# 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.

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.

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Paul Pierett
February 9, 2014 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.
I use the SIDE numbers but they said that since 1900 their numbers are best.
Thank you
Paul Pierett

Toto
February 9, 2014 1:33 pm

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
February 9, 2014 1:39 pm

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

February 9, 2014 1:43 pm

Well, that frequency certainly took a beating.

Larry Brasfield
February 9, 2014 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().

RichardLH
February 9, 2014 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.

RichardLH
February 9, 2014 1:48 pm
Lars P.
February 9, 2014 1:51 pm

“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
February 9, 2014 1:52 pm

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.

February 9, 2014 2:01 pm

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.]

February 9, 2014 2:05 pm

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

ferdberple
February 9, 2014 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.

Paul
February 9, 2014 2:09 pm

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
February 9, 2014 2:21 pm

“…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

ferdberple
February 9, 2014 2:21 pm

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
February 9, 2014 2:23 pm

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/

ferdberple
February 9, 2014 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.
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.

February 9, 2014 2:55 pm

“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.

Carbomontanus
February 9, 2014 3:02 pm

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

M Courtney
February 9, 2014 3:07 pm

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…

February 9, 2014 3:27 pm

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.

gregjxn
February 9, 2014 4:05 pm

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
February 9, 2014 4:05 pm

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
February 9, 2014 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.

Carbomontanus
February 9, 2014 4:14 pm

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.

February 9, 2014 4:29 pm

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
February 9, 2014 4:40 pm

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
February 9, 2014 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 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
February 9, 2014 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?

ferdberple
February 9, 2014 5:01 pm

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
February 9, 2014 5:12 pm

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

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

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.

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…

Richard M
February 9, 2014 6:04 pm

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.

February 9, 2014 6:09 pm

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 ….

February 9, 2014 6:26 pm

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
February 9, 2014 6:33 pm

“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
February 9, 2014 6:39 pm

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.

February 9, 2014 6:40 pm

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.

February 9, 2014 6:42 pm

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.

February 9, 2014 6:46 pm

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
February 9, 2014 6:46 pm

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.

February 9, 2014 6:47 pm

So it is with Milankovitch. Follow the fish. They’ve been around half a billion years. They ought to be able to discern a cycle that is just a statistical repetition of values from something real. The PDO is fish based. Not saying it’s tidal, but I trust those fish.

February 9, 2014 7:18 pm

Willis writes:
“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.”
Again this tidal exercise was done
Scafetta N., 2012. Does the Sun work as a nuclear fusion amplifier of planetary tidal forcing? A proposal for a physical mechanism based on the mass-luminosity relation. Journal of Atmospheric and Solar-Terrestrial Physics 81-82, 27-40.
http://www.sciencedirect.com/science/article/pii/S1364682612001034

MattS
February 9, 2014 7:18 pm

“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).”
So what happens if r is not much, much smaller than d?

JamesS
February 9, 2014 7:22 pm

Mooloo
February 9, 2014 7:24 pm

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.
So the ocean sloshes backwards and forwards twice a day, over a non-flat seabed and round islands, but when it does it by slightly more for a few days, that causes climate change?
Pull the other one!
As Willis has shown, the “cycle” is just a mathematical thing. In the oceans the tides go up and down daily, sometime high, sometimes slightly lower. That once every sixty years they go a bit higher again is so far into noise to be silly.
And why would extreme tides cause more mixing for a start? The water moves one way, then moves the other as a body. It’s not the top moving and the bottom staying still (or it wouldn’t be resonance). The tides seem quite large to us, but as a percentage change in the oceans they are tiny. Each molecule is moving across, on average, what? A nanometer?

February 9, 2014 7:32 pm

Willis,
My calculations are not ready, (which do not deal with tidal models) when they are, you will have the data and everything you need.
I will point out that there are tidal forces on the sun caused by the planets and that I have done “the hard lifting”.

February 9, 2014 7:42 pm

Tonyb says:
February 9, 2014 at 1:39 pm
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

I once attended a lecture by someone from the company Xtek who custom-built a 12-ton 450 kV xray tomography system and shipped it out to Greece, to make a CT scan of the Antikythera mechanism. This is included in the Wiki article – the CT scan doubled the amount of text they could read inside the mechanism. It had more than 50 gears and accurately modelled numerous astronomical cycles. It was made around 100-150 BC, nothing approaching its sophistication was made for another 1500 years.

February 9, 2014 8:01 pm

February 9, 2014 at 7:42 pm
RE: Antikythera mechanism
People have been around in their present form for over five hundred thousand years or more, it shouldn’t be a surprise that a an astronomical model like the Antikythera mechanism was found, there are astronomical models built in stone that are dated before the last ice-age.

David L. Hagen
February 9, 2014 8:35 pm

Hi Willis
What is the story about the near-fortnightly tide component that I found discussed in several quick references?
17.4 Theory of Ocean Tides
Fortnightly Earth rotation, ocean tides and mantle anelasticity., Richard Ray, Gary Egbert
/j.1365-246X.2012.05351.x

The near-fortnightly tide Mf, of period 13.66 d, is the largest of the zonally symmetric, long-period tides. Like all the long-period lunar tides, it may be thought of as a time-varying modulation of the Earth’s permanent tide M0. In the case of Mf, the modulation arises from the twice monthly excursion of the moon off the Earth’s equator.

Toto
February 9, 2014 9:19 pm

Mooloo says:
“So the ocean sloshes backwards and forwards twice a day”
This metaphor will only confuse. Tides are not sloshing in the open ocean, they are a wave, a very fast wave. If you’ve studied waves, the water in them does not move much, just a bit of mini-sloshing, and less of it as you go deeper. In places other than the open ocean and in shallow water, tides can cause currents like in a river.
Willis Eschenbach says:
“Anyone who includes the other planets in tidal is fooling themselves, the effect is miniscule.”
Here are some numbers to support that.
http://staff.washington.edu/aganse/europa/tides/tides.html

Tidal accels (m/s^2) at pts A & B on Earth due to solar system bodies.
———————————————————————-
due to a_T at A a_T at B
——– ———– ———–
Sun 5.05392e-07 5.05456e-07
Moon 1.09338e-06 1.14948e-06
Mercury 3.65155e-13 3.65232e-13
Venus 5.80684e-11 5.80952e-11
Mars 1.98055e-12 1.98103e-12
Jupiter 6.49978e-12 6.49998e-12
Saturn 2.31856e-13 2.31859e-13
Uranus 3.63353e-15 3.63356e-15
Neptune 1.05777e-15 1.05778e-15
Pluto 5.57134e-20 5.57136e-20

Silver ralph
February 9, 2014 9:23 pm

.
Saros Cycle?
I have always known this as the Metonic Cycle. I presume that these are one and the same:
http://en.wikipedia.org/wiki/Metonic_cycle
Ralph

Clay Marley
February 9, 2014 9:23 pm

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.

As an ex-rocket scientist, I’ll offer one caution. The orbital models needed to fly to the moon or Mars only have to be accurate over the time-of-flight. For the moon that’s 3 days. For other planets, longer but still measured in months to years. And even then we can always update the ephemeris data in flight.
The kind of errors the Chiefio is referring to are those that accumulate over many decades to hundreds of years or longer caused by perturbations that aren’t modeled well if at all. Even if data is provided that goes hundreds of years into the past, how would one test the model?
One clever way is to compare past Lunar eclipses predicted by the model to actual observations. One study Chiefio links to does just that, and finds discrepancies. These discrepancies probably wouldn’t cost me a pound of propellant on a flight to Mars, but might affect my estimate of the tidal forces a hundred years ago.

David Falkner
February 9, 2014 9:30 pm

Willis says:
“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 …”
Willis:
Since you bring this up, how do we know that this “reconciliation” you are speaking of hasn’t screwed with the comparability of each year? 1 day every four years means something different on Earth than it does at the Sun, especially over 200 years. In terms of solar activity, things may be considerably different and this may be masked because of a simple little thing like leap years. And missed by people who are quite ready to brush it off as an accounting trick.
You acknowledge it is to keep the seasons straight that we make this adjustment, but what effect would not making the adjustment have? Are we just booking an adjustment because we always have and we don’t have the underlying support? Is this an audit difference?

February 9, 2014 10:19 pm

The [trimmed] Scafetta is back again.
Here is the correction he issued to one of his papers
################################################
“The author would like to substitute the following lines
“Consequently, the IPCC projections for the 21st century should not be trusted.” (Page 126.)
and
“Consequently, the IPCC projections for the 21st century cannot be trusted.” (Page 135).
to
“IPCC projections for the 21st century should be viewed with great caution because the historical temperature data are herein shown to be likely interpretable in an alternative way that stresses the importance of natural cyclical variability, which would lead to very different 21st projections”.
that may more appropriately describe the findings of the paper and the true intention of the author.
The author would like to apologise for any inconvenience caused.
####################
that’s a man of his convictions.. Not.

