1 did … and understandably so, given the ludicrous nature of your claims.
If you and 1sky1 are an example of the signal processing engineers these days, god help us all. Where I come from, signal engineers actually demonstrate that a given low-pass filter exists before they start bothering other people with their theories about the putative filter … and they provide data, facts, observations, and citations to back up their theories.
So you and 1sky1 showing up with nothing in hand but your Johnsons and your big mouths doesn’t impress me in the slightest. I know real signal engineers.
Finally, you need to hone your reading skills. I said:
Since I used his method, if you have problems with the method, you’re talking to the wrong guy. I didn’t pick the method, Nir Shaviv did. Go whine to him, maybe you can convince him you know your tailpipe from a hole in the ground. Me, not so much …
w.
Konrad says:
June 12, 2014 at 2:51 am
Konrad, I’ve been through this before, but you still don’t seem to understand. I’m not the one who is claiming that there is an 11-year solar cycle in various climate datasets. That would be Nir Shaviv and a host of others. I am using their own data and methods to show that they are wrong.
So I’ll thank you to take your unpleasant “straw man” claims elsewhere. I’m not creating a straw man. I am falsifying scientific claims that have wrongly gained currency in the scientific literature.
And falsifying such claims is a legitimate and valuable scientific enterprise. If you don’t like it, then you’re not actually a scientist, because that’s what scientists do.
And if so, if you think such falsification is “stabbing the 11-year straw man”, then what are you doing here? Why aren’t you off where people are doing something important, if this is just straw man stabbing? Truly, if you believe that, take it somewhere else … because whining about straw men here is going to go nowhere. I’m clear on what I’m doing.
w.
Willis Eschenbach says:
June 12, 2014 at 11:28 am
OK, I said no more drawing back in, but I’m not starting a new line of inquiry by stating that IMO 1sky1 makes a good case.
Thomson & Emery’s “Data Analysis in Physical Oceanography” (2nd edition) has this to say on page 519:
“In the ocean, seawater acts as a form of natural low-pass filter, attenuating high-frequency wave or acoustic energy at a much higher rate than low-frequency energy.”
Granted, this refers to sound rather than EM radiation propagation, but IMO tends to support 1sky1’s case.
Willis Eschenbach says:
June 12, 2014 at 11:28 am
Big on claiming how much he knows, full of opinions, and totally lacking in any kind of citation, worked examples, quotations, or facts.
——————————————————-
Despite my limited statistical knowledge, the issue here appears to be the significance level.
If you have a process driven by several parameters plus noise, correlation values must be generally lower than in the single parameter case.
take, for example a function
f = sin(t) + 2 cos(t) + noise(t)
where f is driven by 2 influences and we are correlating only with the a representation of the first sin(t). The correlation value then can never be higher than 1/3. Accordingly significance values assuming a single parameter process are meaningless.
The other processes have to be either reduced before correlating (removal of trends, removal of known drivers such as ocean cycles, volcanoes, etc.) or included in a multi-parameter estimation.
milodonharlani says:
June 12, 2014 at 11:49 am
Dear heavens, don’t go to the dark side, think about what you are saying.
You are saying that something which acts as a low-pass filter for sound at a frequency of say 40-4000 hz will therefore also serve as a low-pass filter for a thermal variation at a frequency of 0.0000000029 hz … do you really believe that? And if so, what is the theoretical framework connecting the two phenomena?
What’s next? Are you going to claim that the low-pass filter in my radio’s equalizer, which like the ocean acts as a low-pass filter for sound at a frequency of say 40-4000 hz, will therefore also serve to attenuate 11-year thermal variations? Because that makes about as much sense.
And 1sky1 doesn’t have a “case”. He has a trivially tossed-off claim that the ocean selectively suppresses 11-year cycles but doesn’t affect 1-day or 1-year or 80-year cycles. If he had advanced even one tiny scrap of evidence in support of that he’d have a case, albeit a weak one.
But right now, all 1sky1 has is a mouth. Oh, and his Johnson in his hand. And to date, despite lots and lots of opinions, and claims as to how brilliant he is and how stupid we all are to not recognize it … a big mouth with nothing in hand but his Johnson is all he’s ever displayed here. Perhaps he’s allergic to data and observations, I don’t know.
