Guest Post by Willis Eschenbach
Dr. Nir Shaviv and others strongly believe that there is an ~ 11-year solar signal visible in the sea level height data. I don’t think such a signal is visible. So I decided to look for it another way, one I’d not seen used before.
One of the more sensitive signal analysis tools in our arsenal is the Fourier transform. If we have a complex signal, like say the sunspot signal, Fourier analysis allows us to see just how strong the different frequencies are that make up the signal. To start with, Figure 1 shows the sunspot record.
Figure 1. New SILSO monthly sunspot record.
As you can see, there is a clear cyclical signal. However, the cycles vary in length. A Fourier periodogram reveals the strength of the various underlying signals:
Figure 2. Fourier periodogram of the data shown in Figure 1. Shortest period shown is four years, as there are no strong cycles with shorter periods.
As you can see, most of the power is in the 11-year and nearby cycles. There is cycle strength out to twelve years or so. There is also a second smaller group of cycles with a period of ten years, of about half the strength of the 11-year cycle.
Now, if there is actually a solar cycle in the sea level height as Dr. Shaviv believes, then it should peak somewhere around 11 years. To look for such a cycle, I decided to look at the sea level records from the tidal stations of the world. These are available from the Permanent Service for the Mean Sea Level. For your convenience in investigating the question, I’ve collated them as an Excel worksheet here.
I like to have an absolute minimum of three cycles of data to use for my longest term analysis. So I started by selecting all of the tide station datasets that have sixty years or more of data, to allow me to look at cycles up to about twenty years. There were 199 such records. Here are some sample periodograms of four of these longest tide records.
Figure 3. Four periodograms of long-term tidal records. Shortest period shown is four months. The scale on the left is the range (maximum minus minimum) of the fitted cycle as a percentage of the range of the underlying tide data.
The largest period in the tidal records, as we might expect, is a one-year cycle. There is also a smaller cycle visible at half a year (six months). However, as you can see, there is no readily apparent strong 11-year cycle, although Swinoujscie (top right) has a small hint of an 11-year cycle … or it may be a random fluctuation.
Now, the averaging of tidal data has some large problems. The different locations have widely varying tidal amplitudes, so the large swings tend to swamp the averages. As a result, I decided to average the periodograms rather than averaging the data. Since all of the periodograms are expressed in scaled units as percentages of the range of their individual underlying datasets, they are directly comparable. And since the random variations would average out, I figured that averaging them should reveal even small signals. Figure 4 shows the 199-periodogram average:
Figure 4. Average of the periodograms of the 199 long-term tidal station records. Note that the error bars are not the error of the mean, which is much narrower. Instead, they reflect the spread of the underlying individual results.
As with the four individual periodograms, the average clearly shows the one-year and the six-month cycles. And as expected, the averaging of so much data allows us to see even very small cycles. I note, for example, a cycle of a bit more than three and a half years. I’ve noticed this same signal before in other natural datasets, and I’ve never discovered its origin.
There is also a similar-sized small peak visible at about six and a quarter years, also of unknown origin.
But the purported ~ 11-year solar-related cycle? Nowhere to be seen. Not a hint, not a twitch.
Conclusion? If there is any ~ 11-year signal in the sea level height, it is so small as to be lost in the noise.
That was a main problem that I had with Dr. Shaviv’s study. He stated that there appeared to be a cycle in the short satellite sea level height data, and he claimed it was a solar cycle … but for me that’s backwards. For me, the starting point for investigation has to be noticing some verified unexplained anomaly in the actual observational records. First we have to find something unusual, then we can speculate as to its causes and consequences. For example, just what is the odd 3+ year cycle in Figure 4? Now that we know that cycle is real, we can speculate and investigate its origins.
So for me, until there is evidence of an actual ~11 year cycle in the sea level height, any speculation as to the possible solar nature of said unobserved cycle is wildly premature.
And that’s the story of the missing ~ 11-year cycle.
w.
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One of the more prevalent features of those trying to sell you something, or indeed those engaged in ideological thinking, and it applies to climate change right down to the core of the IPCCS terms of reference is to slip in an unproven assumption unnoticed as part of what purports to be a discussions about something else.
The IPCC itself has terms of reference that can be couched very simply – to examine the magnitude and effects of human induced climate change.
Never to examine whether there actually is any human induced climate change.
This appears to be the same – to look at subset of a problem that slipped in as an a priori assumption.
‘How bad is the 11 year cyclic influence of the sun on sea levels’ does not allow one to comment on whether there actually is such an influence. In fact the way the question is phrased is designed to move the discussion away and on from that question.
“Have you stopped beating your wife?”
Most prosecuting attorneys prefer “when did you stop beating your wife?”
I do agree with Leo to some degree,but I think Willis question is a fair one because, in this case, he’s looking to find evidence relative to another person’s working hypothesis, not stating the fundamental research question.
Well, the IPCC also appears to have borrowed from another legal saw: “When the facts are on your side, pound the facts; when the Law is on your side, pound the Law; and when neither the facts nor the Law are on your side, pound the table!”
The IPCC and it’s zombies seem to have the “pound the table” bit down…
Shaviv is a sceptic regarding AGW. However, he’s also an astrophysicist and, as such, more or less is constrained to be a theorist first if he wants any other physicists to pay attention. Despite the clear logic of arguing that empirical evidence should take precedence, as Willis does, many scientists will disregard empirical evidence in favor of a theory when there is a conflict. They then look for “evidence” of the theory in the data and astonishingly, they often find it. A theory is an explanation, while a conflict with data is a problem. The nice thing about theories is that they “predict” things, which one can then obtain a grant to go look for. The Higgs boson is a first rate example of this. Consider the cost of the LHC.
