Guest Post by Willis Eschenbach
I’ve been listening to lots of stuff lately about tidal cycles. These exist, to be sure. However, they are fairly complex, and they only repeat (and even then only approximately) every 54 years 34 days. They also repeat (even more approximately) every 1/3 of that 54+ year cycle, which is 18 years 11 days 8 hours. This is called a “Saros cycle”. So folks talk about those cycles, and the 9 year half-Saros-cycle, and the like. The 54+ year cycle gets a lot of airtime, because people claim it is reflected in a sinusoidal approximately 54-year cycle in the for example the HadCRUT temperature records.
Now, I originally approached this tidal question from the other end. I used to run a shipyard in the Solomon Islands. The Government there was the only source of tide tables at the time, and they didn’t get around to printing them until late in the year, September or so. As a result, I had to make my own. The only thing I had for data was a printed version of the tide tables for the previous year.
What I found out then was that for any location, the tides can be calculated as a combination of “tidal constituents” of varying periods. As you might imagine, the strongest tidal constituents are half-daily, daily, monthly, and yearly. These represent the rotations of the earth, sun, and moon. There’s a list of the various tidal constituents here, none of which are longer than a year.
Figure 1. Total tidal force exerted on the Earth by the combination of the sun and the moon.
So what puzzled me even back then was, why are there no longer-period cycles used to predict the tides? Why don’t we use cycles of 18+ and 54.1 years to predict the tides?
Being a back to basics, start-from-the-start kind of guy, I reckoned that I’d just get the astronomical data, figure out the tidal force myself, and see what cycles it contains. It’s not all that complex, and the good folks at the Jet Propulsion Lab have done all the hard work with calculating the positions of the sun and moon. So off I went to JPL to get a couple hundred years data, and I calculated the tidal forces day by day. Figure 1 above shows a look at a section of my results:
These results were quite interesting to me, because they clearly show the two main influences (solar and lunar). Figure 1 also shows that the variations do not have a cycle of exactly a year—the high and low spots shift over time with respect to the years. Also, the maximum amplitude varies year to year.
For ease of calculation, I used geocentric (Earth centered) coordinates. I got the positions of the sun and moon for the same time each day from 1 January 2000 for the next 200 years, out to 1 Jan 2200. Then I calculated the tidal force for each of those days (math in the appendix). That gave me the result you see in Figure 1.
However, what I was interested in was the decomposition of the tidal force into its component cycles. In particular, I was looking for any 9 year, 18+ year, or 54.1 year cycles. So I did what you might expect. I did a Fourier analysis of the tidal cycles. Figure 2 shows those results at increasingly longer scales from top to bottom.
Figure 2. Fourier analysis of the tidal forces acting on the earth. Each succeeding graph shows a longer time period. Note the increasing scale.
The top panel shows the short-term components. These are strongest at one day, and at 29.5 days, with side peaks near the 29.5 day lunar cycle, and with weaker half-month cycles as well.
The second panel shows cycles out to 18 months. Note that the new Y-axis scale is eight times the old scale, to show the much smaller annual cycles. There are 12 month and 13.5 month cycles visible in the data, along with much smaller half-cycles (6 months and 6.75 months). You can see the difference in the scales by comparing the half-month (15 day) cycles in the top two panels.
The third panel shows cycles out to 20 years, to investigate the question of the 9 and 18+ year cycles … no joy, although there is the tiniest of cycles at about 8.75 years. Again, I’ve increased the scale, this time by 5X. You can visualize the difference by comparing the half-year (6-7 month) cycles in the second and third panels. At this scale, any 9 or 18+ year cycles would be very visible … bad news. There are no such cycles in decomposition of the data.
Finally, the fourth panel is the longest, to look for the 54 year cycle. Again, there is no such underlying sine-wave cycle.
Now, those last two panels were a surprise to me. Why are we not finding any 9, 18+, or 54 year cycle in the Fourier transform? Well … what I realized after considering this for a while is that there is not a slow sine wave fifty-four years in length in the data. Instead, the 54 years is just the length of time that goes by before a long, complex superposition of sine waves approximately repeats itself.
And the same thing is true about the 18-year Saros cycle. It’s not a gradual nine-year increase and subsequent nine-year decrease in the tidal force, as I had imagined it. Instead, it’s just the (approximate) repeat period of a complex waveform.
As a result, I fear that the common idea that the apparent ~60 year cycle in the HadCRUT temperatures is related to the 54-year tidal cycles simply isn’t true … because that 54 year repeating cycle is not a sine wave. Instead, looks like this:
Figure 3. The 54 year 34 day repetitive tidal cycle. This is the average of the 54-year 34-day cycles over the 200 years of data 2000-2200.