JP
February 9, 2014 10:32 pm

This is getting too much of a personal Eschenbach outlet here. Nothing personal, but I’m moving over to Bishop Hill for my climate news.

charles nelson
February 9, 2014 10:45 pm

So when you were calculating your ‘tidal forces’ you took the perigees and apogees into consideration did you?
You factored in the Periselene/Pericynthion/Perilune and the Aposelene/Apocynthion/Apolune?
I hope you didn’t forget to do the calcs on the basis that the Earth and Moon orbit about their barycentre (common centre of mass), which lies about 4600 km from Earth’s centre (about three quarters of the Earth’s radius).
And I’m sure you didn’t leave out the 18 year precession of nodes….

charles nelson
February 10, 2014 12:15 am

I think the laughter is mostly directed at you Willis…and by the way do let us know when you ‘calculate’ how many angels can dance on the head of a pin.

Carbomontanus
February 10, 2014 11:20 am

[snip – ok, your off-topic rantings about the “iron curtain” have gone over to the loony zone now. I’m assigning you to the troll bin then since you’ve been warned previously – Anthony]

wayne Job
February 10, 2014 12:32 am

Hi Willis,
Thank you for your explanation, I have but one problem, some large lakes north of the moons track. Have small tides that are measurable. North of the moons path. The tide runs away from the moon, like the water is repulsed, this tends to bother my brain some what.
Maybe you have an explanation, if you have I would like to hear it.

markx
February 10, 2014 12:44 am

JP says: February 9, 2014 at 10:32 pm
This is getting too much of a personal Eschenbach outlet here. Nothing personal, but I’m moving over to Bishop Hill for my climate news.
Ha ha .. that sort of statement is always cute! Can’t control your eyeballs, eh?
What I do if I don’t like something is to skip over it … You could skip every second article here and you’d still get more reading than at Bishop Hill (much as I do appreciate BH).
Hang on a sec, think of the free time I’d generate! Maybe I should follow your lead?

Mooloo
February 10, 2014 1:24 am

Toto says:
This metaphor will only confuse. Tides are not sloshing in the open ocean, they are a wave, a very fast wave.

The problem is that people think that the molecules that propagate the wave are moving a lot. Hence they get the impression that there is a huge shift in the water with each tide, that will somehow mix it, and mix it more if the tides are a bit bigger.
Whereas, a wave doesn’t require very much movement at all by its individual components. They just have to align to move in the same direction for a brief period of time.
The idea that anyone would seriously consider that the long run cycles in tides affects the amount of mixing bothers me.
(I note that many people seem to think that winds are somehow affecting the amount of mixing. I find that very difficult to believe. The surface layer isn’t going to be still at the best of times, so more mixing of a well mixed top couple of metres makes little difference. I doubt strongly that winds cause deep mixing beyond that layer. The concept that winds can cause water to not just pile up, but then force it downwards seems very unlikely IMO. The overwhelming power of the Humbolt Current, Gulf Stream etc are orders of magnitude more important.)

bobl
February 10, 2014 1:41 am

Willis, I do disagree, but its hard to cite what, but I do think your conclusion is unjustified. Recently at a conference I was treated to a very interesting lecture about how the great floods of Queensland, Australia are correlated to solar and lunar juxtaposition. His premise is that floods occur when the sun and moon are both at apogee in the wet season, since the orbital patterns repeat each 18 years the weather effect has an 18 year cycle (except I guess it is the earth at apogee, but you knew what I meant right?). Interestingly this occured in both summer of 2011 and a less pronounced peak in summer of 2013, both of which had great floods.
Anyway, while the tidal forces themselves may have no pattern the way they interact with the seasons and the monsoon certainly does show a pattern. At least in northern Australia.
Where, and when the tidal forces peak is important.

February 10, 2014 2:08 am

The eccentricity of the moon’s orbit around the earth is not constant and is varying on a monthly to yearly basis. I know this sounds crazy – but it really is true. If you plot out the eccentricity values of the moon relative to the earth-moon barycentre using JPL ephemeris – for example take their horizon interface you will get the following :
graph shown here
There are at least 2 regular resonances which at first sight seems odd because neither coincide with the orbital period of the moon (27.32days) nor that of the earth (365.25 days). There are also beats in the amplitude. Following this german article, I made a least squares fit shown as the blue curve which reproduces almost perfectly the signal .
eccentricity(d) = 0.55 + 0.014cos(0.198*d + 2.148) + 0.0085cos(0.0305*d +10.565)
This variation in eccentricity changes the perihelion distance from the earth significantly causing large variations in the strength of spring tides on a yearly basis. The eccentricity becomes a maximum when the semi-major axis of the orbit lines up with the sun. This happens every 205.9 days – more than half a year due to the precession of the orbit every 18.6 years. The 31.8 day variation is I think the regular orbital change in distance from the sun.
The moon is really in orbit around the sun because the sun’s gravitational field on the moon is twice that of the earth’s. The moon’s orbit is locked into that of the earth to give an effective lunar orbit as viewed from earth. It turns out to be impossible to accurately calculate the moon’s effective orbit around the earth far into the past. The error on the lunar eccentricity becomes > 100% more than 1 million years ago as reported in Laskar et al. 2010. Who knows what happens to the lunar eccentricity when the earth’s eccentricity around the sun increases with Milankovitch cycles ? Large changes in the lunar-earth distance will have very large (1/R^3) effects on tides and indirectly on climate.

Greg Goodman
February 10, 2014 2:24 am

“Thank you for your explanation, I have but one problem, some large lakes north of the moons track. Have small tides that are measurable. North of the moons path. The tide runs away from the moon, like the water is repulsed, this tends to bother my brain some what”.
It’s because teh tidal works in both directions ! Yeah, sounds mad and is a bit hard to imagine but the tidal force is due the gradient or divergence of the gravitational field.
Graivity falls off as inv sqr law : 1/r^2 the rate of change with respect to radial distance is thus proportinal to 1/r^3 , hence the r^3 in the formula.
So it’s not just a simple gravitational tug as one would think intuitively.
So the nearest part of the ocean gets more gravitational attraction than the centre of the Earth, Equally the ocean at the opposite side to the moon gets _less_ attraction in about the same measure when compared to the centre of the Earth. The Earth gets accelerated towards the moon more strongly than the far ocean which gets ‘left behind’ so to speak.
That is why many tides tend to happen twice per day. That’s called semi-diurnal. This is a simple case when the moon is over the equator.
When the moon is not over the equator one of these simplistic “bulges” (which don’t actually happen like that in reality) is circling to the north and the other to the south. Thus it is a once a day event as the Earth rotates.
There is some overlap and the result a composite tide with both diurnal and semi-diurnal components.
It took me a long time to find that out because there is an enormous amount of misunderstanding and misinformation even from academic sources.
Hopefully this will help others understand with a lot less effort.