Looking for 11 year signal in climate events is a waste of time, since it is based on the sunspot numbers which have no polarity. Polar fields, north and south hemisphere sunspot polarity are all 22 year periodic events.
Sun has 22 year periodicity, full stop.
22 year periodicity can be found all over place, global, land and ocean temperature, the Earth’s core magnetic field, tectonics etc.
http://www.vukcevic.talktalk.net/5Spectra.gif
Vukcevic,
I totally agree. The solution is to restore the missing 22 year Hale cycle to the sunspot record. The missing low frequency polarity signal can be added to the sunspot count by simply listing all even number cycle sunspots as positive sunspot numbers and turning all odd number sunspot cycle counts into negative sunspot numbers.
Hi Mr. Mulholland
Further problem is that the most of climate data analysed are presented either as annual or monthly sequence of numbers. Sun doesn’t work on 30/31 or 365 days, its effect is directed at the Earth with a peak influence at around 27-28 days depending where in the sunspot cycle sun happen to be (latitude dependant differential rotation)
http://www.vukcevic.talktalk.net/LFC7.htm
This would make a year about 13 ‘solar months’ long, not 12, originally it was 10, then 11 followed by the current 12 (blame the Roman emperors). Yes I know, I could be accused of astrology; no solar rotation has nothing to do with 13 signs of zodiac!
And the 13 months of the Lunar cycle.
And some trivia for you. Manetho, the 3rd century BC Greco-Egyptian historian said the Egyptians originally counted Lunar years (ie: Lunar months) instead of Solar years. This resulted in human lives that were 900 or so years long, as is to been in the early biblical record.
Given that the moon’s gravitational effect on tides is I think 5 times greater than the suns (because it is much closer), I would have expected a lunar component as well. There are a variety of lunar cycles which I think repeat every 18.6 years.
Assigning a sign to the sunspot number is meaningless and just introduces a spurious 22-yr cycle. Take random data between 0 and 1 assigned to each month for 341 years. Invert the sign for every 11 years (132 months), run the spectral analysis and, presto, behold the beautiful 22-yr cycle peak.
And, in addition, the polar fields change sign at solar maximum, not at minimum
Leif,
So there is a 90 degree phase difference between the magnetic signal of the 22 year Hale cycle and my spurious reconfiguration of the sunspot count data?
No, it is more complicated than that:
The polar fields and the solar wind change at solar maximum, but the sunspot polarities in each hemisphere change at solar minimum, and at any given time the sunspot number is made up of spots in both hemispheres with opposite polarities, so no net change. This whole idea of assigning a sign to the total sunspot number which is made up of [approximately] equal number of spots in the two hemispheres with opposite polarities is meaningless.
There is nothing odd about 90 degree phase difference, it is found in all oscillating systems, from pendulum and electric circuits to the N. Atlantic (AMO- Arctic atmospheric pressure)
The Sun is not an oscillator and there is no 22-yr activity cycle.
https://journals.uair.arizona.edu/index.php/radiocarbon/article/download/1450/1454
THE SUN AS A LOW-FREQUENCY HARMONIC OSCILLATOR …
That they claim so does not make it so. There is a difference between a mathematical description and actual physics. A physical harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement. What would that force be? We know of no such force.
It looks like the sync function is smeared over this data. This indicates you perhaps didn’t window the data. Did you window the data?
http://www.physik.uni-wuerzburg.de/~praktiku/Anleitung/Fremde/ANO14.pdf
(or just use google)
Peter
Hi Mr. Sable
If you are referring to my spectral graphs, the analysis is not result of the fast Fourier transform (FFT). Analysis is done by a method developed for analysing audio signals, based on correlation coefficients employing 90 degree phase shifts. Each data set although only had 131 samples, it is extended with zero front and back symmetrical padding to 2000 elements in total (standard I used elsewhere).
Paper? Source code?
You are going to have edge effects with zero padding, and the edge effects depend on how far the signal is away from zero at the edge. Have you verified for edge effects? In general those sudden changes produce a sync signal in the frequency domain…
Peter
Mr Sable
Thank you for your comments, I am well aware of the edge effects and windowing procedure, but for short data series as in this case, windowing would have significant reduction effect on the mid range (as 22 year is) periodicities. I prefer to keep original data as it is and ignore as a noise anything that falls below 6db of the peak component.
If you are up to challenge, I would like you to suggest data series (available on line) of the similar length to the above, than both of us do spectral analysis and compare the results.
I am looking forward to your reply
Hmm…. No response from Mr. Sable; as it often happens many commentators are quick to criticise others but nowhere to be seen when challenged to come up with goods themselves.
It’s the nature of this forum, you can’t easily track responses especially on old topics.
Sure, why not. Why not the actual data above? Why are you unwilling to publish your source code and data?
If you have for example a ramp function, the “noise” of the edge effects is huge, and pretty much takes over the analysis. Your 6db won’t help you. Since you don’t show the time-domain series of this data, I don’t know if there’s a ramp function. There certainly is for temperature, it is going up…
There are other methods than windowing. You can (1) reflect the signal in time and thus make it pseudo periodic (an option for some matlab filter implemetations but not AFAICT FFT), (2) work on the difference of the signal, (3), remove any DC component of the signal (detrending).