Now, as you can see, that is hardly the nice sine wave that folks would like to think modulates the HadCRUT4 temperatures …
This exemplifies a huge problem that I see happening. People say “OK, there’s an 18+ year Saros cycle, so I can divide that by 2. Then I’ll figure the beat frequency of that 9+ year cycle with the 8.55 year cycle of the precession of the lunar apsides, and then apply that to the temperature data …”
I’m sure that you can see the problems with that approach. You can’t take the Saros cycle, or the 54+ year cycle, and cut it in half and get a beat frequency against something else, because it’s not a sine wave, as people think.
Look, folks, with all the planets and moons up there, we can find literally hundreds and hundreds of varying length astronomical cycles. But the reality, as we see above, is not as simple as just grabbing frequencies that fit our theory, or making a beat frequency from two astronomical cycles.
So let me suggest that people who want to use astronomical cycles do what I did—plot out the real-life, actual cycle that you’re talking about. Don’t just grab the period of a couple of cycles, take the beat frequency, and call it good …
For example, if you want to claim that the combined tidal forces of Jupiter and Saturn on the sun have an effect on the climate, you can’t just grab the periods and fit the phase and amplitude to the HadCRUT data. Instead, you need to do the hard lifting, calculate the actual Jupiter-Saturn tidal forces on the sun, and see if it still makes sense.
Best regards to everyone, it’s still raining here. Last week, people were claiming that the existence of the California drought “proved” that global warming was real … this week, to hear them talk, the existence of the California floods proves the same thing.
In other words … buckle down, it’s gonna be a long fight for climate sanity, Godot’s not likely to show up for a while …
w.
THE USUAL: If you disagree with something that I or someone else said, please quote the exact words you disagree with, and tell us why. That way, we can all understand what you object to, and the exact nature of your objection.
CALCULATIONS: For ease of calculations, I downloaded the data for the sun and moon in the form of cartesian geocentric (Earth-centered) coordinates. This gave me the x, y, and z values for the moon and sun at each instant. I then calculated the distances as the square root of the sum of the squares of the xyz coordinates. The cosine of the angle between them at any instant is
(sun_x * moon_x + sun_y * moon_y + sun_z * moon_z) / (sun_distance * moon_distance)
and the combined tidal force is then
sqrt( sun_force^2 + moon_force^2 + 2* sun_force * moon_force * cos(angle))
DATA AND CODE: The original sun and moon data from JPL are here (moon) and here (sun), 20 Mb text files. The relevant data from those two files, in the form of a 13 Mb R “save()” file, is here and the R code is here.
EQUATIONS: The tidal force is equal to 2 * G * m1 * m2 * r / d^3, where G is the gravitational constant, m1 and m2 are the masses of the two objects, d is the distance between them, and r is the radius of the object where we’re calculating the tides (assuming that r is much, much smaller than d).
A good derivation of the equation for tidal force is given here.
Willis Eschenbach says:
February 11, 2014 at 11:04 am
“I haven’t drawn any big conclusions from that, other than that people who claim the 54-year cycle of tides is related to the ~60 year pseudo-periodicity in the HadCRUT data don’t understand the nature of the 54-year cycle … nor did I before I started this analysis. I thought it was a 54-year sine- or approximately-sine wave, like we see in the HadCRUT data. I found out it’s not. That’s valuable information.”
Only along the single 1D vector that is Earth centre – Moon centre. The actual vector that defines the Saros cycle itself. And then you find only the reflected residuals of that cycle in your plot and wonder why?
Let me give you a mental/physical picture that may stretch your mind more.
Go outside on a nice clear night. Lie on your back looking up at the stars. Align yourself so that the Milky Way is a horizontal line across your vision, toes pointing ‘sort of’ Northish or Southish as required.
Now watch carefully for a few minutes where the Milky Way crosses the Earth horizon and see just how you and the Earth ‘fall’ through the Universe, for tonight at least. It changes night to night 🙂
Then stop thinking about just turning round and round like a top and wonder.
P.S. You did get that about North Sea and Global temperatures tracking Lunar periods that TB posted didn’t you ?
http://i29.photobucket.com/albums/c274/richardlinsleyhood/200YearsofTemperatureSatelliteThermometerandProxy_zps0436b1f2.gif
RichardLH says:
February 11, 2014 at 11:38 am
============================================
You could fit a hundred graphic arguments like that on the head of a pin. –AGF
For anyone still having problems seeing how short period variations can add together and produce long period modulation patterns, I’ve plotted the following example
18.631 / 2 + 8.852591 => 9.078 modulated by 356 years.
http://climategrog.wordpress.com/?attachment_id=775
Yes, you only see one line right? They are mathematically IDENTICAL.
and that combined frequency is very, very close to what I found in NH SST data:
http://climategrog.wordpress.com/?attachment_id=755
Now that could just be coincidence but I doubt it.