My favorite time was when I asked him to actually run the analysis he was so strongly urging on me, so I could see how to do it right.
Paraphrasing, of course, he claimed I was trying to get him to perform his valuable work and use his stupendous intellect for free, and that if I wanted him to actually back up his words with observations or data or actual analyses, I’d have to pay him to do so … my advice is avoid him, milodon, he’s bad news.
w.
I haven’t read his comments often enough to know 1sky1’s history, which I have no reason to think you have not accurately characterized. Maybe “case” was too strong a term, but I don’t see a reason to reject low pass filtering effect out of hand. Climate science still lacks basic research.
However, comparing a radio equalizer to seawater isn’t a convincing comparison IMO. Obviously there’s a big physical & energetic difference between the filtering of sound waves & photons, but the same applies to the media of seawater & electrical device parts.
An experiment with optical back-scattering frequencies on seawater with added particles also showed a low-pass filter-like response.
http://iopscience.iop.org/0022-3727/33/4/306;jsessionid=51D0BEC7FB96B43F90239342314A2573.c1
Water molecules absorb in the UV, so they “filter” at the high end of the EM energy spectrum. The effect of seawater of course depends upon its surface & subsurface conditions & the dissolved materials it contains.
I should just let 1sky1 elucidate his own position.
Willis,
I may well have misunderstood. I thought you were saying that you couldn’t find any 11 year cycle, and I thought 1sky1 had made a coherent comment (hence my characterization as a “carefully formulated remark”) in support of your findings, if not your methods. I in turn saw his analysis as consistent with a filtering viewpoint, also supporting your finding if not your methods.
That’s all I was offering. You over-reacted.
Manfred says:
June 12, 2014 at 12:23 pm
Manfred, I guess I have to say it a number of times before people get it. I used Nir Shaviv’s methods and data. If you have a problem with the method, you are in the wrong bailiwick. I didn’t pick the method, so you should go complain to the man who did.
Finally, did you miss the part where I said:
I don’t care in the slightest if folks don’t like my methods. When I looked at Gleissberg’s claims, I used Gleissberg’s methods. When I looked at Holgate’s claims I used his methods. When I looked at the Parana River claims, I used their methods. And in this analysis I’ve used Shaviv’s methods.
So if you think my methods are wrong, Manfred, I’ve already invited you and 1sky1 and bernie and all the rest to use your own oh-so-brilliant methods that avoid all of the obvious and stupid mistakes you claim I’m making, and to grab a climate dataset and apply your whiz-bang math and show us the claimed 11-year cycle.
Unfortunately … y’all either can’t read, or you would rather try to impress me with theory. I don’t care about the theories. Oh, they’re interesting to pass the time with, I don’t mean they’re a bad thing, and I often learn from them either what to do or what to avoid.
But all of that is miles away from the subject of this post. Either someone can demonstrate the 11-year cycle exists in a given dataset as demonstrated by a given method, or they can’t.
And to date, no one has demonstrated such a dataset and method, include all of you big-brained theorists out there telling me where my method is all screwed up. You’re talking to the wrong guy. Ring up Nir Shaviv and get on his case, it’s his method.
That said, your underlying claim about significance in multi-variable process is correct. However, without having any idea of either the size or the nature of any possible confounding factors it’s very difficult to know where to go with that claim in actual practice.
However, you’ve picked a very poor example. Ignoring the error term, your equation is
f = sin(t) + 2 cos(t)
Subtracting and squaring, we get
(f-sin(t))2 = 4 cos(t)2
Using the identity that
sin2 + cos2 = 1,
the equation reduces to
(f-sin(t))2 = 4 (1 – sin(t)^2)
so we can eliminate one of the two variables. Just sayin’ … pick another example.
In the real world, however, this issue is usually dealt with through some kind of filtering, whether Fourier, or “folding” as Shaviv did, or one of many, many other methods, some devised for one peculiar unique situation and others of general utility, to clarify the muddy waters so that we are only looking at the signals of interest. The purpose of these filters is to attenuate the other confounding factors so that they don’t significantly affect the outcome, and in general, they work surprisingly well.