I’ve only got a window implementation done, it’ll take time to implement the other two. Which did you do?
I’m working on a “low frequency analysis” toolbox, which is necessary because all the defaults in R, Matlab, Octave, etc. are exactly wrong for this. (the defaults are okay for mid-frequency analysis).
Peter
Oh look, no response from Mr Vukcevic. However I assume he’s just not reading this thread anymore because it’s hard to read old threads.
In response to this challenge:
Here it is. Code that figures out what the resolution of period analysis is given the length of the data.
?dl=0
?dl=0
The simple answer is: It is very error prone to resolve any two periods whose differences in samples/period are less than two samples part across the length of the data. This seems to correspond well with the Nyquist criterion.
For example, if you are looking at 314 years of sunspot data, if you were to notice a peak at 41.5 years, this peak might actually be the result of peaks of multiple periods between 37 years and 48 years. It could be a single component at 41.5 years, but you can’t tell. Note that for 37 years there’s 8.5 samples/year and for 48 years there’s 6.5 samples a year.
In general I wouldn’t trust any periodogram that attempted to show periods of the length of the data divided by 5. The errorbars get extremely large above 5. For example with 314 years of sunspot data, 314/5 = 63 years. Note that the actual range of combinations of periods that could result in this signal is from 52 years to 79 years. Pretty large error bars.
Here’s two graphs that you should test your analysis code against. The first tests the resolution of the process using sine waves that are very close together (2 samples/period close), and the second shows analysis of sunspot data with an overlay of sine waves created at the size and period of peaks found in the sunspot data. I’ve taken the liberty of putting errorbars based on +/-1 sample/period from the observed peaks.
This should all run in octave and probably matlab. Source code here (any files with “-” in them are scilab and should be ignored):
https://www.dropbox.com/sh/xsu1mr76bqhlgz1/AABJTKn4Pj96YVjTyfbkhA_ba?dl=0
And in particular these two files of code and the file of period resolution data I created that you can import into your tool of choice:
https://www.dropbox.com/s/5tk2rjdl8ki6je0/vallowfrequencyanalysis.m?dl=0
https://www.dropbox.com/s/d46k0v71jiw563m/testlowfreqanalysis.m?dl=0
https://www.dropbox.com/s/92yulrwkswvhq2k/test-sin-res.csv?dl=0
best regards,
Peter
While I think it unlikely that there is a detectable relationship between sunspots and sea level, I’m not sure this is how you would detect one if it did exist.
The effect of solar via clouds is always going to be slight – even if it exists. It would be like looking for a candle flame when said candle is standing in front of a floodlight. Not surprising that orbital characteristics dominate. Allowing for argument that solar has an effect, then we might expect c.11 year variations in the rate of rise in sea level, i.e. accelerations of the overall trend, not of the sea level itself.
Twentieth century sea level: An enigma, A Paradox, Another example of the cult of CAGW’s shenanigans.
Willis,
You cannot find a correlation between ocean level rise and solar changes as the majority of the ocean level rise is due to seagate manipulation of the ocean level satellite data. Tidal gages, the earth’s rotational speed changes, and mass balance and maximum possible thermal expansion support the assertion that the ocean level is rising at 0.5 mm/yr to 1.2 mm/yr, not 3.2 mm/yr. 3.2 mm/yr is impossible based on mass balance and thermal expansion.
There are four fundamental problems with ocean sea level.
1. Sea level rise is a fundamental pillar to push AGW madness in the climate wars. When the Envisat satellite data shows the sea level is falling, the solution is to just change the data without explanation. (See Seagate link below.)
2. The sea level rise prior to the recent fall cannot be explained based on mass balance and/or thermal expansion. Something caused the oceans to expand. The something is now reversing. This is a real paradox. The warmists do not include a breakdown of the estimated physical reasons for the 3.2 mm/year sea level ‘rise’ as that would force them to acknowledge a sea level rise of 3.2 mm/year that is physically impossible, if sea level rise forcing is limited to more water in the ocean (mass balance) and thermal expansion.
3. The sea level increase does not track planetary temperature. It is too smooth.
4. The sea level increase does not track ice sheet volume. Greenland ice sheet mass has now started to increase. The increase for this year was 200 Gt.
http://joannenova.com.au/2012/05/man-made-sea-level-rises-are-due-to-global-adjustments/
Man-made sea-level rises are due to global adjustments
ftp://falcon.grdl.noaa.gov/pub/bob/2004nature.pdf
http://www.pnas.org/content/99/10/6550.full.pdf
Envisat’s satellite failure
http://www.esa.int/Our_Activities/Observing_the_Earth/Envisat/ESA_declares_end_of_mission_for_Envisat
http://wattsupwiththat.com/2012/04/12/envisats-satellite-failure-launches-mysteries/
Current Surface Mass Budget of the Greenland Ice Sheet (Note the increase of 200 Gt this year)
http://beta.dmi.dk/en/groenland/maalinger/greenland-ice-sheet-surface-mass-budget/
Seagate
http://www.21stcenturysciencetech.com/Articles_2011/Winter-2010/Morner.pdf
I know it’s a bit boring & deja vu. I still remember that marvelous BBC2 Horizon programme 35/40 years ago which was all about the Sun & Sunspots, as we then knew the science of the day. It may have been coincidence, but they drew examples of things like the rise of Beatlemania & the rise of skirt hemlines, with rises & falls of Sunspot numbers, & much else! As an engineer I am no supersticious chump, but I still have a quiet hunch that the big shiney ball thingymabob in the sky, that possesses 99.9% of the mass of the Solar System, has more of an influence upon this little planet than most people like to think. Human beings are fallible creatures & the brain can be influenced by many things if it’s not aware! Could it be that a rise in Solar activity over the past few years will match the rise in greenalism, followed by a decline in greenalism following the decline in Solar activity through cycles 24, 25, & 26 +? May be, may be not, who knows? Perhaps I’ll ask Big Al when he’s finished counting his $squillions!
