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.

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If one takes your formula it almost equals the low.and high points in the century long sunspot cycles not including the lunar numbers.
I use the SIDE numbers but they said that since 1900 their numbers are best.
Thank you
Paul Pierett

Willis Eschenbach

Paul Pierett says:
February 9, 2014 at 1:20 pm

If one takes your formula it almost equals the low.and high points in the century long sunspot cycles not including the lunar numbers.

Sorry, Paul, but that makes no sense. Which “sunspot cycles”? Why would sunspot cycles “include the lunar numbers”?
w.

Toto

Love the title. I just found a value for the tidal force on a Wikipedia page:

The tidal accelerations at the surfaces of planets in the Solar System are generally very small. For example, the lunar tidal acceleration at the Earth’s surface along the Moon-Earth axis is about 1.1 × 10−7 g, while the solar tidal acceleration at the Earth’s surface along the Sun-Earth axis is about 0.52 × 10−7 g, where g is the gravitational acceleration at the Earth’s surface.

My point is that the force applied is one thing, the response is another. The final paragraph of Willis’s Wikipedia reference is worth reading. The dynamic theory takes into account the properties of the ocean basins, such as resonance. “The equilibrium tide theory calculates the height of the tide wave of less than half a meter, while the dynamic theory explains why tides are up to 15 meters.”
BTW, predicted tide heights are extremely good.

Tonyb

Hi Willis
I imagine you would be interested in this mechanical device invented by the ancient Greeks to predict eclipses amongst other things. They keenly observed cycles and we could perhaps still learn things from them
http://en.wikipedia.org/wiki/Antikythera_mechanism
It is an absolutely fascinating story of the devices rediscovery and an fascinating story of how it’s purpose was put together. The BBC did a wonderful programme on it a couple of years ago.
Tonyb

Well, that frequency certainly took a beating.

Larry Brasfield

I cannot get this to make sense: ”
the combined tidal force is then
sqrt( sun_force^2 + moon_force^2 + sun_force * moon_force * cos(angle))
“.
When the cosine factor is 1, meaning the angles are aligned, the expression should simplify to ”
sqrt(sun_force^2 + 2 * sun_force * moon_force + moon_force^2)
“.
I think there must be a factor of 2 missing in the term containing cos().
Best regards from an admirer of your work.

RichardLH

I rather suspect that it is not the Saros cycle itself but the path it traces on Earth that matters.
In order to understand how this all plays out you need the elevation changes from some point on Earth, not just the time the pattern repeats for whatever happens to be underneath at the time.
That is like saying each year is the same when in fact there is a 4 year pattern to the system as is well known.
How long does it take for the Moon to return to the same point in the sky at the same time of month, year, etc.
And how does that interact with the 4 year Solar cycle?
And then add back in the Saros cycle.

RichardLH
Lars P.

“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 …”
Oh yes. I just landed accidentally on a warmist site claiming there is a scientifically proven link between “climate change” and “weird weather on steroids” and I just gave up on posting anything as answer there to ask for the evidence….
Tonyb says:
February 9, 2014 at 1:39 pm
Oh yes Tony that is a very interesting mechanism, looks like they were much more advanced then it was thought in designing and using such machines.

tty

The motion of the Moon is very complicated. That’s why determining the longitude by lunar distances which was long known to be theoretically possible did not become practical until the late eighteenth century, just about the same time the chronometer was perfected and made it unnecessary.
There is also a much longer cyclicity in tidal strength due to changes in the eccentricity of the Earth’s orbit which varies in a 413 000 year cycle, overlain by several shorter components. This may have important climatic effects, since the amount of vertical mixing in the ocean is strongly affected by tides, and it is probably very important for the stability of ice-shelves as well.