RichardLH
February 10, 2014 2:30 am

Willis Eschenbach says:
February 9, 2014 at 5:33 pm
“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.”
Ok, this is going to get long. Sorry in advance for those who have to wade through it.
So we have Earth, Moon and Sun in a constant, never quite repeating gravitation dance with very minute additional factors that influence both of the TWO components of the gravitational field and its impact here on Earth.
Now I really do not know the answer to all this and it may well end up in the ‘Meh – Who cares’ bucket that you (and Leif) so quickly placed it in but, as people are calculating temperatures to 1/100s of a degree C, I hope you will bare with me whilst I try to lay the case out.
Firstly the vertical component to the field is as you plotted at the top. This should strictly be plotted around the barycentre (but others have mentioned that already). The vertical field is every so egg shape – pointy end towards the Moon – as this is the sum of two different forces to make the one field (otherwise we would have only one tide a day). Picky points but 1/100s of a degree is picky also. Now this plot gives the vertical field on a water only globe (rotating or not as you wish).
We still have the other component, the tangential to the surface field that happens at 45 to 60 degrees to the orbital plane as shown by me above (from Wiki). This is the part of the picture, overlooked so often, that I believe may be what is the important bit here. This is a force not seeking to raise the water/atmosphere up and down but to push it sideways back and forth along the surface. It operates across the whole cross-section of the water/air column and does not have the same high speed pattern that the vertical vector does because it is an almost constant angle despite the rotations.
So we have the two ellipses of the two orbits beating horizontally now. We are still missing the other major factor. The vertical beating. The two orbits are not aligned to each other vertically. So there is another supple beat happening there as well. That IS influenced by Saturn in particular which moves the path up and down (I know not very much but details again).
Whilst we are at it lets bring in the fact that the Earth is not rotating at right angles to the orbital plane either. Not important so much if this was a water only globe but if that was the case we wouldn’t be here to worry about this stuff.
With a land/ocean mixed globe this now becomes much more important. Now we have to worry about fixed points on the globe as it rotates. That brings in the Leap Year ‘same point in the sky, same time of day, same day of the year’ detail as well as the Saros cycle.
Now we have the ‘lever’ reasonably well defined and it modulates around its central value but how does that operate here on Earth. What ‘fulcrums’ are there against which it can operate?
Now land/ocean geography plays its part.
That tangential field. It operates at 45-60 degrees or so, and the important Geography appears to lie in the Northern Hemisphere. And the vertical field (much smaller) also operates on the North Pole (and the South Pole as well but that is all land). This vertical component operates with the same periodicity as daylight and we all know how daylight operates at the poles. Not the same quick pattern as tides/daylight elsewhere.
So we have a multi chamber, geographically defined, pumping system driven by the vertical field and ported to the rest of the rest of the Oceans through some very small Straights and Cills that surround the Northern Oceans. This sucks water in and out through the Straights and the resultant opposes or helps the currents that otherwise flow through them.
Then we have the tangential component also helping or preventing current flow though the other major Straights and Cills between Greenland to Scotland.
These are tiny flows of a few knots at best and it is the percentage change that matters, not the absolute value. Anyone who sails knows that tidal stream can well affect motion over the land and this is the sort of effect we are seeking. A few meters rise in the Ocean surface if a Cill height is only a few hundred meters or less matters also. Current will flow much easier in one case than the other.
The atmosphere may also be of interest when considering the tangential component as well. This 45-60 degree band is precisely where the Polar and Ferrel Cells meet. Does that ‘along the surface or slightly upwards/downwards’ vector affect where it forms or not?
And now we are in territory that is well beyond that of simply downloading data from JPL and running a plot. This is super-computer land and I don’t have one of those to hand.
Hence the curiosity.
Can simple, physics based, field vector maths and some fluid dynamics explain the longer term patterns we see? No exotic theory. Just a simple application of known physics to the case in hand.
Anyone got a research grant? Oil money?……

RichardLH
February 10, 2014 2:36 am

Willis Eschenbach says:
February 10, 2014 at 1:08 am
“47, everyone knows that.”
I thought it was 42 (and that mice and dolphins were the reason) 🙂

Kasuha
February 10, 2014 2:40 am

Venus and Earth trajectories around Sun can be thought of as independent periodical signals. And you may say that there’s nothing like a 243-year period after which the cycle repeats, it’s just how the two independent signals add up.
Except that Venus transits over Sun happen at such period.
I don’t really disagree with any of your conclusions, but I can see your methods. When you want to prove there is a period, you use periodicity analysis and declare it better than fourier transform. When you want to prove there is not the period, you use fourier transform.
The truth is, the strongest tidal effect event happens with the 54-year period. It may not be much stronger than other local maxima, but similarly to the Venus transits, there is certain period to them.

Greg Goodman
February 10, 2014 2:47 am

Clive Best: “The eccentricity of the moon’s orbit around the earth is not constant and is varying on a monthly to yearly basis. I know this sounds crazy – but it really is true. ”
It’s not that odd. The changes in the moon’s orbit are due to the graviational effect or the other planets. How they interact and line up will be very complex. Also the sun is not stationaly with respect to a inertial frame of reference. It has its own path relative to the solar system barycentre.
Since the earth and the moon are orbitting the sun we get pulled around with it.
So Willis is quite correct that the direct effect of planetary gravity on Earth is neglibible but it is wrong to conclude that the postition of the planets has no effect or the Earth or the moon.
The moon’s orbit is somewhat eccentric, at it’s most extreme the difference between closest approach (perigee) and furthest distance (apogee) is about 14% . The produces a difference of around 40% in r^3 hence the lunar tidal force. It goes from one extreme to the other and back in 27.55 days.
I have detected this period in the Arctic ice data:
http://climategrog.wordpress.com/?attachment_id=757
The alignment of the this excentricity is called the line of apsides and it too rotates with respect to rest of the system with a period of 8.85 years
It really requires some mental gymnastics to try to visualise all this but it is not neither simple nor negligible, in view of the 40% change in tidal force.
Oh, and just for added fun that 40% goes up and down about twice a year ( in fact rather more than 6 months).
I think that’s what Clive’s plot was showing.

cd
February 10, 2014 2:51 am

Willis
The article seems rather terse. Could you answer a few queries:
1:
I’ve been listening to lots of stuff lately about tidal cycles. … 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.
There is no background literature provided, you have the reader at a disadvantage. Is there any that pertains to this data/approach.
2:
Your Fourier analysis plot is a bit unconventional (by my experience). Are your amplitudes computed as the magnitude of the complex form (sin and cos). It’s seems an unusual way to plot these; mixing frequency and time domain. I’m guessing you have simply converted wave numbers to their wavelength for ease of expression?
Have you looked at the phase spectra? Would this offer anything?
3:
sqrt( sun_force^2 + moon_force^2 + 2* sun_force * moon_force * cos(angle))
I don’t get this. Surely you should just modulate the sun_force with the magnitude of the dot product (i.e. |cos(angle)|):
sun_force = sun_force * |cos(angle)|. Then:
F=sqrt(sun_force^2+moon_force^2);
Perhaps not but could you explain why?
4:
Finally, what is the point of the article? What is the take home message? And why is it important?
Is it that the 54 cycle point is lost do you mean there is meant to be one and you’ve showed there isn’t. I could be missing something but you don’t seemed to have shown this.

Greg Goodman
February 10, 2014 3:01 am

Mosh’ says: “that’s a man of his convictions.. Not.”
No that’s a man who is prepared to make a correction when he overstated the case in a published article.
Constast that to someone like lsvalgaard Vaghan Pratt who will argue till they’re blue in the face rather than admit he made a mistake. That kind of “conviction” I can do without.
Scafetta’s correction seems honorable. At least he has the humility to admit he overstated the case and correct it. That should be applauded, not used in a mud slinging exercise.
If you try to shoot down people every time they correct themselves you lessen likelihood of it happening.
That is just yahboo politics, not scientific debate.

Greg Goodman
February 10, 2014 3:06 am

Willis , are you able to provide a precise value for the peaks in fig2 ?
In particular the ones that look to be circa 27, 29 days and 13 months.

February 10, 2014 3:06 am

Scafetta could satisfy 99.9% of his critics with a full release of data and code in order to enable replication of his papers, which currently cannot be treated as much more than anecdotes. Then he could be actually shown to be right or wrong and the majority will go where logic goes. As long as he continues to evade his responsibility as a scientist, criticism will increase, not abate.

RichardLH
February 10, 2014 3:31 am

charles the moderator says:
February 10, 2014 at 3:06 am
“Scafetta could satisfy 99.9% of his critics with a full release of data and code in order to enable replication of his papers, which currently cannot be treated as much more than anecdotes.”
Well I have continuously shown that there is a ~60 year pattern to the data, with or without Scafetta data and code.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Extendedtempseries-secondpass_zps089e4c7d.gif
Now with added proxy data as well to satisfy Jai who is SO convinced that it does not exist as well 🙂 ).
This is just simple ‘Gaussian’ low pass filter stuff but it independently confirms at least part of his case.

Greg Goodman
February 10, 2014 3:42 am

AW says: Well, that frequency certainly took a beating.
Willis:”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.”
Once thing you may not be realising Willis, and relates to all the comments I left yesterday trying to explain the way cycles combine in what we may loosely call “beats” or modulation.
The point is the equivalence of modulation (two signals multiplied together) and two different cycles that are added.
Now fourier analysis, by definition only captures single frequencies of fixed amplitude. So if you have data with a modulation it can not detect it as such. Instead what you get in the spectrum is two cosines that , added together, mathematically equivalent to the modulated form and will reproduce it perfectly if added together.
This is the old half-the-sum * half-the-difference game again. (Talking in freq, not period).
Again you can see an example in my arctic ice plot.
http://climategrog.wordpress.com/?attachment_id=757
There is 4.31 year modulation but this does not show up in the spectral analysis as 4.31 years. It shows as a triplet of peaks at
p1=27.1256
pc=27.6006
p2=28.0939
The central peak may sometimes be negligible . It is p1 and p2 that represent the modulation that in reality is 4.31 years. ie in a totally different part of the spectrum.
Similarly when you look at charts of tidal periods these are also “fourier” components and may (will) add together to give long period cycles. Thus absence of long periods in the list does not mean there are not long period cyclic patterns in tides.
There is clearly some kind of modulation pattern in your figure 3
It looks pretty sinusoidal and constant across that data, so probably results from just two components.