Best regards,
w.
milodonharlani says:
June 12, 2014 at 1:19 pm
I reject it out of hand because there is no apparent filtering out of daily or annual signals, which is the definition of a low-pass filter—it attenuates the daily and annual higher-frequency signals.
w.
Willis Eschenbach says:
June 12, 2014 at 1:26 pm
I used Nir Shaviv’s methods and data.
——————————————————-
No you didn’t,
your figure 3 (I was talking about) was your method. Shaviv did a correlation with linear trends and a ENSO component removed (his figure 4).
And about figure 5, you were expanding thereafter in your comment, you wrote, it looks “so convincing”.
Of course, I would agree with the point that data and code should be available for verification as a verification or expanding analysis of the sea level data would be very interesting to see..
Willis said June 12, 2014 at 1:31 pm in part in reply to milodonharlani :
“…I reject it out of hand because there is no apparent filtering out of daily or annual signals, which is the definition of a low-pass filter—it attenuates the daily and annual higher-frequency signals….”
A length of copper wire is a low-pass filter if your signal source is a flashlight. It’s the same with any frequency as high as 1/11-years striking the ocean. You could likely DETECT the attempted invasion, the input, AT THE INTERFACE (the light beam striking the metal, or a daily or yearly temperature change at a suitably limited ocean surface layer). But that’s low-pass – IF you have correctly located the filter output point, the signal does not get through.
Maybe in coming years Argo floats will provide observational data adequate for detecting an 11-year signal in ocean temperature, to go with the rainfall data for which the CACA Team has been more willing to allow a solar effect, or possibly so far as to admit the possibility of regional warming effects.
Still, solar activity & earth’s modulation of irradiance into insolation have been shown to the satisfaction of most since the 1970s to play an important role in climate on longer time frames.
Bernie Hutchins says:
June 12, 2014 at 1:14 pm
Dang, did I misread his comment? Hang on while I find it again …
Bernie, please, show me one fact in there. All we have are claims. There’s no analysis. There’s no data. There’s no examples. It’s 1sky1 once again making unsubstantiated claims. Some sub-set of those claims are likely right, but without a scrap of data or citation, there’s no way to know.
In addition, the maximum correlation in Figure 3 is not lagged at all, it’s at t = 0. What “LAGGING relationship” is he claiming when max correlation is with no lag at all?
Also, as is totally typical with 1sky1’s posts, he never, ever tells us or shows us how it should be done. Re-read his comment. It is confined entirely to how I’m doing things terribly wrong. Well, maybe so … but until a man can demonstrate that he can do it right, I must confess that I pay little attention to his claims that I’m doing it wrong. Particularly in this case since I’ve asked and he’s refused to show us how to do it right, more than once. He’s had a variety of excuses, including that I’d have to pay him to do such a complex analysis …
It’s actually quite curious. It seems he’ll tell me that I’m doing it wrong for free, but he wants money to tell me how to do it right.
In any case, his point seems to be that because the power spectra of sunspots and sea surface temperature don’t overlap much, it’s inappropriate to use standard significance levels for correlation.
To see why this is incorrect, let’s suppose the opposite were true and their spectra DID mostly overlap. In order to do that, the temperature would have to show a peak in the spectrum around 11 years … and of course, at that point we’d get high correlation, and from that we’d conclude that the sun was indeed affecting the temperature.
And this means that the fact that the spectra don’t overlap much is a SYMPTOM of the lack of a physical effect. If there were such a physical effect, if the 11-year solar cycles actually were affecting the SST, the spectra would overlap much more, the temperature data would be more narrow-band.
In any case, Bernie, if 1sky1 wants to show us the right and proper way to deal with what he calls the “LAGGING correlation” in Figure 3, which isn’t lagging, I’m all ears. I’ve made the offer up top, use any methods that you might think are appropriate. So until he stops his incessant whining about how I’m doing it wrong, wrong, wrong and actually shows us how to do it right, I’ll continue to mostly just ignore his postings.
w.