Time and the Tides Wait for Godot

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.

day by day tidal force earthFigure 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.

Fourier analysis tidal forceFigure 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:

repeating 54 year tidal cycleFigure 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.

The climate data they don't want you to find — free, to your inbox.
Join readers who get 5–8 new articles daily — no algorithms, no shadow bans.
0 0 votes
Article Rating
528 Comments
Inline Feedbacks
View all comments
RichardLH
February 12, 2014 1:41 am

Willis Eschenbach says:
February 11, 2014 at 5:34 pm
“You’ll be telling me next these don’t exist either.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/200YearsofTemperatureSatelliteThermometerandProxy_zpsd17a97c0.gif
What does that have to do with what Mosher said? If you disagree with someone, QUOTE THEIR DANG WORDS like I asked.”
Steve:
“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.”
I would have thought that both you and he would have recognised what I was talking about. The long term stats bit and observing a regular pattern to the data.
I was (and am) suggesting that a simple treatment of the data says that it has a cyclic nature, with an obvious periodic structure around ~60 years. In the long term, statistic sense.

RichardLH
February 12, 2014 1:45 am

Greg Goodman says:
February 11, 2014 at 5:13 pm
“Richar, what’s this 4y thing you’ve mentioned a couple of times?”
The simple observation that the Sun only returns to the same point in the sky, at the same time of day, one the same day of the year ever 4 years. It is why we have Leap Years.
On the intervening years a different part of the Globe is under the Sun at any given ‘noon’ say so you would expect to find a very low level 4 year signal in the data, land and ocean being so different. I have done a ‘4 year normal’ treatment of the daily CET data set and found something that could be just low frequency noise but could also be this 4 year pattern.

RichardLH
February 12, 2014 1:50 am

Willis Eschenbach says:
February 11, 2014 at 5:45 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.”
The point is that people DO use filters for Day, Month, Year and even Decade as you mention. All I am doing is extending that concept very slightly to 15 years and I get accused of all sorts of malpractice.
The statistic analysis I am using at the present (though it can get a higher statistical value if required) is the most basic of statistical comparison, Graphical. You know Broad Street Pump handle and all that. The very earliest days of statistics. Still a valid methodology even today.
Correlation of waveform to waveform.

RichardLH
February 12, 2014 1:54 am

Willis Eschenbach says:
February 11, 2014 at 5:45 pm
“Nor do I look at a couple of what look like cycles and say OMG, the cycles are inherent in the data.”
Now you do me a great disservice. I do NOT draw any conclusions – only observations.
If YOU see a ~60 pattern to what the data itself draws then it is up to YOU to say why it is present. Or come up with good reasons why it is just all co-incidental.
Explanations – not hand waving.

RichardLH
February 12, 2014 1:59 am

Willis Eschenbach says:
February 12, 2014 at 1:04 am
“Horizontal flow rate, 83, metres/hour, or
0.05, miles per hour, or
0.08, km per hour
Now, 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 …”
And if the world were indeed completely covered in Oceans you would be correct. Unfortunately it is not. The affects of land, reducing depth, narrow straights, basins and all the rest modifies this in a very dramatic way.
The multipliers thus created make that 0.3m, deep ocean wave into something that can be awesome to behold. 10’s of meters high. And vast flows in and out through straights. Some very important ones of those being North-South restrictions.

RichardLH
February 12, 2014 2:05 am

Willis Eschenbach says:
February 12, 2014 at 1:44 am
“Tidal forces exist between the near and far sides of any two objects whether in orbit or not.”
The forces involved are a lot more complex that the single, ID, Earth- Moon vector you have potted.
You also have not yet addressed the observations about the full ‘Tide Generating Force’ vector map and the Wood et al paper mentioned previously and the also fact that your vector actually follows one component of the Saros Cycle and thus tries to compare itself to itself – you will only ever see the residuals, not the whole picture.