This engineer tends to agree and notes that cyclical mechanisms tend to manifest on a spinning planet with an orbiting moon and lots of surface fluid all orbiting that dirty great star with a set of other planets and various other interplanetary detritus especially when we know there are sun spot cycles and solar polarity cycles and who knows what other cyclical phenomena in evidence.
Well! Next you’ll be saying that because water vapour is 95% of the greenhouse gases then it’s more important than CO2. Heretic!
Willis,
It’s inconceivable that there should be no correlation at all between sea level rise and the solar cycle. But, clearly, the effect will be tiny: 11 or 22 years is a very short period and the oceans are vast.
You probably need to look at the global average rather than individual records. And, because the effect will be very small, you need a more precise measure: the rate of change, rather than the actual level.
Holgate published a graph showing the rate of change for the 20th century. Steve McIntyre commented on the graph:
“… The maxima and minima of the solar cycles seem to match the fluctuations in sea level rise rather uncannily. While the resemblance is impressionistic (I don’t have a digital version of Holgate’s series), offhand, I can’t think of any two climate series with better decadal matching. I think that this resemblance is pretty obvious….”
http://climateaudit.org/2007/02/11/holgate-on-sea-level/
Here the two records are plotted together by David Archibald:
http://wattsupwiththat.com/2009/04/07/archibald-on-sea-level-rise-and-solar-cycles/
I know you claimed to disprove this correlation. Your proof relied on a very low R2 value. But R2 is very limited because it assumes a linear relationship. A low R2 could simply mean that the correlation is complex and non-linear, which is almost certainly the case.
I’ve run a few hundred random graphs and none showed a correlation remotely as good as this.
So, here’s a suggestion: why not run a periodogram on Holgate’s rate of rise data? I would guess it would show a pretty strong peak around 11 years.
Chris
argument from incredulity
“You probably need to look at the global average rather than individual records. And, because the effect will be very small, you need a more precise measure: the rate of change, rather than the actual level.”
If you’re trying to tease out a small signal from hopelessly noisy data, that would be a good way to do it if you don’t mind fooling yourself. (1) Taking averages involves loss of information, and (2) derivatives are less precise, not more precise than raw numbers.
3.5 year X 3 =~11
6.25 X 2 =~11
1 =X 11 =~ 11
0.5 x 22 = 11 and so on all the way to 0! But why does it mean or are you trying to say?
The one year “period” and its sub harmonic at two years is a spurious signal known as an alias. It is (most likely) caused by the sampling of the signal at intervals close to a day or half a day.
“The one year “period” and its sub harmonic at two years”
Ed, Willis calls out signals at one year, and half year periods. sub-harmonic at two? typo?
And how would day or half day sampling cause an alias at 365 days?
The simple Fourier transform is not ideal for something with a variable period, it may be better first to resample the data so that all cycles are exactly 11 “years” long (1 “year” = 1/11th of the period between successive cycles).
This is the classic problem of detection of a weak signal in background noise. In sonar systems one chops up the data into a sequence of segments and looks for the signal in each segment, an operator would only make a visual detection on several segments with a consistent signal.
There are umpteen high performance (and therefore very complicated) algorithms for this kind of thing, but one needs either very expert knowledge or blind faith to put any trust in them, so I’d stick to the sonar operator method, must see a persistent signal in a sliding sub-window of data.
climanrecon August 19, 2015 at 3:41 am
The Fourier transform finds the solar signal clearly and evidently. Why would it not find the effect of the solar signal?
w.
I have one suggestion as to why the 11-year signal is not visible. In Dr. Shaviv’s paper his equation (2) represents the solar term as cosine function with amplitude of “a”. Later down in the paper he reports that their model uses a value of 2.5mm for “a”. In other words, the total amount of sea level change attributable to solar (according to Dr. Shaviv’s paper) is only +-2.5mm.
Now, I am a little confused as to the vertical axis in your plots as they are in percentages of the total range, not mm. If I interpreted the data in your spreadsheet correctly, this range is typically somwhere in the neighborhood of 500mm peak to peak. Dr. Shaviv’s model says there is a 5mm peak-to-peak solar signal in there. If I’ve got your vertical axis wrong then please correct me.
I suspect that perhaps there is not enough accuracy in the tidal data (and/or too much measurement noise) to be able to see the signal, even if it is there. Can you check the vertical axis of some of your plots in mm to see if a 2.5mm signal would be above the noise level at 11 years?
I’m not that knowledgable about tides versus mean sea level…but there also might additional “noise” in tidal data because these are measurements made only along coastlines whereas the satellite data is (I presume) not.
Thank you Willis. After reading through your Kerfuffle with Dr Shaviv, I’d considered doing a Fourier Analysis on the sea level data, but since I haven’t done one for 30 years, I think it might have taken me six weeks to collect and learn a tool set. You’ve saved me that.
A few comments — none of which should affect your conclusions at all:
1. Sunspot creation seems to act like a relaxation oscillator. Relaxation oscillators often aren’t that great at timekeeping. So I find it a bit unnerving that your eleven year peak is so narrow. I suspect, but couldn’t prove, that that is an artifact of your analytic approach.