RichardLH
February 10, 2014 3:51 am

Greg: Lief: Willis: Whoever…
This thing about adding or multiplying for frequencies. The true answer is that it is always both.
So we get FM radio type stuff with addition where the frequencies are a long way apart.
And we get moiré interference patterns where the two are closer together.
For frequencies that are neither obviously one or the other often both factors are visible quite easily.
Thus 60 and 4 gives 4, 56, 60, 64 and 240.
2000 and 4 gives 4, 1996, 2000, 2004 and 8000.

Greg Goodman
February 10, 2014 3:57 am

N. Scaffeta also used ephemeris data in one of his papers to look at how the moon affected Earth’s orbit of the sun. By comparing spectra of Earth speed relative to the sun and that of the Earth-Moon ensemble (speed of EM barycentre) he showed that there was a 9.1 year variation that was caused by the presence of the moon.
I thought that was pretty ingenious.

Greg Goodman
February 10, 2014 3:58 am

Richard, “So we get FM radio type stuff ”
frequency modulation is another can of worms entirely , is that what you meant?

February 10, 2014 4:27 am

So it was this “spring” tide and not CO2 that gave Hurricane Sandy that extra push to help flood NYC and NJ?:
http://news.nationalgeographic.com/news/2012/10/121029-hurricane-sandy-path-storm-surge-full-moon-nation-weather-science/
I thought it was CO2 and so did the President, the Governors, and Al Gore…(sarc)

February 10, 2014 5:13 am

Incidentally, I still think it should be abs(cos(theta)) because there are two spring tides every month. The graph shows only one spring tide per month.
Sun – moon – earth. Theta =. O. Cos(theta) = 1.0. New moon
Sun- earth – moon. Theta = PI. Cos(theta) = -1.0. Full moon
Neap tides occur when theta = pi/2 and 3pi/2
The tidal bulge on the opposite side to the moon is mainly caused by the centripetal force of the earth rotating around the barycenter like a pair of scatters in a spin. When the sun is on that side the solar tide then increases this effect further. So we get a second spring tide when theta = pi.
IMHO the second bulge is NOT caused by an increased gravity on the near side surface to that on the centre of the earth. It is a pure rotational effect.

February 10, 2014 5:25 am

Of course that should be “a pair of skaters in a spin”
How I hate auto-correction on iPads !

Greg Goodman
February 10, 2014 5:38 am

As Willis says, this is just the theoretical tidal force or tidal potential. It is not in any way a measure of tides or the movement of water that actually happens.
The force calculated here exerts a force on the oceans , where and how the water actually moves is a whole other storey, that has as much to do with the 3D shape of the ocean basins and coastlines as it has to do this the primary driving force.
The hypothetical “bulges” get amplifies as the enter shallow waters , reflect of irregular coastlines and flow back out to sea. The passage of the moon is constantly moving on both a monthly and annual scale. The resulting tides are so complex that they still can not be modelled in anything but the vaguest terms and we still rely on empirical charts specific to each geographical locality as Willis discovered in the Solomans.
In fact tidal patterns progress in all directions and there are some points on the global called amphidromes that do not have ANY tides at all. Others have four tides a day, others just one.
http://en.wikipedia.org/wiki/Amphidromic_point
What Willis has plotted is the _magnitude_ of the tidal force. What is not shown is its direction.
The sun moves from one tropic to the other and back again in a year. The moon follows this but in addition moves +/- 5 degrees either side in cycle that takes 27.2 days. This “draconic” month is again different from the 27.55 day period I mentioned above.
The draconic cycle is the 2 ascending and descending moon people often confuse as being the same thing as the visible waxing and waning cycle. 29.53 days average.
Now all this really matters if you want to talk about real influence on the tides because force is a vector, with magnitude and direction, not a scalar as Willis has plotted.
When the sun is at it’s most southerly point 23.5 S the moon can go 5.1 degrees further south. This means tides will be at their most displaced from the equator and there will be a minimum of the semi-diurnal and a maximum of the diurnal components.
Willis linked to this paper yesterday which suggest 18.6 years is the relevant long period not the “saros” cycle of 18.01 that Willis is focusing on here.
http://www.jstor.org/discover/10.2307/621006?uid=3738032&uid=2&uid=4&sid=21103363205771
18.6 is the period of the precession of the lunar nodes. This is what affects the “declination angle” or the height of the moon in the sky , ie time between the 23.5+5.1 degree extremes I mentioned above.
Because of the ‘push-pull’ nature of tides it is the magnitude of the declination angle that determines whether sun and moon tides are focused on equator or pulling out to N,S extremes simultaneously.
Thus the period of water being draw towards or out of the tropics will be 18.6 / 2 years.
That will not be included in Willis plots or his spectra since he has explicitly ignored the directional component of the resultant force (though he did correctly us it to sum the forces).
So Willis found a little peak around “8.7” years. I would suggest more detailed examination would reveal it is 8.85 , the precession of lunar apsides. He did not find 9.3 and that is to be expected as I said from that analysis.
So far so good. We have picture of what long periods may be produced. Next step is to see whether there is any evidence of them in climate data.

RichardLH
February 10, 2014 5:39 am

Greg Goodman says:
February 10, 2014 at 3:58 am
“frequency modulation is another can of worms entirely , is that what you meant?”
It was an observation that frequencies always both add and multiply.
We just use that fact in different ways at different times. It can be very difficult to spot that they are there at times as it often just ends up as spreading the peak rather than them being visible as separate frequencies – but the maths says they are both there all the time.

RichardLH
February 10, 2014 5:46 am

Greg Goodman says:
February 10, 2014 at 5:38 am
“As Willis says, this is just the theoretical tidal force or tidal potential. It is not in any way a measure of tides or the movement of water that actually happens. ”
Indeed. The plot is for the vertical component only and for a water only Earth.
As I tried to point out above, it is how all this, the tidal bugle in a Sea/Ocean basin coupled with the tangential vector, into a tidal flow that affects the water/air movement through the Cills and Straights North/South is likely to be the main factor of interest. And that is a very much slower and complex cycle than the daily tides.
That tangential vector is almost never discussed or mentioned.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Tidalvectors_zps4fd5800f.png

Greg Goodman
February 10, 2014 5:47 am

CliveBest: “The tidal bulge on the opposite side to the moon is mainly caused by the centripetal force of the earth rotating around the barycenter like a pair of scatters in a spin. When the sun is on that side the solar tide then increases this effect further. So we get a second spring tide when theta = pi.
IMHO the second bulge is NOT caused by an increased gravity on the near side surface to that on the centre of the earth. It is a pure rotational effect.”
I was of that impression too at one stage but no. You need to understand that tides are caused by gradient of gravitational field ( grad operator in 3D) and not by gravitational attraction. That is confirmed by the 1/r^3 dependence not 1/r^2. They are essentially equal except for minute higher order corrections. I went into that in some more detail above.
Centrifugal force would be much stronger in the case of the sun and it would be very obvious in relation to the lunar tides. Solar is about 1/4 of lunar because of inv. cube. An inv. sqr effect would stick out a mile.

RichardLH
February 10, 2014 5:52 am

Greg Goodman says:
February 10, 2014 at 5:47 am
“They are essentially equal except for minute higher order corrections.”
I believe that the true filed is slightly ‘egg shaped’, pointy end towards the Moon. The Solar one is more equal. AFIK.

Henry Bowman
February 10, 2014 5:54 am

Willis writes

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.

I don’t agree with your assessment, but if you are interested in more modern methodology, I suggest you check out the software package TSoft, developed and maintained by the Royal Observatory of Belgium, continuing Melchior’s decades-long efforts to study tides.

Greg Goodman
February 10, 2014 5:58 am

http://climategrog.wordpress.com/?attachment_id=757
Here we have the anaomalistic lunar month in arctic ice extent. Modulation is detected as 4.31 years
http://climategrog.wordpress.com/?attachment_id=774
frequency spectrum of Indian ocean SST reveals a strong peak at 9.32 years.
Looks a lot like 18.6 / 2 years.
The Indian ocean shows temperature records quite different from the other main oceans that are connected north and south. Here the declination angle seems to produce a prominent cycle.