Willis,
Nice post – however I think it should be abs(cos(angle)) in your formula
sqrt( sun_force^2 + moon_force^2 + sun_force * moon_force * cos(angle))
When angle ~ 0 there is a new moon and when angle ~ pi there is a full moon. Both cause spring tides because there are two tidal bulges reinforcing each other when they align. I did exactly the same as you and downloaded the JPL ephemeris. My calculations are almost the same as yours apart from scale and the cosines difference.see graph here
Please correct me if I am wrong.
What is interesting is that January had 2 perigean spring tides. The first on Jan 1 and the second on Jan 30. The two storms in the UK which caused most coastal damage coincided more or less with both extreme spring tides. In the NH winter the earth is at closest distance from the sun.
[ANSWER: Thanks, Clive. Turns out we were both wrong. As someone else pointed out, I left out a “2” in the formula, which should have been:
sqrt( sun_force^2 + moon_force^2 + 2 * sun_force * moon_force * cos(angle))
Just shows the value of revealing all of your data and code, it makes finding mistakes quick and easy. -w.]

Otter (ClimateOtter on Twitter)

Saros? Didn’t he make the One Ring, to bind all others………….. no?

Toto says:
February 9, 2014 at 1:33 pm
My point is that the force applied is one thing, the response is another.
===========
like a small child pumping on a swing. small cyclical force leads to large response so long as it is in-phase and damping is low.

Paul

Figure 3 is weird, the maximum varies but the minimum is flat. Looks to me like aliasing of some kind, either in your reconstruction or plotting.
[It was an error in the calculations, now fixed. w.]

KLinTexas

“…like saying each year is the same when in fact there is a 4 year pattern to the system as is well known” (from RichardLH)
erm, you do realize that the 4 year pattern in calendar years is a kludge to account for the actual time used as our world travels around the sun which is not an even number of days long? That there’s approximately a quarter-day extra over the 365, which is then roughly accounted for by the Feb 29 leap day? This is the big change that was made by the Gregorian calendar, the one that when it was finally adopted in Protestant Great Britain shifted George Washington’s birthday by something like 11 days…during his actual lifetime yet. That must have been startling. (Perhaps not as startling as the extended time period when the Catholic countries were on Gregorian dating and the Protestant countries weren’t yet, and you could find yourself in a different month by traveling from one capital city to another. And I’m not sure but I think the different countries adopted the Gregorian dating at different times, even.)
So no, there isn’t a 4 year pattern to the year “as is well known.” Calendar dates are an approximate map of the system, they are not the system itself.
I don’t understand how a cycle can be said to trace a path on the earth, either, but maybe it’s just me. (unattributed pronoun? dunno.)
best

Tonyb says:
February 9, 2014 at 1:39 pm
http://en.wikipedia.org/wiki/Antikythera_mechanism
============
we did a tour through Turkey and Greece some years back. It is fascinating how many modern “inventions” have been found in the ruins of the ancient world. Almost as though human development halted or took a step backwards for the better part of two thousand years.

Coldlynx

Willis,You miss the elephant in the room
Moon Inclination and Earth axial tilt.
Moon Inclination 5.145° to the ecliptic (between 18.29° and 28.58° to Earth’s equator) and Earth axial tilt of 23.26° cause the tidal acceleration to have a different angle toward Earth’s equator.
This acceleration will probaly have an effect on acceleration and deacceleration of the earth fluids,
atmosphere and oceans. Overlay this with your pure force calculation and I am sure You will have a very intresting graph.
Here is an example http://tallbloke.wordpress.com/2009/11/

What I find most fascinating about tidal calculations is that they require no understanding of the underlying mechanism. Indeed, if you try and calculate them from first principles like global climate models, you are doomed to failure.
Instead we record the height of the tides and the position of the sun and moon in the heavens. When the sun and moon repeat, so will the tides. If you want to improve the accuracy even more, throw in Jupiter, mars and Venus. For all intents and purposes, this is Astrology.
As a result, cause and effect is not important. You don’t need to understand the mechanism. You don’t even need a mechanism. You can simply say “reason unknown”. It will not affect the accuracy of the method.