2. As vukcevic points out, there probably should be a substantial second harmonic peak in the sunspots around 22 years. Not there. Not that I know much about sunspots.
3. Your reasons for using tidal gauge are good ones, but you should be aware of the limitations of tidal gauges.
a. Their coverage is lousy — only at land-sea boundaries and mostly in the Northern temperate zone.
b. They are affected by seasonal wind, water temperature, air-pressure, and in some cases nearby river flows. That’s probably the one year signal you find.
c. Most, maybe all. are subject to local tectonic forces that are probably comparable to or possibly larger than sea level rise. We possibly won’t have that sorted out for many decades. Mostly these forces are probably either constant or have timeframes of centuries or longer. Shouldn’t affect your analysis I think
4. If I understand Dr Shaviv’s work (and mostly I don’t) he’s talking about the rate of change in sea level, not the sea level itself. I suppose it’s conceivable that there is a signal in the change (dh for lack of a less loaded term) that is somehow washed out of h which is what you are (I think) examining.
Anyway, Another nice paper.
P.S. If clarity of explanation is a valid criterion you beat Dr Shaviv by orders of magnitude. His exposition reminds me of a 1970s computer wizard who was noted for his complex verbiage. That guy once wrote an abominable 300 word paragraph that probably said, “Sometimes you have to use big words because small words won’t do”
I would have said:
Sometimes you have to use big words because diminutive words won’t do.
Apologies to the ancient website milk.com (if it still exists)
Before I read milk.com my vocabulary was small, now it’s big.
Willis,
Your approach here is practically guaranteed not to find any evidence of solar cycles in the data if such cycles exist. Your approach only demonstrates that the amplitude of seasonal tidal variation is far larger than interannual variation – something I think we could have guessed without the benefit of any analysis.
If you really wish to look at the evidence for or against a periodic interannual component in MSL with periodicity similar to solar cycle length, then you have to eliminate the obscuring effect of the seasonal variation; otherwise you are wasting your time. The easiest way to do this is to convert your monthly tide gauge data into annual differences for the same month e.g the February value is replaced by the change in February value from the previous year. This will deseasonalise the data and differentiate the data, while retaining the original periodicity of any oscillatory components. You can then carry out a Fourier analysis on the resulting series to find the dominant interannual periodicities.
You should then find clear evidence for quasi 11-year cycles in the data.
Paul
I would have thought the same thing but there is still (at best) a very weak solar signal in the short-term data. Shaviv, et al., reported:
But their attributions to ENSO and other non-solar cycle influences suggest an even smaller component directly attributable to solar forcing.
http://sealevel.colorado.edu/content/2015rel3-global-mean-sea-level-time-series-seasonal-signals-retained
http://sealevel.colorado.edu/content/2015rel3-global-mean-sea-level-time-series-seasonal-signals-removed
giving homework to Willis
Paul_K August 19, 2015 at 4:07 am
Thanks, Paul. I don’t believe for a minute that interannual variability obscures an 11 year signal. That makes no sense at all. In any case, I gave you the dang data in a most accessible spreadsheet form. Do the math, establish your case with actual calculations, come back when your idea has some observational support and we’ll talk.
w.
You are correct Willis.
However noise and accuracy issues in tide gauge data can obscure this signal quite easily. I said it above and repeat here again — I don’t think that tide gauge data is of sufficient quality to be able to see such a small signal (+-2.5mm).
I’m not taking sides on whether this signal is really there or not, I’m just saying that tide gauge data will not reveal the signal (if it is there) due noise and quality issues.
For example see here:
Hanan, John. The Difficulties in Using Tide Gauges to Monitor Long-Term Sea Level Change
International Federation of Surveyors, Article of the Month, July 2010.
(I was able to view this paper on Research Gate web site)
In essence what I think you have done is proven what is perhaps an unstated premise of Dr. Shaviv’s paper — that this signal was not visible prior to having satellite altimetry data. And again, I am not taking a position on whether the signal is either there or not.
wxobserver,
The whole point of Fourier analysis is that things like noise often operate at different frequencies than the signal you are looking for. There almost certainly IS noise associated with Tide Gauge data (and any other kind of sea level data) But, that noise is almost certainly not running at a frequency of 11 years. So, even though the noise might obscure the signal in the observed data, it won’t obscure it in the Fourier transform. Again, that’s the whole point of doing a frequency analysis like this.
Willis writes “So for me, until there is evidence of an actual ~11 year cycle in the sea level height, any speculation as to the possible solar nature of said unobserved cycle is wildly premature.”
I’m pretty sure that Dr Shaviv was never looking at solar activity vs sea level height. He was looking at solar activity vs the rate of change of sea level height. Two entirely different things…
Tim, he regressed his “harmonic solar component” (a sine wave) directly against the sea level, not against the change in sea level. Look at his equation 1. Clearly he is looking at sea level height.
w.
It doesn’t look like that to me. His equation is the differential of sea level as a function of time. Besides I think he explicitly mentioned it in his initial reply to you.
Re: change vs rate of change
If the signal contains sin(x) as Shaviv claims, then the derivative of the signal will contain sin(x)+pi/2 (aka “cos(x)”). You’ll get the same sinusoid, just shifted to the right 90 degrees.
… oops, make that sin(x) – pi/2
And you’ll see it if its the only signal that applies, but if there are other drivers of sea level then it’ll be lost. We know there are other drivers of sea level…
“First we have to find something unusual, then we can speculate as to its causes and consequences.”