Editor
February 10, 2014 6:04 am

Normally, I’m hesitant to jump onto the “planetary influence” bandwagon, but…
I notice that in your “monthly” tidal forces graph, there’s a peak at just over 13 months. My first thought was the Chandler wobble http://en.wikipedia.org/wiki/Chandler_wobble but that’s 433 days, over 14 months, so it’s not the answer. Now let’s look at at some planetary orbital data http://nineplanets.org/data.html
Earth orbits Sun in 365.26 days
Jupiter orbits Sun in 4332.71 days
The “beat frequency”, i.e. time between conjunctions, is…
1 / (1/365.26 – 1/4332.71) = 398.89 days
Can you “zoom in” on your analysis and see if that period matches the peak just past 13 months?

cd
February 10, 2014 6:07 am

Greg Goodman
Now fourier analysis, by definition only captures single frequencies of fixed amplitude. So if you have data with a modulation it can not detect it as such.
Fig. 1 looks like a modulated signal of:
high frequency carrier (pure sinusoid) * long range variation (structural signal)
Surprisingly, the spectra does not seem to show the “modulation” fingerprint.
But great points all the same.

Coldlynx
February 10, 2014 6:10 am

Atmospheric tide:
“Atmospheric tides are also produced through the gravitational effects of the Moon”
http://en.wikipedia.org/wiki/Atmospheric_tide
Do not forget the smaller solar tide.
Add to that the earth axial tilt and get a tide induced movement of air towards the poles in summer and from the poles in the winter.
The largest daily horisontal tidal force are during sunrise which accelerate air eastwards. Small force but rather long time of acceleration for some hours every day. In NH summer northeast due to earth tilt. During sunset is the largest tidal force deaccelerating the same airmass northwest in NH summer. Net force north but since day is longer than night and the net movement of the atmosphere be northeast.
In winter will the morning horisonal acceleration be southeast and evening retardation be southwest. The net force south and net movement southwest due to longer nights.
This will have an impact on winds patterns and climate. Not big but the effect will be there.
The Coriolis effect is also a small force with huge impact.
http://en.wikipedia.org/wiki/Coriolis_effect

Greg Goodman
February 10, 2014 6:23 am

North Atlantic SST shows 9.066 as main peak:
http://climategrog.wordpress.com/?attachment_id=217
Cross-correlation of N.Atlantic and ex-tropical N. Pacific shows a strong peak at 9.06 years
http://climategrog.wordpress.com/?attachment_id=755
As detailed in the text with the plot this could be a combination of 18.6 / 2 and 8.85 years.
In contrast to the Indian ocean there seems to be both declination and aspides cycles at play here.
A similar frequency was recently reported by BEST team by looking at cross correlation of AMO and PDO. I preferred actual SST to the processed PDO “index” but essentially the same period is found.

Greg Goodman
February 10, 2014 6:26 am

cd “Surprisingly, the spectra does not seem to show the “modulation” fingerprint.”
You won’t see it _directly_ in a spectral analysis.
That’s whole point of my comment which you read but apparently did not understand.

Greg Goodman
February 10, 2014 6:29 am

walterdnes says: Chandler etc.
Not planets. Probably 14 lunations. 29.53*14 = 413. = 1.13 years.
I haven’t got Willis’ code load properly but may be he can provide a central value for that peak.

Greg Goodman
February 10, 2014 6:40 am

Richar: That tangential vector is almost never discussed or mentioned.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Tidalvectors_zps4fd5800f.png
I did not get your point last time you posted that.
The point is , even without looking at the tangential vector, for a high tide to happen water has to come from somewhere else. When you look at water movement it does well-up from the deeps it is mainly a horizontal movement of water.
To create a high tide, surface water comes in from all around.
If there are temperature differences in SST, movement like that carries thermal energy.
As declination angle pulls tides towards or away from the equatorial zones in a 9.3 year cycle this will displace large amounts of heat energy. It is easy to see why this period is recurrent basin wide SST records.

February 10, 2014 6:40 am

Greg,

You need to understand that tides are caused by gradient of gravitational field ( grad operator in 3D) and not by gravitational attraction. That is confirmed by the 1/r^3 dependence not 1/r^2. They are essentially equal except for minute higher order corrections. I went into that in some more detail above.

Yes I am well aware that tides are caused by the gradient of the gravitational field. Hence the 1/r^3 dependence. Hence the the reason the lunar tide is about twice the solar tide despite the sun being 27 million times the mass of the moon. You haven’t understood what I am saying
It is the tractional component of the gravitational force of the moon acting on the oceans which gives rise to a tidal bulge. The tractional gravitational component is the projection onto the spherical surface of the earth which increases with angular distance from the vector joining the moon to the center of the earth. This works out as 1/r^3 effective tidal force and explains the cause of the bulge on the surface facing the moon. However the bulge on the opposite side has a different origin. The centripetal force is caused by the rotation of the earth about the earth-moon barycenter (located 4000km from the centre of the earth) during the lunar month. The change in centripetal force across the spherical surface of the earth also leads to a 1/r^3 dependence. A point on the earth perpendicular to the moon-earth vector feels no centrifugal force. A point opposite the moon feels maximum centripetal force. Somewhere in the middle the ocean feels a component of centrifugal force that is parallel to the earth’s surface. This parallel component then leads to the tidal bulge opposite the moon.
The centripetal force of the earth’s orbit around the sun is much smaller as the pivot point is 93 million miles away and the angular velocity is much smaller.
I just don’t buy the argument that the difference in gravity between the lunar facing surface, the centre of the earth and the opposite facing surface causes the second bulge.

RichardLH
February 10, 2014 6:41 am

Greg Goodman says:
February 10, 2014 at 5:58 am
“The Indian ocean shows temperature records quite different from the other main oceans that are connected north and south. Here the declination angle seems to produce a prominent cycle.”
I suspect that this is because the tidal flow is limited by the West – East land block to the North. This severely limits the effects in the Indian Ocean. You also need to consider how the orbital inclinations of both Sun and Moon interact with the normal ‘vertical’ globe we tend to think of. The maximum, central point is always some form of elliptical line running across the surface. In the case of the Indian Ocean this falls on land a lot of the time.

February 10, 2014 6:42 am

Important paper on tidal influence on climate:
Ray, RD, 2007: Decadal Climate Variability: Is There a Tidal Connection?. J. Climate, 20, 3542–3560. doi: http://dx.doi.org/10.1175/JCLI4193.1

RichardLH
February 10, 2014 6:46 am

Greg Goodman says:
February 10, 2014 at 6:40 am
Richard: That tangential vector is almost never discussed or mentioned.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Tidalvectors_zps4fd5800f.png
“I did not get your point last time you posted that.”
Look again at the diagram. The tangential to the surface force varies very slowly. It is at an angle to the orbit and only changes with that. It does not follow the normal daily pattern. It is much slower and more likely to be the ~60 year interaction.
This is a force that is horizontal to the surface. One that is likely to affect flows of all sorts North-South.
Sure flows caused by different vertical effects in basin North – South will also be in there, but they are on a much faster Daily timescale.

RichardLH
February 10, 2014 6:59 am

clivebest says:
February 10, 2014 at 6:40 am
This is always how I have believed the two tides explanation was supported in Physics.
http://i.stack.imgur.com/aE7Gd.jpg
from
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics
http://physics.stackexchange.com/questions/46792/tidal-force-on-far-side

February 10, 2014 7:00 am

Greg,

What Willis has plotted is the _magnitude_ of the tidal force. What is not shown is its direction.

No – he has plotted the magnitude of the “sub-lunar” tide and has ignored the “antipodal” tide. In other words when there is a full moon with the moon is on the opposite side to the sun the tidal force is again at a maximum. What he has plotted is just one tide per day and ignored the second tide. This error is compounded because at full moon he has the solar tide subtracting from the sub-lunar tide , whereas the opposite is the case. This subtle effect is now due to the alignment of the “antipodal” tide with the sun’s tidal force.

Greg Goodman
February 10, 2014 7:04 am

CliveBest: “The eccentricity becomes a maximum when the semi-major axis of the orbit lines up with the sun. This happens every 205.9 days – more than half a year due to the precession of the orbit every 18.6 years. ”
There’s the answer to the “13mo” peak.
Twice that value is almost exactly the 14 lunations that I suggested. It’s the alignment of max eccentricity with the visual lunar phase. ie full moon and max eccentricity (closest approach “perigee”) being at max lunar+solar tidal force alignment.
I’m a little curious why this is showing as a separate peak since the individual components should already be present in the rest of the spectrum. This implies a non linearity.
Since the ephemeris is essentially empirically based, perhaps it is picking up some slight variation in the E-M orbit due to ocean movement.

RichardLH
February 10, 2014 7:08 am

clivebest says:
February 10, 2014 at 7:00 am
“No – he has plotted the magnitude of the “sub-lunar” tide and has ignored the “antipodal” tide.”
And only for a water only Earth. Also one that doesn’t matter where the spin axis is. The real Earth has both of the complications to add as well.