“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 …”
Correct! However, meanwhile, people are quietly slipping away to deal with more pressing matters.
http://joannenova.com.au/2014/02/australia-more-skeptics-than-believers-and-few-really-care-about-climate-change/

Carbomontanus

[snip -more pointless off-topic latinizing -mod]

M Courtney

Curious:
Figure 2 Top give a cause for the division of months into approximately 30 days; therefore the use of 12 x 30 days for a year.
This was defined by Ancient Babylon who gave us the 360 degrees in a circle.
So what is curious?
Babylon was not a maritime nation. It’s now Iraq. Their earliest surviving literature (Gilgamesh) refers to a great flood.
This looks like evidence for an earlier people with astronomy than Babylon.
Woah… or maybe woo…

Willis Eschenbach

Larry Brasfield says:
February 9, 2014 at 1:45 pm

I cannot get this to make sense: ”
the combined tidal force is then
sqrt( sun_force^2 + moon_force^2 + sun_force * moon_force * cos(angle))
“.
When the cosine factor is 1, meaning the angles are aligned, the expression should simplify to ”
sqrt(sun_force^2 + 2 * sun_force * moon_force + moon_force^2)
“.
I think there must be a factor of 2 missing in the term containing cos().
Best regards from an admirer of your work.

Many thanks, Larry. You are 100% correct, and this slightly affects the results, in that it shows a tiny cycle at 8.75 years. I’ve updated the graphics to reflect the correct calculations.
w.

Willis Eschenbach

RichardLH says:
February 9, 2014 at 1:45 pm

I rather suspect that it is not the Saros cycle itself but the path it traces on Earth that matters.
In order to understand how this all plays out you need the elevation changes from some point on Earth, not just the time the pattern repeats for whatever happens to be underneath at the time.
That is like saying each year is the same when in fact there is a 4 year pattern to the system as is well known.
How long does it take for the Moon to return to the same point in the sky at the same time of month, year, etc.
And how does that interact with the 4 year Solar cycle?
And then add back in the Saros cycle.

Good questions, Richard. The Saros cycle is where the sun, moon and earth come back to (approximately) the same relative locations … but as you point out, the subsolar spot on the earth is different.
However, after three Saros cycles, the three bodies line up again (of course), but this time the points under the earth are (again approximately) the same. So regarding your question, viz:

How long does it take for the Moon to return to the same point in the sky at the same time of month, year, etc.

… the answer is, three Saros cycles.
I don’t know the answer to your question about the “4 year Solar cycle”, because I don’t know of any such cycle except the leap year cycle, which is just an accounting convenience to keep the seasons from drifting …
w.

Berényi Péter

Tidal forces, especially speed of tidal flows in the boundary layer have tremendous impact on vertical turbulent mixing in oceans, hence on ocean currents; as pure mechanical energy input they can drive three orders of magnitude larger heat flows than tidal energy dissipation itself. That in turn drives much of climate.
Deep Sea Research Part I: Oceanographic Research Papers
Volume 45, Issue 12, December 1998, Pages 1977–2010
doi: http://dx.doi.org/10.1016/S0967-0637(98)00070-3
Abyssal recipes II: energetics of tidal and wind mixing
Walter Munk &. Carl Wunsch
I wonder what periodicity is observed in rate of turbulent mixing and how is it related to temporal changes of tidal forces.

Willis Eschenbach

ferdberple says:
February 9, 2014 at 2:40 pm

What I find most fascinating about tidal calculations is that they require no understanding of the underlying mechanism. Indeed, if you try and calculate them from first principles like global climate models, you are doomed to failure.
Instead we record the height of the tides and the position of the sun and moon in the heavens. When the sun and moon repeat, so will the tides. If you want to improve the accuracy even more, throw in Jupiter, mars and Venus. For all intents and purposes, this is Astrology.

Thanks, ferd. Anyone who includes the other planets in tidal is fooling themselves, the effect is miniscule. At its closest, Venus’s tides on earth are four orders of magnitude smaller than the tides of the sun and the moon (1/ 10,000)
w.

Willis Eschenbach

ferdberple says:
February 9, 2014 at 2:07 pm

Toto says:
February 9, 2014 at 1:33 pm

My point is that the force applied is one thing, the response is another.

===========
like a small child pumping on a swing. small cyclical force leads to large response so long as it is in-phase and damping is low.