Makes sense.
So, what are the known consequences of that 11 year solar cycle?
Can we please move on to something important like fraudulent adjustment of temperature data?
Willis: Do you have access to the the actual satellite data that Dr. Shaviv used in his analysis? Why should you expect that looking at tidal data, presumably on data on the continental shelf, would give the same results as measurements taken over the entire globe? Also, it would appear that you have not included tidal measurements from the southern hemisphere where there is much more ocean than land.
BTW what is the accuracy of the satellite data when it come to measuring sea level?
Walt D. August 19, 2015 at 5:00 am
Thanks, Walt. I just spent the last couple of posts discussing the actual satellite data. It is too short for Fourier analysis of an 11-year cycle, as it is barely over two solar cycles long.
Because the global signals can’t contain the signal unless at least some of the tidal gauges contain the signal.
I’ve used all datasets in the PSMSL data with records longer than 60 years.
Over what period and what area?
w.
According to NASA’s discussion of the JASON-2 mission,:
http://www.nasa.gov/mission_pages/ostm/overview/index.html#.VdS_aUukPwI
And further:
http://www.nasa.gov/mission_pages/ostm/spacecraft/index.html
According to NASA’s discussion of the JASON-2 mission, the best satellites can do is get within a few centimeters. Beyond that, it is adjusted by application of various corrections and assumptions:
http://www.nasa.gov/mission_pages/ostm/overview/index.html#.VdS_aUukPwI
And further:
http://www.nasa.gov/mission_pages/ostm/spacecraft/index.html
Sorry about the duplicated posting.
I thought Shaviv said you need to look at the first differential of the height data. It should show up in both if it were to exist but it might be worth the exercise.
Two things. First, if it exists in the first differential, it exists in the signal. Second, Shaviv regressed his sine wave against sea level height, not against the first differential. See his Equation 1 for confirmation.
w.
Willis –
I see that Dr. Nir Shaviv commented on your post “My Thanks, Apologies, and Reply to Dr. Nir Shaviv” on August 17, 2015 at 2:10 PM. Based on some of your comments here, it seems that maybe you missed his response.
I’d be interested on your reaction and rebuttal of his argument.
Thanks
Dan
DanMet’al August 19, 2015 at 12:09 pm
Thanks Dan. I read it, and I thought about it, and I decided to let it go. I understand what he is saying about using the integral to do the harmonic analysis. And he’s right, using a sine wave does simplify the analysis, because the integral of sin is – cos, and the integral of cos is sin. But all you get are answers about sine waves. You can’t use the integral of the sunspot data the way you can the integral of the sine wave. The integral of the sunspot data is NOT a simply 90° lead/lag as it is with the sin/cos.
And fitting a 12.6 year sine wave to a 23-year dataset doesn’t even pass the laugh test, especially as part of a six-parameter model.
For these and other reasons, I decided that we’re just too far apart on this question for further discussion to be profitable. Instead I’ve been looking to see if his purported cycle is real using averaged periodograms. I can’t find any sign of it.
Regards,
w.
3 1/2 yr cycles? That’s the run- up to US elections and attendant billiousness..
The issue raised by Willis is very interesting but there is no chance to show a correlation between the sunspot number and the sea level measured near the coastlines. To my knowledge, the only place where the correlation is possible is where baroclinic waves resonate with solar cycles. Where the resonance occurs the cross-wavelet analysis of sea surface height reveals two antinodes in opposite phase, as occurs in the North Atlantic for the 8-year period Rossby wave. Off the Cape Hatteras, the Gulf Stream leaves the eastern North American coast around 35°N. At the westernmost antinode facing east, along the subtropical gyre, the sea level oscillates on few centimeters (http://climatorealist.neowordpress.fr/
).
For periods between half a year and eight years, the forcing of these gyral waves is induced from the sequence of warm and cold waters conveyed by western boundary currents, and causes the oscillation of the thermocline of the gyre (the surface height anomaly is -0.0025 times the amplitude of variation of the thermocline depth). But these gigantic gyral waves also have the ability to tune with the long-period solar cycles of one to up to several centuries, as well as Milankovitch cycles that affect the occurrence of glacial and interglacial periods, throughout tens of thousands of years, while filtering out the effects of the best known, the 11-year solar cycle: the gyral waves resonate at 1, 4, 8, 64, 128,… year periods (11 yrs is too far from those natural periods, despite the large bandwidth of the 11-yr period cycle).
So, two good reasons not to see correlation with the 11-year cycle, the location of measurements and the selected solar cycle.
Jean-Louis Pinault August 19, 2015 at 5:43 am
Somehow, you know the only secret place on earth where a solar cycle would be visible in the ocean … and you know this how?
w.
Willis,
Solar cycles should be visible at the antinodes of quasi-stationnary baroclinic waves, i.e. along the subtropical gyres where the western boundary currents leave the coasts, inducing sea surface height (SSH) anomalies. Unfortunately, SSH series are not long enough to show such SSH oscillations. However, SST anomalies may be highlighted since SSH anomalies result from the thermocline oscillation: the deeper the thermocline, the higher the positive SST anomaly, and the shallower the thermocline, the lower the negative SST anomaly. The 128-yr SST anomaly forced from the Gleissberg cycle can be evidenced in the Northen Atlantic, from long SST series (http://climatorealist.neowordpress.fr/). The 11-yr period cycle is not perceptible but the 8-yr period cycle inherited from the tropical oceans is strong.