RichardLH
February 10, 2014 7:10 am

Greg Goodman says:
February 10, 2014 at 7:04 am
“This implies a non linearity.”
As I mentioned above – the tide is egg shaped which may well be what you are seeing.

February 10, 2014 7:12 am

Richard,
Yes – this is exactly right !

It is only the horizontal component of those vectors that is moving any water in the oceans.

dan
February 10, 2014 7:37 am

Generally agreed that the tide-stuff is “tiny” but depending on the context, “tiny” can still have implications. Curious of opinions…

Greg Goodman
February 10, 2014 7:44 am

http://i.stack.imgur.com/aE7Gd.jpg
Where does that come from Clive? Is the ‘egg’ shape due to the addition of a centrifugal component?

February 10, 2014 8:59 am

Greg,
Yes I think the egg shape is due to the combination of the centrifugal force of the earth’s orbiting the earth-moon barycenter and the vectoral sum of the lunar and solar tidal forces.
One clear climate effect of the month can be seen in measured TSI data- see http://clivebest.com/blog/?p=2996. The earth changes its distance from the sun by up to 8000km each lunar month. This change in net solar insolation induces a regular change in global temperatures of ~0.02C.

cd
February 10, 2014 7:47 am

Greg Goodman
That’s whole point of my comment which you read but apparently did not understand.
No a simple DFT of an AM signal gives a very characteristic spectral signal: symmetry about the peak for the fundamental frequency of the carrier (double sideband fingerprint). Rather elementary stuff really.
Understand perfectly – not so sure you do though.

Greg Goodman
February 10, 2014 7:52 am

“It is only the horizontal component of those vectors that is moving any water in the oceans.”
‘Only’ I don’t think so. It’s all part of the effect. If the perpendicular force was not pulling up, the horizontal force would be fighting terrestrial gravity to pile up the water. It needs to be viewed as a whole.
Since none of the happens anyway be cause we don’t not live on a water only planet it’s just a thought experiment to see how forces act. This only one part of the story of actual tides, it’s just initial driving tidal forces.

RichardLH
February 10, 2014 8:00 am

Greg Goodman says:
February 10, 2014 at 7:52 am
““It is only the horizontal component of those vectors that is moving any water in the oceans.”
‘Only’ I don’t think so. It’s all part of the effect. If the perpendicular force was not pulling up, the horizontal force would be fighting terrestrial gravity to pile up the water. It needs to be viewed as a whole. ”
Indeed. The combination is the thing. Vertical forces acting on a Basin/Ocean can only be supplied by water flowing in and out from somewhere. Some of it is East to West to be sure but some has to be North to South.
Which is why all of this is about tidal flow not tidal height.
And the point is that the tangential vector is at an orbital not daily modulation.
Think daylight and how it varies over the planet over the year. That is how the tangential vector modulates. At the North Pole for instance that vertical vector of the field only changes over a 12 month cycle, not a daily at all. At the equivalent of the Arctic Circle (not the real one because this is Moon orbit, not Solar) then it is all Tangential.
The further and further away from the poles you go, the more the Vertical, daily, component becomes important.
This is all very complex stuff and well beyond a simple JPL plot I’m afraid.

David L. Hagen
February 10, 2014 8:01 am

Willis and Charles the Moderator
Willis: Re: ” no data, no code, no science.”
Charles the Moderator: Re: “Scafetta could satisfy 99.9% of his critics with a full release of data and code in order to enable replication of his papers, which currently cannot be treated as much more than anecdotes.”
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?
Now he may have errors in his software/calculations (I have found errors in my own code etc.).
His releasing his code would help others to see if there is or is not.
However, if its public data and clearly explained method, I do not see how you can fault him for that.
Per your link to New Scientist, “Sceptical climate researcher won’t divulge key program”

” emails between Benestad and Scafetta over the past week, in which Scaffetta repeatedly refused to provide the code. “If you just disclose your code and data, then we will manage to get to the bottom of this,” Benestad writes in one email. “I really do not understand why you are not able to write your own program to reproduce the calculations,” responds Scafetta.
In response to direct questions from New Scientist, Scafetta said the code in question had been submitted to a scientific journal and that if “the journal takes its time to publish it, it is not our fault”. Benestad says the code he is asking for relates to papers already published.

Charles “Scafetta could satisfy 99.9% of his critics” – hyperbola.
Unlikely satisfy climate alarmists –
And I have my doubts that even that would satisfy Willis.
In an alternate theory, QB Lu suggests halogenated hydrocarbons have a major contribution to earth’s climate. e.g.
COSMIC-RAY-DRIVEN REACTION AND GREENHOUSE EFFECT OF HALOGENATED MOLECULES: CULPRITS FOR ATMOSPHERIC OZONE DEPLETION AND GLOBAL CLIMATE CHANGE 2013

Greg Goodman
February 10, 2014 8:02 am

It needs to be viewed as a whole….
What Willis has calculated it seems is one point value along the axis. This is OK to give an idea of form but what is required to calculate the force is a 3 dimensional integral that would include all the forces at all angles.
I think what he has done is fine for the needs of looking at the cycles. E&EO

RichardLH
February 10, 2014 8:07 am

clivebest says:
February 10, 2014 at 7:12 am
“Richard,
Yes – this is exactly right !
http://i.stack.imgur.com/aE7Gd.jpg
It is only the horizontal component of those vectors that is moving any water in the oceans.”
Not strictly true. The lumps being pulled round twice daily have to be fed from somewhere and those big bits of land get in the way of a purely East – West movement.
(Interesting SF plot in there somewhere about a completely water based world with a few islands where the bulge has time to build to astonishing proportions 🙂 )

Greg Goodman
February 10, 2014 8:08 am

Richard, I now see what your “egg shape” comment is , since the tangential vector is slightly closer than the central section of the planet and the tangential components are not parallel.
This is what would be found by a full 3D integration and it what I earlier referred to as higher order effects.
Clive seems to be correct, in Willis’ R code the cosine can be negative.

RichardLH
February 10, 2014 8:10 am

Greg Goodman says:
February 10, 2014 at 8:02 am
“I think what he has done is fine for the needs of looking at the cycles. E&EO”
I would dispute that.
Please consider how the tangential vector can influence both tidal and atmospheric flows North to South.

Greg Goodman
February 10, 2014 8:14 am

cd “Surprisingly, the spectra does not seem to show the “modulation” fingerprint.”
“Understand perfectly – not so sure you do though.”
Ok. so what precisely are you expecting to see that would be the fingerprint? Numbers , frequencies and where you would expect to see them on which graph.
If you’re surprised it’s not there you must know where to look.

February 10, 2014 8:15 am

“Generally agreed that the tide-stuff is “tiny” but depending on the context, “tiny” can still have implications.”
tell that to the folks who believe c02 has no effect because its tiny

RichardLH
February 10, 2014 8:20 am

Greg:
Please consider how the two sectors marked in red and green vary in time over the appropriate orbital periods for both Sun and Moon.
The vertical component at the Pole is orbital not Earth rotation modulated.
The tangential component at the ‘Arctic Circle’ is also orbital, not daily.
The unmarked sector is all daily (with a small orbital in there as well)
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Tidalvectors2_zpsc9b57e6a.png
Now put this all on a tilted, rotating planet and you will see the sort of driving force complexity involved.
As you say this is just a cross sectional view. To move to full 3D and the add in the Geography along with the fluid mechanics…..
As I said above, anyone got a super-computer, a research budget lying around? Oil money …. PLEASE.

Greg Goodman
February 10, 2014 8:20 am

R: “I would dispute that. ”
Sorry, I’m presuming you’ve read the short-comings that I’ve also commented on in detail above and referred to with E&EO (errors and omission excepted) here.
I’ve already said Willis’ graph is only half the story because he does not use the direction of the resultant vector. That is the declination angle that is all important in relation to 18.6 , 9.3 and all the plots I have posted here showing physical evidence of these periods in climate data.