Thanks, ferd, and that’s quite true.
However, this kind of resonant driving is uncommon in nature, for an odd reason. It’s because nature is always running at the edge of turbulence. Natural heat engines act to increase the total of work done plus turbulence. So things like thunderstorms and such typically are heavily damped. We know this because of their lack of “momentum”—they die out quite quickly once the driving conditions are removed.
As a result, it’s not common to find natural systems where, in your words, “damping is low”.
Regards,
w.

gregjxn

Willis says: “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?” The analysis then proceeds to look at the characteristics of predictions based on astronomical data. In a way, this is a sort of model of the tides, not the tides themselves. If we had perfect, actual tidal data, then the Fourier analysis could be applied to that and perhaps locate cycles not to be found in the “model”. Perhaps we know that the “model” is so good that such a thing cannot be even though it is a logical possibility.

RichardLH

Willis Eschenbach says:
February 9, 2014 at 3:18 pm
“I don’t know the answer to your question about the “4 year Solar cycle”, because I don’t know of any such cycle except the leap year cycle, which is just an accounting convenience to keep the seasons from drifting …”
No it is more than that. It is the time taken for the Sun to be the same point in the sky at the same time of day on the same day of the year for any given position on Earth. The world under-rotates 6 hours per year to make the 4 years to get back to the same position. Hence the Leap Year. So it is more than just accounting.
As I said, Wood et al is an example of how complicated this apparently very simple cycle gets.

RichardLH

Willis Eschenbach says:
February 9, 2014 at 3:33 pm
“Anyone who includes the other planets in tidal is fooling themselves, the effect is miniscule.”
Except for the tiny detail that planets DO affect the precise orbital path of the Moon around the Earth. Mostly in an up and down direction.

Carbomontanus

To all and everyone
On calculating the lunar effect.
In once asked my father, “What about the moon for the weather?”
“no, he said. it has been shown that it does not matter!
And that was the history of the Norwegian University Almanach. Christopher Hansteen was responsible, and corrected the almanach on that point. Before that, they repeated the weather forecasts along with the 18 .6 year lunar period. For several reasons, Hansteen who communicated with H.C Ørsted, found this….. silly.
It is grasped if you do not give a damn to The Grandfather Clock and its second pendulum in the earth gravitational field, and to Ole Rømers definition of the Royal Danish Foot.
“1`= 12 /38 of the matematical pendulum that swings 1 sec at sea level at 45 deg North!”
That is to state CHECKERS! to the Pope, because that is exacly across the St Marcus square in… Venetia!
It is slightly bigger and better in Norway you see. That inferiour English foot is defined by terribly irratinal number down in the muds at Greenwhich, just to pleace the foot of an arbitrary potentat further up at the Thames.
Remark the Elegance of Ole Rømers definition.
At the observatory, Observatoriegt. 1, there is a kepplerian telescope and Gallileis Pendulum on fixed mount. Sideroical time is observed on the second by a fix star twinkling out over a fixed edge in the ocular focus. And next by is the official solar clock that is adjusted to keep in step with the year knowing siderical time and the vernal eqvinox.
I have such a Long- Tick-Tack. I can adjust it within 1 minute per week. The scientific devices are highly refined with temperature compensated pendulum and finely grades to see the pendulum amplitude.
From Observatoriegaten 1 and from the Greenwhich, there is an electrical lead up to Westminster or down to DOMVS ACADEMICA to a next Long- tick- tack with display out of the window, so that Winston Churchill / Henrik Ibsen can adjust their pocket watches quite exactly and scientifically.
Thus never give a damn to HOROLOGIVM OSCILLATORIVM ( Christiaan Huyghens 1770) ,and to Big Ben. Telescopivm and Horologivm both are noticed on the southern star map.
According to Bakers Astronomy 6th edition 1959, the moons mass is 0.012 of that of the earth. And the moons distance is 60 times the earth radius. Thus simply 1/60 ^2
* 0.012 = 0.0000033. That is 3.3 ppm. ( simplicity works Mr Watts, ain`t I quite ingenious?)
Then 1 norwegian cartoon of milk is one liter weighing one Kg. And we place it on the shore.
How much does the moon “drag” on that liter of water? 3.3 milli- gram.
incredible,… so we take a man weighing 100 Kg and put him on the shore. He will be dragged by 330 milligram. How much is that? 20 drops is a milliliter times 0.33 is 6.6 drops of,….. piss!
I repeat…..! and quite exactly.
You can also count how many pills of aspirine in his pocket more or less, and if you do not drink milk you can count paints or barrels of beer.
So I think we give both Rømer and Hansteen right.
Any effects of that kind would have been stated in the nautical almanacs and in Bakers Astronomy. And objections to that are IMMATVRVS. If not ADLTERARE.
and if you are not even convinced of that,..
“Nature and natures law lay hidden in darkness and night
God said Let Newton be, and all was bright,” SANN! (William Blake)
Because we take it from Newtons law of gravitation f = g m1 * m2 / r^2 and from Newtons pendulum law.
Only Immaturers discuss gravity without having heard of the grandfathers clock and its physics.
And only Adulterarers , namely alian enemies of the British Empire, try and mess up with the Big Ben.