Greg Goodman
February 12, 2014 2:06 am

“Note that a planet free-falling into a sun may be torn apart by tidal forces before hitting the sun, despite the fact that it may be neither rotating nor orbiting the sun.”
Good illustration. Even NOAA get into the centrifugal trip. However, once you stop your frame of reference rotating and and introduce _fictitious_ centrifugal forces to make newtonian equations still work you also need to introduce Coriolis forces. I have NEVER seen that done.
The first of the two links Richard provided seems the better approach. Accept the fact the E-M system is revolving and apply a straight-forward forces.
I think the problem here is that since real tides are so far removed from all this talk of ‘bulges’ that none of it can be verified. People (especially academics teaching the stuff) are free to spout any hotch-potch “theory” of tides because it’s largely non verifiable.

RichardLH
February 12, 2014 2:10 am

Clive Best says:
February 12, 2014 at 12:43 am
“I have a derivation of the tidal “force” acting on the oceans.”
A very nice formula for the 2D vector map.
The complication that needs to be added to this is the fact that the rotational axis of the Earth is not aligned top bottom to that diagram.
So you then need a Lunar Month and Solar Year orbital calculation (along with delta changes to those) added to the above to get how that vector map actually plays out. Now it is starting to get really messy – and we still are on a totally water covered globe!

RichardLH
February 12, 2014 2:14 am

Willis Eschenbach says:
February 12, 2014 at 2:09 am
“First, you showed a graph, saying Mosh will be claiming that “these” don’t exist. You don’t say what “these” are. It’s a graph of smoothed climate, one that’s been shown dozens and dozens of times.”
No – its a description of the frequencies involved in the storage and release of energy in the system over long periods of time.
This ‘smoothing’ thing is how people slide past that true, physics based, observation.
“And from that, we’re supposed to guess that you were referring to Mosh’s statement that 30 years is an arbitrary limit, and that climate is just the long-term stats about weather? Really?”
That was, and is, a separate point. I have now moved it to ’10 years or so’ without changing the wording that much. Same message though.
Short filters = good.
Long filters = bad.
Talk about discrimination.

RichardLH
February 12, 2014 2:15 am

Willis Eschenbach says:
February 12, 2014 at 2:09 am
“Yes, that’s the result of a simple analysis as you say—you think you see regular cycles in the data.”
I observe that the data draws an apparently cyclic pattern. Does the line wriggle? What do you think is the cause? Why can you see it there anyway?

RichardLH
February 12, 2014 2:20 am

Willis Eschenbach says:
February 12, 2014 at 2:09 am
“Don’t you realize that cyclomaniacs have been making your same claim for decades? ”
I’ll thank you not to say/jibe that I am a cyclomaniac.
I am an engineer. Drawing engineering observations. The data and summaries of the data only. These patterns whatever they are need explaining. Go for chance if you like. You cannot just say ‘they don’t exist’ which was the main point of the Geek – Climate Scientist conversation in case you hadn’t noticed.

RichardLH
February 12, 2014 2:25 am

Willis Eschenbach says:
February 12, 2014 at 2:09 am
“We’re not that much into simplistic explanations around here. In part this is because more sophisticated and detailed examination of the data shows that natural cycles emerge for a while, seem like they are permanent, then fade out and are replaced by other cycles”
Prepared to ignore these simple observations however.
The high quality data sets that would allow for full examination of the exact periods, magnitudes, numbers, interference, etc. of the very likely more than one cycle (if any exist) are along way into the future. As Nate Drake PhD said – we need 300 years of high quality data to be SURE that a ~60 year cycle is present. You think I can’t do stats? I only too well know the risks that just 2 (TWO – that’s in coin toss land) apparent cycles in the data provide.
I am not prepared to just say, oh well – we will have to wait ’till we have enough data before we address these issues, that’s all.

RichardLH
February 12, 2014 2:33 am

Willis:
By the way – I can tell that you sailed the Southern Ocean with its great depths and steep islands. Me – I sailed Poole Harbour with its shallow, narrow entrance and incredible tidal flows.
Just a different perspective is all 🙂

RichardLH
February 12, 2014 2:42 am

Clive Best says:
February 12, 2014 at 12:43 am
“Jupiter for example has no tidal effect on the earth.”
It does have a slight effect on the Moon’s orbit though. It ‘pushes’ it up and down against the orbital plane (or so I believe). I will see if I can find the reference for it on the ‘net.