The Indian ocean does not have this mix, just 9.329 (cf 9.3155)
http://climategrog.wordpress.com/?attachment_id=774
If we do the same process with 9.08 and 10.4 it gives a modulation frequency of 143 years so the “beat” period of each bulge in amplitude is 71.5 . So it is possible for an interplay of lunar and solar forces to produce the kind of long cycles seen in the climate record.
The actual period will be as variable as the solar cycle length is variable, it is not a stable 10.4 years.
The lunar frequencies are clearly present in the ocean basins. The next step is see how it relates in phase and try to work out a possible mechanism.
“Geek: How do you define Climate?
Climate Scientist: Longer than 30 years.”
wrong. that’s not the definition of climate.
30 years is an arbitrary number pulled out of hat used to calculate “normals” for particular weather variables.
some climate scientists recognize that the climate doesnt actually exist as an entity.. its just anoter word for long term stats– where long term is defined opportunistically.
agfosterjr says:
February 11, 2014 at 11:45 am
“You could fit a hundred graphic arguments like that on the head of a pin. –AGF”
But you can’t ignore them if they come from a simple low pass/bandbass filter. You can draw all sorts of lines. This is what the data draws all on its own if you quieten down the ‘noise’.
“You could fit a hundred graphic arguments like that on the head of a pin. –AGF”
Agreed, far too vague. Almost as tenuous as the long term rise and ln(CO2 ) – well almost.
Greg Goodman says:
February 11, 2014 at 11:45 am
“and that combined frequency is very, very close to what I found in NH SST data”
And supported by the paper TB linked to.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/200YearsofTemperatureSatelliteThermometerandProxy_zps0436b1f2.gif
I see 18.0 and 18.6 in that model , where do you see 9.08?
Hagen
“I understand Scafetta to say that he documents his use of publicly available data, and fully describes his method in his peer reviewed papers sufficient for others to replicate his results.
While I would encourage him to show his code as well, I thought data and a full published method to be sufficient for the scientific method.
Is the data or his method not sufficiently clear?
################################
1. scaffetta claims to use publically available data. So Did Jones. Don’t you remember how people supported Willis, Steve, and I when we pressed Jones to release the data that he ACTUALLY used. Don’t you remember the support we got when we demanded more than a link to the data he purported to use? Don’t you remember that we wanted to see the data that he ACTUALLY used rather than merely taking his word for it.
2, His method is not fully described. Now, Jones made the same argument. McIntyre tried to replicate Jones method AS DESCRIBED and he could not. Mac requested code. Jones said no.
When I read the climategate mails we found out WHY Mac could not replicate. Jones left a step out of the description. In his mail to mann he explained that he knew why mac could not replicate his results. Jones recipe wasnt perfect.
Now to Scaffetta. In the first place gavin and benestad could not replicate Scaffetts results from the description in the paper.
Two things could be true
1. the description is inadequate
2. they screwed up.
To settled matters they requested code. Scafetta refused. Benestad has a long history of sharing code I might add. In any case at this point McIntyre and readers at Climate Audit tried to
replicate. They could not. Scaffetta came to climate audit and played some games.. refuse to give the code, refuse to provide any assistence in replication. He does not want people to check his work OR to build on it if it is correct.
There is no scientific justification for this behavior. You defend him to your detriment.
What Mosher said about Scafetta
Steven Mosher says:
February 11, 2014 at 11:46 am
“Geek: How do you define Climate?
Climate Scientist: Longer than 30 years.”
“wrong. that’s not the definition of climate.
30 years is an arbitrary number pulled out of hat used to calculate “normals” for particular weather variables.
some climate scientists recognize that the climate doesnt actually exist as an entity.. its just anoter word for long term stats– where long term is defined opportunistically.”
All right, if you want it another way (that is slightly less catchy – why do you think slogans were invented)
Greater than decadal, less than multi-decadal. Where DOES Weather stop and Climate begin?
Steven Mosher:
You’ll be telling me next these don’t exist either.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/200YearsofTemperatureSatelliteThermometerandProxy_zpsd17a97c0.gif
Where DOES Weather stop and Climate begin? It depends how long the “pause” lasts 😉
Greg Goodman says:
February 11, 2014 at 12:14 pm
“Where DOES Weather stop and Climate begin? It depends how long the “pause” lasts ;)”
Well my 15 year S-G projection say its over already ;-). Mind you, S-G is almost as unreliable as LOWESS. Helps if you do have a factual, full kernel, backbone to compare its parameters to though.
Mosh’ says: “To settled matters they requested code. Scafetta refused. …. There is no scientific justification for this behavior. ”
I agree. I don’t understand why he’s not being more open.
What result was it that they could not replicate?