RichardLH says:
February 9, 2014 at 4:07 pm
Except for the tiny detail that planets DO affect the precise orbital path of the Moon around the Earth. Mostly in an up and down direction.
That detail is too TINY to have any effect on the timescales of interest.

John

Thanks for a clear description of the data.
Would it be possible to graph your data on a log-log scale, so that everything is on one plot and you can immediately see the relative size of the peaks.

Henry Bowman

Longman [ref. below] provides formulae for solid-earth tides [i.e., accelerations] due to the sun and moon. The results plains depend on one’s position on the earth. I’m nt sure your results are correct. A simple calculation using Longman’s formulae reveals many peaks between 0 and 55 years.
I have codes available to calculate such acceleration (in python, Perl, C, and Fortran). Let me know if you are interested. I think that I also have a scanned copy of Longman’s article if you wish.
Reference: Longman, I. M. (1959) Formulas for computing the tidal accelerations due to the moon and the sun, Jour. Geophysical Research, 64(12), 2351-2355.

wayne Job

Odd is it not that the tides can not be calculated using our gravity formulae they are calculated over time using observation and precedents? What are we missing?

Willis Eschenbach says:
February 9, 2014 at 4:00 pm
As a result, it’s not common to find natural systems where, in your words, “damping is low”.
==========
Most of the large scale motion in the universe demonstrates low damping. Thus the ocean tides on earth don’t run down, except perhaps at extremely long time scales, and are much higher in many locations than is explained by tidal forces.
One obvious explanation for climate change is a change in the ocean mixing rate. One of the main drivers for this could easily be the ocean tides and harmonics. The tides don’t run down. Like the kid on the swing they keep pumping and pumping. And like the kid on the swing, it makes a difference if they are in-phase or not. For example: http://www.pnas.org/content/97/8/3814.full
A small force over a long time has no less energy than a large force over a short time. However, it is easy to overlook cause and effect when events take thousands or millions of years to develop. One of my favorite examples is the rotation of Venus. The tidal force from Earth is small, yet the same face of Venus always presents itself at closest approach. Conventional wisdom is that this is co-incidental, because the force is so small. Yet, to me the odds of this are so fantastically low as to be zero.

Steve Fitzpatrick

Willis,
It is always a pleasure to read what you write, even if I sometimes disagree with your conclusions. In this case, there is no disagreement.
SF

Willis,
I think you will find that JPL is a model, not actual data. These folks also use a model, but with terms that show a significant set of lunar / tidal cycles:
http://www.pnas.org/content/97/8/3814.full

In a previous study (3) we proposed a tidal mechanism to explain approximately 6- and 9-year oscillations in global surface temperature, discernable in meteorological and oceanographic observations. We first briefly restate this mechanism. The reader is referred to our earlier presentation for more details. We then invoke this mechanism in an attempt to explain millennial variations in temperature.