RichardLH
February 10, 2014 8:28 am

Greg Goodman says:
February 10, 2014 at 8:20 am
“Sorry, I’m presuming you’ve read the short-comings that I’ve also commented on in detail above and referred to with E&EO (errors and omission excepted) here.”
I was only objecting to your suggestion that it was “fine for the needs of looking at the cycles”.
I agree with all of your other points, though you did [lose] me at one point but I now think I see what you were getting at:-)

Gail Combs
February 10, 2014 8:50 am

I do not see anyone mentioning this paper:

The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change
Abstract
Variations in solar irradiance are widely believed to explain climatic change on 20,000- to 100,000-year time-scales in accordance with the Milankovitch theory of the ice ages, but there is no conclusive evidence that variable irradiance can be the cause of abrupt fluctuations in climate on time-scales as short as 1,000 years. We propose that such abrupt millennial changes, seen in ice and sedimentary core records, were produced in part by well characterized, almost periodic variations in the strength of the global oceanic tide-raising forces caused by resonances in the periodic motions of the earth and moon. A well defined 1,800-year tidal cycle is associated with gradually shifting lunar declination from one episode of maximum tidal forcing on the centennial time-scale to the next. An amplitude modulation of this cycle occurs with an average period of about 5,000 years, associated with gradually shifting separation-intervals between perihelion and syzygy at maxima of the 1,800-year cycle. We propose that strong tidal forcing causes cooling at the sea surface by increasing vertical mixing in the oceans. On the millennial time-scale, this tidal hypothesis is supported by findings, from sedimentary records of ice-rafting debris, that ocean waters cooled close to the times predicted for strong tidal forcing.
[Body of text]
…We propose that variations in the strength of oceanic tides cause periodic cooling of surface ocean water by modulating the intensity of vertical mixing that brings to the surface colder water from below. The tides provide more than half of the total power for vertical mixing, 3.5 terawatts (4), compared with about 2.0 terawatts from wind drag (3), making this hypothesis plausible. Moreover, the tidal mixing process is strongly nonlinear, so that vertical mixing caused by tidal forcing must vary in intensity interannually even though the annual rate of power generation is constant (3). As a consequence, periodicities in strong forcing, that we will now characterize by identifying the peak forcing events of sequences of strong tides, may so strongly modulate vertical mixing and sea-surface temperature as to explain cyclical cooling even on the millennial time-scale….

The entire paper is available at that address.

accordionsrule
February 10, 2014 8:52 am

Is it just me, or is Figure 3 undulating?
Must be a landlubber when even a tidal graph makes me seasick.

Tom In Indy
February 10, 2014 8:55 am

Steven Mosher says:
February 10, 2014 at 8:15 am
“Generally agreed that the tide-stuff is “tiny” but depending on the context, “tiny” can still have implications.”
tell that to the folks who believe c02 has no effect because its tiny

Mosh, I don’t think anyone is claiming that tides are the “control knob” of the earth’s climate, like the CAGW crowd claims CO2 is the climate control knob. Or, is the CAGW crowd not making that claim any longer? If not, then why are we debating climate sensitivity to man-made CO2 and destroying economies to reduce man-made CO2 emissions?

cd
February 10, 2014 9:04 am

Greg Goodman
so what precisely are you expecting to see that would be the fingerprint?
Side bands about the carrier frequency which we know in the case of Fig. 1. But then I’m not sure how/what he’s plotting in Fig. 2. If we assume that he’s simply converted wavenumber to wavelength then they’ll have to be inferred – but then I’m not sure what he has done (as stated originally).
It would be a lot easier to plot these as a function of frequency then we’d be sure to see the sidebands if present – given the times series. Plotting the “amplitude” on a log scale might help also. What is clear is that there IS amplitude modulation going on. And he’ll need to identify these if he wishes to properly decompose the signal.
Given that there is no drift in the data I’d:
Compute the autocorrelation using a window function and get the FFT from this. Start at the smallest window size to the largest. At each step you’ll be able to spot the carrier signal. Remember, Willis is only concerned with finding the fundamental frequencies.

Jim G
February 10, 2014 9:10 am

As pointed out by many, including the author of this post, the data, and therefore the point of the analysis, has no relationship to out 3 dimensional world. May I use the term “model” to describe it? I would name it the “ceteris paribus” model of tidal activity. It sheds little light on anything of significant import that can be tested in any way.

cd
February 10, 2014 9:13 am

Greg
To make clear the sidebands are symmetric, so if Fig. 2 is amplitude vs wavelength then this will not be the case hence the need to convert to frequency.

RichardLH
February 10, 2014 9:16 am

Nylo says:
February 9, 2014 at 6:39 pm
“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.”
You are indeed perfectly correct. When we get temperature data of sufficient length for this to become a significant factor, then a suitable correction will need to be added.

February 10, 2014 9:22 am

Wikipedia has also got it wrong http://en.wikipedia.org/wiki/Tide
So too has : http://physics.stackexchange.com/questions/46792/tidal-force-on-far-side
Here is someone who explains it properly. ( http://www.moonconnection.com/tides.phtml)

Water on the opposite side of Earth facing away from the Moon also bulges outward (high tide), but for a different and interesting reason: in reality, the Moon and the Earth revolve together around a common gravitational center between them, or center of mass. Here’s a rough but helpful analogy: picture yourself swinging a heavy object attached to a rope around your body as you rotate. You have to lean back to compensate, which puts the center of mass between you and the object. With the Earth-Moon system, gravity is like a rope that pulls or keeps the two bodies together, and centrifugal force is what keeps them apart. Because the centrifugal force is greater than the Moon’s gravitational pull, ocean water on the opposite side of the Earth bulges outward.
The same forces are at play as the Earth revolves around the Sun. The Sun’s gravity pulls ocean water toward the Sun, but at the same time, the centrifugal force of the combined Earth-Sun revolution causes water on the opposite side of Earth to bulge away from the Sun. However, the effect is smaller than the Moon, even given the greater mass of the Sun (greater mass means greater gravitational force). Why? Simply because The Sun is so far away — over 380 times farther away from the Earth than the Moon.

Greg Goodman
February 10, 2014 9:29 am

That’s interesting Clive. Could tie in with Scaffeta’s paper I mentioned above. He finds 9.1 years in JPL data that is attributable to the moon’s presence. I had not thought that it may be related directly to change in insolation but to distance. I knew the perihelion was notable but not the Earth’s orbit around the moon 😉
One main reason is probably that TSI is usually shown “corrected” for 1AU, ie this cycle is actively removed.
I think what you are plotting is a manifestation of the fine scale of what Scaffeta investigated. I also see the variations in TSI sometimes match your red line in amplitude other times its less or broken up. Symptoms of another cycle.
Obvious choice is the perigee cycle. 8.85 . I’ve already suggested several times the Scaffeta’s 9.1+/-0.1 is in fact 9.08 which is produced by superposition of 9.3 (declination / 2) and 8.85.
18.631 / 2 + 8.852591 => 9.078 modulated by 356 years.
Cross-correlation of N.Atl and N.Pac SST shows same thing.
http://climategrog.wordpress.com/?attachment_id=755
18.631 /2 = 9.3155
Indian Ocean:
http://climategrog.wordpress.com/?attachment_id=774
Good idea of Willis’ to start this thread, it’s bringing a lot of things together.

RichardLH
February 10, 2014 9:31 am

Gail Combs says:
February 10, 2014 at 8:50 am
“I do not see anyone mentioning this paper:”
I did reference Fig 1. from there above as to the very complicated state of the Moon/Earth gravitational interaction and asked if Willis was attempting to refute it.

RichardLH
February 10, 2014 9:34 am

clivebest says:
February 10, 2014 at 9:22 am
“Wikipedia has also got it wrong http://en.wikipedia.org/wiki/Tide
So too has : http://physics.stackexchange.com/questions/46792/tidal-force-on-far-side
Here is someone who explains it properly. ( http://www.moonconnection.com/tides.phtml)”
I believe that the ‘egg shaped’ resultant field is correct though.

Greg Goodman
February 10, 2014 9:44 am

“Here is someone who explains it properly.”
Properly because…? who are they apart form the provider of some naff app ? They don’t even say who they are beyond “moonconnection.com”.
I don’t even bother reading WP for shit like this any more because it’s like global bar-talk. Everyone’s an expert, and those that argue the longest prevail on WP.
Where did your egg plot come from earlier? Was that derived from “centrifugal” ideas or gravity gradient?
I may buy the idea that there is some inertial component but I want something solid with numbers. I thought that was the case a while ago but the relatively small solar tide argues against it.

dan
February 10, 2014 9:54 am

Way to not even look at the link and see what the hell was even being referred to, Mosh

RichardLH
February 10, 2014 10:09 am

This is probably the best reference for explaining the slight egg shape to the tidal bulges (one tide is larger than the other on most days)
http://co-ops.nos.noaa.gov/restles3.html
And this for explaining why it is not due to centrifugal forces 🙂
http://www.lhup.edu/~dsimanek/scenario/tides.htm

February 10, 2014 10:23 am

Greg,
Years ago I went through the calculations to “derive” the 1/R3 dependence. I also convinced myself that the differential centrifugal force on the opposite hemisphere to the moon was indeed the cause of the second bulge. I don’t have my notes here but will try and reproduce them.
One other known climate effect : Moonshine !
Don’t laugh – but reflected sunlight from the moon at night is the only direct energy source on earth. Globally this is expected to add vary about 0.004C of warming between new and full moon. What is even more interesting is the effect that the moon has in polar regions during the long dark winters. The warming effect is then proportionately much more, and lunar atmospheric tides bring in circulation in from higher latitudes. Any effect must depend strongly on the 18.6 year cycle as the tidal bulge moves to higher latitudes.