Greg Goodman says:
February 11, 2014 at 12:24 pm
“I agree. I don’t understand why he’s not being more open. ”
+1
Steve:
Climate Scientist: I want a tool to examine Climate Temperatures.
Geek: How do you define Climate?
Climate Scientist: Longer than 10 years.
Geek: So you want a tool that will show how the planet’s temperature responds in periods of more than 10 years?
Climate Scientist: Yes.
Geek: Well basic theory says that a Low Pass filter with a corner frequency of 15 years will do exactly what you want.
Climate Scientist: But that’s not complicated enough and anyway that does not show me what I like to see. It says that there are natural oscillations in the signal and my theory says they don’t exist.
Geek: ??????????
Richar, what’s this 4y thing you’ve mentioned a couple of times?
Of interest:
SOURCE
RichardLH says:
February 11, 2014 at 12:13 pm
What does that have to do with what Mosher said? If you disagree with someone, QUOTE THEIR DANG WORDS like I asked.
When you don’t, as in this case, nobody has a clue what your HadCRUT 15-year Savitsky-Golay has to do with Steven Mosher, and you end up looking like an idiot.
w.
PS—Look carefully at your legend. Note the dot-dash pattern for the purported HadCRUT 15-year S-G graph line … sadly, I couldn’t find it on your graph. Go figure …
RichardLH says:
February 11, 2014 at 1:50 pm
I don’t get this. People in climate science use all kinds of low-pass filters. I use them all the time, generally Gaussian or lowess because they’re well-behaved.
What I don’t do is use the smoothed data for my statistical analysis. You can create totally fictitious correlations that way.
Nor do I look at a couple of what look like cycles and say OMG, the cycles are inherent in the data.
So your 1-D portrayal of climate scientists is way off the mark.
w.
“Because these waves are generated by tides, they occur at tidal frequencies and are called internal tides. ”
I’ve been saying for some time that El Ninjo/Ninja cycle is slow, basin-wide, deep water tides on the thermocline.
http://media.eurekalert.org/multimedia_prod/pub/web/68404_web.jpg
If you estimate the density difference at the thermocline and compare to that between air and water at the surface , the equivalent major resonance at the surface (12h tide) becomes a couple of years.
Because of the feeble density difference it would cause massive but very very slow waves. That cross-section looks to fit the bill. There is also a brief animation that I’ve linked in the past that clearly shows the Pacific Ocean thermocline moving like a giant wave. Can’t recall who provided that just now.
Here we go:
http://www.esrl.noaa.gov/psd/people/joseph.barsugli/anim.html
BTW the first one is just a simulation , see bottom of page for data derived anims.
I have a derivation of the tidal “force” acting on the oceans.
see here
Net force per unit mass = 2GmRcos(theta)/r^3 where m is the mass of the moon, r is its distance from earth, and theta is the angle away from the central point of the bulge.
Notice that there are 2 equal and opposite bulges theta = 0 and theta = pi.
Tides can only exist between 2 bodies in orbit. So the earth is only effected by the sun and the moon. Jupiter for example has no tidal effect on the earth. Tides result from an imbalance in the gravitational force and the orbital centrifugal force acting on the oceans at the surface.
All planets have a tidal effect on the sun.
There is also an exact solution for the earth tides without approximations (phi etc.) but the formula is very complicated. This contains vertical components which increase towards the poles and corresponds more to the egg graph shown previously.
Folks say things like this:
The point of this post, in part, was to encourage people to run the actual numbers, even if they are just back-of-the-envelope numbers, for the claims they are making. This is a good example.
If the world had an ocean all the way around, if we looked at a cross section of the planet and ocean, we’d see that the tide heaps up the water on the quarter-circle nearest and furthest from the moon (high tide), and the quarter-circles on each side would have low tides. The figure below shows the cross-section.
Now, when the tide changes, the water needs to flow through both ends of the sector, at the dotted diagonal lines. Each side about the average ocean depth of 3,000 metres, so we have about 6,000 metres for the flow.
Given that ocean tides are about 2 feet (0.6 metres), the numbers work out like this:
Ocean Sector Length, 10,000,000 , metres Total Tide, 0.6, metres at center, 0 at ends Triangular area, 3,000,000 , sq. metres Flowing through, 6,000 , metres total depth both ends Total Flow, 500 , metres per tide change Time per change, 6 , hours Horizontal flow rate, 83, metres/hour, or 0.05, miles per hour, or 0.08, km per hourNow, does this mean that there is no horizontal flow from the tides? Absolutely not. Instead, it shows that the cause of the horizontal flow in the open ocean is not the ocean flowing to fill or empty the tidal bulges—it is the fact that in the image above, the earth is rotating with a surface speed of about a thousand miles an hour …
w.