The “previous study” link is:
http://www.pnas.org/content/94/16/8321.abstract?ijkey=dd006ea42e6e72cc934ffde5bc98f60cede0d5c9&keytype2=tf_ipsecsha

To explain both by a single mechanism, we propose that extreme oceanic tides may produce changes in sea surface temperature at repeat periods, which alternate between approximately one-third and one-half of the lunar nodal cycle of 18.6 years. These alternations, recurring at nearly 90-year intervals, reflect varying slight degrees of misalignment and departures from the closest approach of the Earth with the Moon and Sun at times of extreme tide raising forces. Strong forcing, consistent with observed temperature periodicities, occurred at 9-year intervals close to perihelion (solar perigee) for several decades centered on A.D. 1881 and 1974, but at 6-year intervals for several decades centered on A.D. 1923. As a physical explanation for tidal forcing of temperature we propose that the dissipation of extreme tides increases vertical mixing of sea water, thereby causing episodic cooling near the sea surface. If this mechanism correctly explains near-decadal temperature periodicities, it may also apply to variability in temperature and climate on other times-scales, even millennial and longer.

Does look a tiny bit more complicated than your analysis…
BTW, historical eclipse data does not support the notion that the accepted model of lunar orbit changes is correct. I think the model is lacking some terms:
https://chiefio.wordpress.com/2014/01/25/a-remarkable-lunar-paper-and-numbers-on-major-standstill/
https://chiefio.wordpress.com/2014/01/24/the-moons-orbit-is-wrong-it-can-change-a-lot-and-tides-will-too/
So my “suspicion” is that you’ve done a simple analysis on a model and found the model is simple. IMHO, reality is more complex than that. Some other folks have also done such analysis, found cycles that matter. Some other, other folks have done some looking at historical data and found it doesn’t match predictions from the accepted orbit description. In other words, the data doesn’t match the theory. So I think you have based your analysis on too simple a view, of too simple a model, that does not agree with long term data.
Oh, and since tidal forces tend to cause odd circulations rather than just up and down, it isn’t just a simple “calculate the gravity and be done”, but involves the actual basin dynamics too. Even Newton didn’t like trying to calculate tides…
http://en.wikipedia.org/wiki/Celestial_mechanics

There is no requirement to stop at only one cycle of corrections. A partially corrected solution can be re-used as the new starting point for yet another cycle of perturbations and corrections. The common difficulty with the method is that usually the corrections progressively make the new solutions very much more complicated, so each cycle is much more difficult to manage than the previous cycle of corrections. Newton is reported to have said, regarding the problem of the Moon’s orbit “It causeth my head to ache.”

So if your head does not ache, I think you didn’t have a complicated enough description of things to capture the real complexity…
It’s the perturbations that will get you on lunar orbit… every time…

Willis Eschenbach

RichardLH says:
February 9, 2014 at 4:07 pm

Willis Eschenbach says:
February 9, 2014 at 3:33 pm

“Anyone who includes the other planets in tidal is fooling themselves, the effect is miniscule.”

Except for the tiny detail that planets DO affect the precise orbital path of the Moon around the Earth. Mostly in an up and down direction.

The key word being “tiny” … look, Richard, any planet, moon, asteroid, and planitesimal affects the orbit every single other planet, moon, asteroid, and planitesimal. That’s not the question.
The question is, how much? So … can you provide us with some numbers that have to do with the effect you are indicating?
Thanks,
w.

Willis Eschenbach

Henry Bowman says:
February 9, 2014 at 4:41 pm

Longman [ref. below] provides formulae for solid-earth tides [i.e., accelerations] due to the sun and moon. The results plains depend on one’s position on the earth. I’m not sure your results are correct. A simple calculation using Longman’s formulae reveals many peaks between 0 and 55 years.

Perhaps … but Longman’s paper appears to be an ad-hoc, empirical method. Nothing against that, and for 1959, it was state of the art … It contains a number of formulas which give close values empirically, but are merely good approximations and not solutions of the underlying equations.
As a result, I’m not surprised that there would be a variety of peaks in the results.
That’s why I used the celestial ephemeris data from JPL.
w.