Reply to  RichardLH
February 12, 2014 7:05 am

Jupiter has a gravitational effect on the moon and on the earth but not a tidal effect on either.
There seems to be a problem of definition as to what is meant by tidal force. If you fall into a black hole feet first then you will be stretched apart by the gravitational attraction being greater on your feet than on your head. Is that a tidal effect ?
I would argue that this isn’t the same effect as the lunar and solar tides on earth where the bodies are in orbit. The difference in gravitational force between the surface and the centre of the earth could only really explain one lunar tide – not both. Arm waving about the earth moving away from the ocean on the far side simply doesn’t add up, and can’t explain why the two tides are equal. Only including the centrifugal force can you properly explain the second tide.

RichardLH
February 12, 2014 3:00 am

Willis Eschenbach says:
February 12, 2014 at 2:48 am
“Dear heavens, Richard, find the supporting documents before making the claim. You say you are a scientist …”
The Internet is a big place and I read this quite a few years ago. I failed to record exactly where it was that I read it and Google has not proved very helpful so far but…..

RichardLH
February 12, 2014 3:10 am

Willis Eschenbach says:
February 12, 2014 at 2:45 am
“So your point is that we don’t have enough data to say whether there are actually cycles in the data … but by god, that’s not going to stop you from speculating …”
Not speculation – observation. They are different you know.
“It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts”
All I ever do is draw attention to the facts.
“So now you pop up, squint at the data, and say well, we don’t have the data to show it, but by gum, I think there’s a cycle of sixty years or so in there … take a number, Richard. Your claims have been anticipated. And discussed. And rejected. See Riding A Pseudocycle, we’ve been over all of this, you’re late to the party.”
Thank you for the jibe. I long ago recognised not to rise to such bait.
Please tell me why the apparent ~60 cycle is visible in the data. That the data itself draws. Go on, stop avoiding it.
It is all just chance? The fact that both in satellite, thermometer and proxy data there are natural periodicities of similar length and magnitude?
That have multiple observations from multiple sources to back them.
Tide gauges
Polar Vortex
Fish
PDO
Tornadoes
AMO
Stadium Wave
North Atlantic Temperatures
and the list goes on.
All chance? I think Sherlock would disagree.
And that ‘single 1D vector’ observation and Wood et al you are so quick to ignore – whilst you’re at it.

Greg Goodman
February 12, 2014 3:23 am

A key point to visualising it is to resist the temptation to see the earth _rotating_ about EMB as well as revolving around it.
The solid earth has to revolves as one body and all minute elements make the same circular path, not some bits on the surface going with a big radius and some near the EMB with smaller ones.
The centripetal force that acts on the solid earth is its net gravitational attraction acting through it’s centre of mass. ( A point mass is a reasonable approximation for the E-M separation).
The wet shell of water gets distorted like Willis’ planet falling into the sun. It gets stretched by the divergence of the gravity field.
Each drop of water experiences a centripetal force that is the gravity it experiences. Less gravity, less centripetal force, larger radius.
If the gravity field fell off uniformly (constant grad) the wet shell would be an oblate spheroid. Since it is 1/r^2 it is egg-shaped.
No centrifugal or Coriolis needed.
We also notice that the instantaneous “centripetal” forces are towards the centre of the moon and only slightly divergent not the the centre of the revolution : EMB. the solid earth can be approximated as a point mass but the oceans are fluid.
The watery shell would be stretched and ripped apart like Willis’ falling planet were it not constrained by the earth’s gravity as well. However, that does not prevent horizontal movement only radial movement.
The water is relatively unconstrained to move where the forces are tangential.
At this point we have to let the Earth start spinning again and realise that the volume of water is not a floating shell but is getting pulled along with the continents. It is ultimately stopped by how far it can get in the six hours of rising force before it gets pulled back the other way or bounced around by a coastline.
At that point all bets are off. It gets so fiendishly complicated and we may as well try to model the climate system from first principals, which would be an insanely futile exercise as we all know.
So what did we get for all that?
No Coriolis , no centripetal, slight egg-shaped and tidal forces having mainly horizontal effects on the wet shell.
It does not seem to me that the slightly lower back tide every 12h matters. However, maybe the separation of semi-diurnal to diurnal as we move away from the equinox could be a factor. The ‘far side’ in this case being N/S and the moon basically following the sun on it’s annual trip.
Now bigger S bulge , smaller N bugle would imply a mass (hence energy) transfer across the equator. That is just an annual cycle along with the seasons however, the magnitude of that transfer will vary depending upon the various lunar cycles like the distance of perigee (40% variability in tidal force) and its timing w.r.t the annual seasons. ie is the N/S flow adding to the seasonal change or opposing it.
eg when the closest perigee happens in the NH, is the sun down under or is it NH summer?
All these phases just slides around in relation to each other so will produce progressive cycles.
since we don’t understand the real tides well enough to model them we’ll just have to look for physical evidence of lunar periods and then try to find a physical explanation.
http://climategrog.wordpress.com/?attachment_id=774
http://climategrog.wordpress.com/?attachment_id=755
I think there’s a prima facea case to answer. Someone now needs to have a closer look at Indian Ocean which seems to be the least complicated and strongest lunar-like signal.