Willis Eschenbach August 19, 2015 at 9:31 am Edit
Jean-Louis Pinault August 19, 2015 at 10:23 am
Merci, Jean-Louis. So your claim is that you know the only secret place on earth where the solar cycle would be visible, but you don’t have the data to demonstrate that with actual observations …
Pass.
w.
Willis,
the lunar month should be an extremely powerful signal in your analysis, so where is it?
“The lunar month should be an extremely powerful signal in your analysis, so where is it?”
Interesting pointt, however, PSMSL data seems to be monthly (or annual) averages with daily/ monthly tidal fluctuations therefore averaged out. And in any case, Willis cut of his analysis on the low side at 4 months.
John A August 19, 2015 at 5:55 am
It’s monthly data … so a monthly signal is too short for much meaningful analysis. In addition it’s immaterial to this discussion, so I’ve started the analysis at four months.
w.
Oh,it should not be confused gravitational waves and baroclinic waves. I think that Willis is looking for baroclinic waves (which store or restore heat) resulting from forcing from the variation in solar irradiance.
Hi Willis,
I just wanted to make sure of a few things regarding your analysis.
1) For your analysis, does it matter that the data has underlying trends? I ask this as someone is not near well-enough versed in Fourier analyses. From what little I do know, I’m guessing it doesn’t effect anything, but I wanted to have this verified by someone who knows the nuts and bolts of this type of analysis.
2) One of the points raised by Dr Shaviv, if I understand his criticism of you properly, was that the signal should be present in the rate of sea level change, not necessarily in sea level itself. Would it be possible to extend your analysis into a rate of change? I still don’t expect there to be an 11-year signal, but it’s one of those things that you don’t know until you try.
3) You mentioned that you limited your analysis to data sets of sufficient length, which I agree is the proper way to do it. I was just wondering if there might be some spurious signals when the data is not subject to such a limitation, and that this might be why some people are misled into thinking a real signal exists.
Jimmy August 19, 2015 at 6:53 am
I’ve detrended all of the sea level data before Fourier analysis, as is the usual practice.
If it exists in the derivative it exists in the signal, because the signal is nothing but the cumulative sum of the derivative. Also, Dr. Shaviv did NOT regress his sine wave against the differential. He regressed it against sea level himself, meaning that he expects to see the signal in the sea level.
Spurious signals in sea level are a huge problem, and in fact you need more than three cycles to have confidence in your data.
w.
Thanks for the reply, Willis. You said “If it exists in the derivative it exists in the signal, because the signal is nothing but the cumulative sum of the derivative.” I’m having a little bit of trouble wrapping my head around this, which I think is because I lack a sufficient enough understanding of the fourier analysis. Do you have any good links for educating myself about it?
Swinoujscie is a site on the Baltic Sea coast, where Oder enters the sea. The Baltic Sea is quite isolated from the oceans. There is none or little sign of tides there. On the other hand, the capricious flow of Oder is likely to affect what happens there. So using Swinoujscie data in this context is not a good idea.
Land mounted tide gauges are generally quite inaccurate and, of course, local, also loaded with systematic errors. The satellite data, on the other hand, is truly global, telling us something about the behavior of the global ocean on our planet, also offering better and uniform accuracy of instruments used.
Solar cycles are driven by various mechanisms, internal and external ones. Interactions with Jupiter and Saturn show there. Observe that Jupiter’s year is about 11.86 earth years long. Saturn’s year is about 30 earth years long. Correspondingly, we see “11-year” (it’s not exactly 11, you see) and “60-year” oscillations in solar activity. The earth ocean may very well respond thermally to solar activity and dynamically to Jupiter’s and Saturn’s pulls. The question is how accurate we would have to be, to observe this.
Gus August 19, 2015 at 7:08 am
Thanks, Gus. No, what is not a good idea rejecting datasets because you think they don’t contain the signal. Before analysis you don’t know whether the solar signal is present in Swinoujscie, nor do I. Rejecting datasets based on your prejudices is not science.
That’s not true at all. You just made that up. A tidal gauge with a stilling well is very accurate. And they are not “loaded with systematic errors”, you made that up too. They typically contain a spurious trend because of continental uplift/subsidence. But over the short time in question (centuries) these are linear in nature, and thus are removed when the data is detrended prior to analysis.
Look, the data is sensitive and accurate enough to show us the tiny ~3.75 year cycle of unknown origin. Why would it not show us an 11-year cycle?
Yes, and if we had 60 years of it for Fourier analysis I’d use it in a heartbeat, with the usual caveats … but we only have about 23 years of satellite data, far too short.
w.
“>> A tidal gauge with a stilling well is very accurate. And they are not “loaded with systematic errors”, you made that up too. They typically contain a spurious trend because of continental uplift/subsidence. <<"
This ground movement is exactly what I'm referring to calling it "systematic error," because this is what it is. The other systematic error is the sinking (under its own weight) and thermal stretching of the gauge itself. I am not making any of it up. And, of course, there is also the locality problem. We know, from satellite observations, that the ocean does not behave uniformly, even when all ground movements are taken into account and subtracted from observations. We know, for example, that the ocean level rise rate is different in the southern hemisphere than in the north, or different in the Indian Ocean from what is observed in the Pacific. In the Pacific itself, there is a bulge in a part of the ocean that accounts for all ocean level rise, other parts of it subsiding.
And I see in your reply that you know of these problems and value, as I do, satellite measurements. So, we are not in disagreement here.