Willis Eschenbach

wayne Job says:
February 9, 2014 at 4:49 pm

Odd is it not that the tides can not be calculated using our gravity formulae they are calculated over time using observation and precedents? What are we missing?

We’re not missing anything. It’s due to the strange shapes of the oceans and continents, and how the water sloshes about in those basins.
w.

Richard M

Another complication to this whole mess is the Earth itself has a liquid core. That means it is also influenced by tides. I don’t think anyone really knows if the core itself is in equilibrium so there may be convection and currents of unequal density. Not to long ago the core was found to be rotating at a different speed than the surface. Our ocean currents could be influenced by core currents that we don’t even know exist.

Sorry to be OT – here’s another issue that might interest you Willis.
http://hockeyschtick.blogspot.com.au/2014/02/new-paper-finds-excuse-8-for-pause-in.html
As you will see from my hasty comment on Hockey Schtick, I smell a rat ….

Willis Eschenbach

E.M.Smith says:
February 9, 2014 at 5:28 pm

Willis,
I think you will find that JPL is a model, not actual data.

Thanks, Chiefio. Since it has given me the positions of the sun and moon until the year 2200, I’m pretty sure that they didn’t observe the positions, they modeled them …

These folks also use a model, but with terms that show a significant set of lunar / tidal cycles:
http://www.pnas.org/content/97/8/3814.full

I’ve put the data I used, the math I used, and the computer code I used out there. If you think there’s an error in it, hey, I’m happy to have you point it out.
In any case, between the model of Wood and the model of JPL … well, I’ll take JPL. They use their numbers to send rockets to Mars and Saturn, good enough for me.
Next, you say that

BTW, historical eclipse data does not support the notion that the accepted model of lunar orbit changes is correct. I think the model is lacking some terms:
https://chiefio.wordpress.com/2014/01/25/a-remarkable-lunar-paper-and-numbers-on-major-standstill/
https://chiefio.wordpress.com/2014/01/24/the-moons-orbit-is-wrong-it-can-change-a-lot-and-tides-will-too/

You refer to a paper that found a difference in the rate of change of the eccentricity of the moon. The moon’s orbit is slightly out of round, with an eccentricity of 0.0549.
The paper that you think makes a difference says that the change is NOT really an increase in the eccentricity of 0.000000000009 per year … it’s really an increase of 0.000000000016 per year. Obviously, over the period in question of 200 years, that doesn’t make the slightest difference. It’s a change in eccentricity of 0.0000026% … that’s 2.6 MILLIONTHS OF A PERCENT. The paper is here.
As a result of your claim about the difference in annual eccentricity change of 0.000000000007 between the two methods, you diss the JPL data saying

So my “suspicion” is that you’ve done a simple analysis on a model and found the model is simple. IMHO, reality is more complex than that.

Well, my suspicion is that you didn’t run the numbers on your claim about eccentricity.
And the JPL ephemerides are “simple”? Since when is the iterative solution of an n-body gravitational program “simple”? That’s way wrong. You might start here for a discussion of their model. I assure you … this IS rocket science …

Some other folks have also done such analysis, found cycles that matter. Some other, other folks have done some looking at historical data and found it doesn’t match predictions from the accepted orbit description.

Well, that’s useful information. Somebody somewhere found something. I’ll keep that in mind …
C’mon, Chiefio, this is far below your usual standard.
w.

I’m afraid that your investigation using FFT is not showing the whole picture. Because I make ENSO predictions and ENSO is an important cause of variations in global mean temperature I like to add a comment.
With linear regression analysis or Fourier analysis you can only prove that there is a connection. You can not disprove that there is a connection or disprove if there exist any form of cause and effect.
What I have found is that ENSO is driven by changes in a combination of tidal forcing, magnetic forcing as measured by the Ap and Kp indexes, by other unknown factors and by the inertia of the affected sea currents. ENSO has a semi oscillation pattern. Because of this, the input from its drivers often has complicated time lag patterns on the output. As a result of this the output signal is noisy and it is difficult with ordinary statistical method to discern influence from the input of these different drivers.
BTW! You only looked at 2 dimensions, but our world is 3 dimensional, excluding the 4th one.

anengineer

“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.”
Shouldn’t this be something like 1800-2000?