RichardLH
February 12, 2014 3:29 am

Willis:
Try
http://mb-soft.com/public/tides.html
for a full mathematical treatment of the single 1D vector that you have plotted along with much other useful information including a calculation of the exact difference between front and back tide as well as observations on how this simple calculation is only a small part of the much bigger picture when plaid out here on Earth.
Interesting observations on the possible explanation for the Moon and who we got where we are today also.
http://mb-soft.com/public/moon.html

Greg Goodman
February 12, 2014 3:31 am

“Jupiter for example has no tidal effect on the earth.”
Well I just stated looking at radial speed of earth from sun ( r dot in the ephemeris data ) and it looks like one of the few strong peaks is almost exactly the period of Jupiter. there’s also a tiny blip from Venus.
Now I don’t know what that about, maybe its more to do with how it affects the Sun’s motion than the earth directly. Just a curiosity since I have not looked at it any more than that.

RichardLH
February 12, 2014 3:49 am

Greg Goodman says:
February 12, 2014 at 3:31 am
“Now I don’t know what that about, maybe its more to do with how it affects the Sun’s motion than the earth directly. Just a curiosity since I have not looked at it any more than that.”
I don’t have the data, skills, (or Google power apparently) to press this further. I believe that the Jupiter orbit in resonance plays with the Moon’s orbit. I think that this was in an up-down relative to the orbital plane (as the Moon’s orbital plane is slightly out of line to the Sun – Earth orbital plane) but it could be in-out.
My problem is that this was a long while ago and Google lists Jupiter’s Moons way above the Earth’s Moon in its listings. It will be somewhere down in the hundreds of urls – if there at all.

E.M.Smith
Editor
February 12, 2014 5:32 am

@Willis:
My “somebody found something” was just a summary statement of what those papers, that I did cite, found. Complete with who and what. From the “tell ’em what you told them” pattern. A “wrap up line”.
You have chosen to make a big point about a small number, but not address that the small number matters enough that historical records of eclipse locations and dates do not match what is “postdicted” by the orbital models used by the same folks who send rockets to the moon. It does matter that they left something out of the rocket model.
Oh, and predicting an orbit a week in advance is much much simpler than getting it right over a 1500 year period (as evidenced that the actual eclipses didn’t match the model). Even then we used ‘mid course corrections’ as a fix.
In short, a model used to run rockets over a few months span is not the same as reality or as what happens over decades. When looking at decade to century and longer scales, that matters.
OK, you have chosen to close your eyes rather than look at more data and other POV. Fine with me. I have no axe to grind here. Just thought you might enjoy comparing your stuff with the stuff in the papers and I was giving a couple of ideas of where to look. Your response is that I ought to go look. Well, it’s your posting, not mine… I’m not interested in being adversarial over this stuff, but your responses are increasingly so. ( I understand. Really I do. I found myself becoming defensive and adversarial defending postings and had to actively defend against it.)
Best of luck, and remember that the moon orbits the sun, and the earth has lesser influence. We are a binary planet system in mode of behaviour. This, too, matters.

1 10 11 12 13 14 21