But you despair that we only have 23 years of satellite data, so you seek to use gauge data where satellite data is not available. I just don't trust old gauge data to any degree at all, when we're talking about global ocean level rise and other global ocean dynamics features, some expressed in terms of (1.7 +/- 0.6)mm/year. I don't see how you can make this kind of measurement, with this level of accuracy using gauges that you only have in a handful of points around the ocean's periphery and none at all in the middle of it. Satellite data, perhaps. Even here there are doubts about the error range and they are being discussed in the literature.
My preference is to admit that we don't have trustworthy, global data for more than 23 years back, so we can't say anything "trustworthy and global" on the subject. I agree that to extract an 11-year signal from a 23-year sequence is "stretching" credibility. We need at least a century of satellite observations, not only regarding this particular issue, but everything else claimed to be "global."
Sun spots, incidentally, are not a good measure of solar activity. There are better, more precise measures, such as 14C, 10Be and 18O production.
Sun spots, incidentally, are not a good measure of solar activity. There are better, more precise measures, such as 14C, 10Be and 18O production.
Actually not. The deposition of these radionuclide proxies are influenced by, among other things, climate itself. See e.g. http://arxiv.org/ftp/arxiv/papers/1003/1003.4989.pdf and http://arxiv.org/ftp/arxiv/papers/1004/1004.2675.pdf
“We have compared the yearly production rates of 10 18 Be by cosmic rays in the Earths polar atmosphere over the last 50-70 years with 10Be measurements from two separate ice cores in Greenland. These ice cores provide measurements of the annual 10Be concentration and 10Be flux levels during this time. The scatter in the ice core yearly data vs. the production data is larger than the average solar 11 year production variations that are being measured. The cross correlation coefficients between the yearly 10Be production and the ice core 10Be measurements for this time period are less than 0.4 in all comparisons between ice core data and 10Be production, including 10Be concentrations, 10Be fluxes and in comparing the two separate ice core measurements. In fact, the cross correlation between the two ice core measurements, which should be measuring the same source, is the lowest of all, only ~0.2. These values for the correlation coefficient are all indicative of a “poor” correlation. The regression line slopes for the best fit lines between the 10Be production and the 10Be measurements used in the cross correlation analysis are all in the range 0.4-0.6. This is a particular problem for historical projections of solar activity based on ice core measurements which assume a 1:1 correspondence.
We have made other tests of the correspondence between the 10Be predictions and the ice core measurements which lead to the same conclusion, namely that other influences on the ice core measurements, as large as or larger than the production changes themselves, are occurring. These influences could be climatic or instrumentally based. We suggest new ice core measurements that might help in defining more clearly what these influences are and-if possible to correct for them”
The data you’re using is composed of calendar monthly averages of some sort (the exact derivation of which we don’t know, calendar months are not equal). Your blunt instrument is picking out the interference pattern of 12 mashed up calendar monthly data points with something we know full well has a lunar dominant frequency.
This illustrates well the “Fallacy of Fourier”. It can often be used to indicate a suspicion for further investigation but never, ever to prove a negative. Usually it doesn’t work at all when the dominant real time base is close but not equal to the sample rate. All you end up with are spurious interference harmonics.
Sure enough, you’ve picked up the annual seasonal cycle, an expected subharmonic and bugger all else. Isn’t numerology wonderful stuff, hours of fun and frolics 🙂
However, I’m sure numerologists everywhere will be having a field day with this new dataset. Bring on the Bayesian nut brigade, oblique media fodder for months 🙂
No sooner said …
http://www.dailymail.co.uk/news/article-3203534/My-harvested-hackers-says-SNP-MP-included-list-millions-Ashley-Madison-users-released-massive-hack-infidelity-website.html
AJB August 19, 2015 at 7:24 am
And yet the Fourier analysis has no problem picking out the sunspot signal, which also has the exact same “12 mashed up calendar monthly data points” … if as you claim the months are a problem with the sea level data, why are they no problem with the solar data?
The “Fallacy of Fourier”? Is that a thing? Google finds exactly two entries for that, so I fear you’re just dressing up your own prejudices by wrapping them in quotes and pretending that they are widely shared.
As to whether Fourier analysis can “prove a negative”, nothing can prove a negative. Which is why my conclusion was:
Note that I was very careful to not say that the signal doesn’t exist, because we can’t prove that.
w.
I think AJB’s point was not simply that the data starts with mashed up months, but that it is mashed up months that have an imbedded dominant 29.5 day cycle (something that you don’t have to contend with in examining the solar data).
Atkers1996: Precisely.
Bedtime reading …
http://www2.ece.ohio-state.edu/~schniter/ee700/handouts/wavelets.pdf
… and yep, I’ll be sure to use italics next time lest we have more dressed up Google inspired impugnation. Did it try inferencing “Fourier analysis limitations” or similar. Nope, of course not.
Unless I am doing something wrong the SH SST shows a decent blip at around 11 years. I wouldn’t expect a large spectral anomaly associated with the 11 year solar cycle in of Earths climate metrics because TSI only deviates by 1 Watt over the 11 year cycle, but nonetheless it is there, whereas the 1 year cycle is associated with Earths axial tilt and the eccentricity of Earths orbit which causes a change in TSI of almost 100 watts over the course of a year.
http://www.woodfortrees.org/plot/hadsst3sh/from:1900/fourier/magnitude/normalise/to:100/plot/sidc-ssn/from:1900/fourier/magnitude/normalise/to:100
Willis, where’s the source code?