Nylo

RichardLH says:
February 9, 2014 at 4:05 pm
Willis Eschenbach says:
February 9, 2014 at 3:18 pm
No it is more than that. It is the time taken for the Sun to be the same point in the sky at the same time of day on the same day of the year for any given position on Earth. The world under-rotates 6 hours per year to make the 4 years to get back to the same position. Hence the Leap Year. So it is more than just accounting.
Sorry but it is not 6h, By considering the year length of 365 days, you make an error of either 5h 48m 45.25s (if considering equinox to equinox, which is what interests us for the seasons) or 6h 9m 9.75s (if considering same orbital point). The leap year only corrects for 6 extra hours, which leaves an average error of 12m 14.75s per year. After 100 years, the error has grown to ~20.4 hours. We reduce it to ~-3.6 hours by deciding not to take a leap year every 100 years. So every 100 years we are accumulating some error in the other direction. To compensate it, every 400 years we DO take a leap year in a multiple of 100. Which again corrects for most but not all… But we are everytime making smaller errors over longer time periods. This final correction is currently considered “good enough”. There is still a minimal drift of the seasons in the calendar, but it is a drift of less than half a day every 400 years.

Willis,
“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.”
A sensible suggestion, I personally think the tidal forces of the planets that do effect the sun are very small, although it’s not an insignificant effect, there is after-all a barycentric motion. Still, I’m not convinced at-all one bit that the planets cause the sunspots and therefor drive earths climate.
I am convinced that there is a relationship between the sun and the planets, Leif himself has stated that “the sun runs the planets” it’s actually encouraging to see you taking an active interest in the subject. The other two areas of interest which are actively being researched are the solar/climate how much the sun influences earths climate, and orbital/climate how much orbital changes effect earths climate, long term orbital changes originate from the outer solar system and solar changes originate from the inner-solar system.
As for signal processing of planetary beats and pattern recognition etc.. I believe the research is important, as a scientific tool it sheds light on underlining processes.Willis,
“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.”
A sensible suggestion, I personally think the tidal forces of the planets that do effect the sun are very small, although it’s not an insignificant effect, there is after-all a barycentric motion. Still, I’m not convinced at-all one bit that the planets cause the sunspots and therefor drive earths climate.
I am convinced that there is a relationship between the sun and the planets, Leif himself has stated that “the sun runs the planets”, it’s actually encouraging to see you taking an active interest in the subject. The other two areas of interest which are actively being researched are the solar/climate how much the sun influences earths climate, and orbital/climate how much orbital changes effect earths climate, long term orbital changes originate from the outer solar system and solar changes originate from the inner-solar system.
As for signal processing of planetary beats and pattern recognition etc.. I believe the research is important, as a scientific tool it sheds light on underlining processes.

Willis,
“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.”
A sensible suggestion, I personally think the tidal forces of the planets that do effect the sun are very small, although it’s not an insignificant effect, there is after-all a barycentric motion. Still, I’m not convinced at-all one bit that the planets cause the sunspots and therefor drive earths climate.
I am convinced that there is a relationship between the sun and the planets, Leif himself has stated that “the sun runs the planets” it’s actually encouraging to see you taking an active interest in the subject. The other two areas of interest which are actively being researched are the solar/climate how much the sun influences earths climate, and orbital/climate how much orbital changes effect earths climate, long term orbital changes originate from the outer solar system and solar changes originate from the inner-solar system.
As for signal processing of planetary beats and pattern recognition etc.. I believe the research is important, as a scientific tool it sheds light on underlining processes.

Sorry I botched my first comment, I always try to copy it just before I submit it, I must have hit paste. D’oh…

Nylo

Correction, the yearly error after correcting for leap years is 11m 14.75s which after 100 years is roughly 18.74 hours and when not taking the leap year is reduced to roughly 5.26h in the other direction, which after 400 years has accumulated to roughly 1 day (21.04h) and that’s why we DO take the leap year in years multiple of 400, leaving a final error of less than 3h every 400 years.