RichardLH
February 10, 2014 10:26 am

clivebest says:
February 10, 2014 at 10:23 am
“I also convinced myself that the differential centrifugal force on the opposite hemisphere to the moon was indeed the cause of the second bulge.”
You might want to re-think that explanation.
http://www.lhup.edu/~dsimanek/scenario/tides.htm
(I am sorry I picked the site I did for the egg shape – I did not check the text – only saw the image – bad boy!)

February 10, 2014 11:10 am

Richard,
What I wrote was indeed wrong – sorry!
The centrifugal force is the same for all points on the earth including that at the centre of the earth. The gravitational force of the moon on the centre of the earth is exactly balanced by the centrifugal force. Oceans on the surface of the earth experience different gravitational forces according to their distance from the centre of the moon. These are now not in balance with the centrifugal force. The differential of this net force causes the tides. For the surface facing the moon gravity “wins” resulting in a bulge. On the other side the centrifugal force “wins” causing the opposite bulge.
This gives the correct description : http://co-ops.nos.noaa.gov/restles3.html
Clive

RichardLH
February 10, 2014 11:49 am

clivebest says:
February 10, 2014 at 11:10 am
“What I wrote was indeed wrong – sorry! …This gives the correct description: http://co-ops.nos.noaa.gov/restles3.html
Yes I know – our posts must have crossed.

Greg Goodman
February 10, 2014 12:18 pm

Thanks for the two links Richard.
This whole thing is very inadequate. the NOAA description is quite good but when they show a “centrifugal” force pointing towards the centre of rotation, I see we’re not out of the woods. That may work for the solid earth on the basis that its all connected. It does not work for the fluid part. BTW when you bring in one ‘fictitious force’ you usually need the other : Coriolis.
I prefer the lhup.edu presentation working in an inertial frame of reference.
Luckily, for the purposed of this thread we can tell the eggs to beat it.

February 10, 2014 1:56 pm

I was slow to come around to this super tide theory, don’t have much invested in it, but don’t see much reason to back off of it yet, because: 1) it depends on zonal tides, capable of moving water north and south; 2) the fortnightly zonal tide is the strongest tide, at least as far as LOD is concerned. See: http://hpiers.obspm.fr/eop-pc/index.php?index=realtime&lang=en
Choose LOD; don’t remove “tidal variations” except for comparison.
One reason zonal tide is so strong is that its bulge can easily keep up with a fortnightly gravitational pull, unlike diurnal or semidiurnal tides, whose bulges can only move a few hundred mph in the shallow ocean. The latter are limited to idiosyncratic oscillations governed by basin bathymetry. The fortnightly zonal tide is conspicuous by its absence on Willis’s chart.
–AGF

Greg Goodman
February 10, 2014 2:07 pm

” The fortnightly zonal tide is conspicuous by its absence on Willis’s chart.”
Indeed, and that’s because he dropped the direction part of the resultant vector he calculated and just plotted the magnitude of the tidal force. The zonal (north/south) flow is primarily determined by the declination angle, which as what produces the 18.6 year cycle.
Because of the presence of the ‘opposite’ tidal force as well, its the deviation from the equator that matters, resulting in 9.3 year variations in the zonal tides.
AGF, was it you I discussed this with last year on another thread about the Stuecker paper and you did some back of envelop calculations on heat transport?

Greg Goodman
February 10, 2014 2:26 pm

Thanks for the EOP link, useful tool.
However it looks like that is the anomalistic cycle that is coming up clearly. Plot for last 136 days and you get pretty clearly ten bumps, or 5 full cycles.
This appears to be perigee cycle not tides. Would you agree?

February 10, 2014 2:58 pm

Yes, GG, you witnessed my reluctant conversion, and yes the zonal tide you see is not very fortnightly. –AGF

Greg Goodman
February 10, 2014 3:18 pm

Unfortunately I can’t get Willis’ code to load properly. Maybe he’ll pop in later to correct it.
It would be interesting to plot the deviation of the resultant force vector’s angle from the equator.
That will be similar to the lunar declination angle but taking into account sun’s contribution too.
Cross-correlate that with the Indian ocean SST and it may start to get interesting.

Ulric Lyons
February 10, 2014 3:25 pm

Willis Eschenbach says:
“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.”
The exeligmos cannot occur at the same time of year as the cycle is not a whole number of years, but the eclipse will be at a similar Earth location. One Saros is 6585.32 days so one eclipse occurs ~120° ahead of the previous on the Earth’s surface, so it takes three Saros cycles for an eclipse to reoccur at the same surface location.
I would have looked at Lunar precession rather than eclipse cycles, not that I can see it forcing climate cycles.
I’m curious about the 13.44 month spike in your analysis (lunar phase perigee cycle), surely there is a king tide at half of that frequency as alternate full and new Moon coincide with lunar perigee?

Greg Goodman
February 10, 2014 3:32 pm

“…. surely there is a king tide at half of that frequency as alternate full and new Moon coincide with lunar perigee?”
cliveBest has pointed out that Willis should have done abs(cosines) in his code but Willis hasn’t been by since to comment on that.

charles the moderator
February 10, 2014 3:49 pm

David L. 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?

That is almost verbatim the same excuse used by CRU to avoid FOI requests before Climategate. And no, no one I know of is able to replicate his work. Until you apologists drop your double standards and apply ethics equally to all sides, your hypocrisy will continue to rule the day.
It is a scientist’s job to make it as easy as possible for critics to scrutinize their work. This is how science grows and self-corrects. Science is not a bunch of trade secrets.
As long as Scafetta refuses to produce data and code, his work is nothing more than clever, albeit kinda boring, anecdotes.

February 10, 2014 5:49 pm

Greg Goodman says:
February 10, 2014 at 2:26 pm
This appears to be perigee cycle not tides. Would you agree?
===============================================================
Back to the keyboard. Not sure what you’re getting at. Perigee is neither zonal nor fortnightly. Declension is both. That is, perigee could affect diurnal earth and sea tides over a 4 week period, while the zonal bulge both grows and moves poleward according to lunar declension. So now it’s a matter of lining up the LOD graph with declension data. Haven’t done that. –AGF

February 10, 2014 6:20 pm

Perigee calculator here: http://www.fourmilab.ch/earthview/pacalc.html
Declination here (astrology no less): http://www.astropro.com/features/tables/cen21ce/mo-dcl-2013.html
And I see what you mean. The declination frequency modulates a perigee amplitude. Or something like that. –AGF

Jeff Alberts
February 10, 2014 6:27 pm

Willis Eschenbach says:
February 9, 2014 at 7:03 pm

Sparks says:
February 9, 2014 at 6:40 pm

As a result, I could care less what you personally think.

So you DO care then.

Gail Combs
February 10, 2014 6:33 pm

RichardLH says: @ February 10, 2014 at 9:31 am
I did reference Fig 1….
>>>>>>>>>>>>>
I saw your figure 1 but wanted to make sure the link to the whole paper was available. (It is a long thread)

February 10, 2014 6:52 pm

Willis, how much grant money or “big oil ” money do you receive for your substantial work.
It must take a lot of time and much work to do what you do. Do you have a website with a donate box just in case you are not receiving compensation for the work that you do??
Even though there seem to be a lot of posters that question your work, I believe most respect what you do.
How do you think that this fascinating article you posted relates to “climate” or “global warming” claims? Does it relate at all to climate – tidal cycles?

February 10, 2014 8:50 pm

I notice in Figure 1 that the minimum combined tidal forcing will be shifting position to where the minimum is going to start at the beginning of winter season. Is there going to be consequences from that alignment?
Also, in taking note of the 8.75 year ‘tiny’ cycle, I am reminded of a 100 year temperature chart someone had posted several weeks ago. In that chart, which showed US temps if I remember right, the center of the chart from the mid 40s till the mid 70s showed a steadily rising then descending trend. Either side of that time period showed ‘pulses’ of approximately 8 to 9 years. There were 3 pulses that were clear to see, both before and after the 1940s to 1970s period. I had asked the author ‘what is the cause of the pulses?’, to which he replied that he had no idea. I cannot remember which post this was on, but I will look back at my comments to find it.

Jeff Alberts
February 10, 2014 9:32 pm

So I fear that as is quite common in English, the proponents of logic are on the losing side of the vote. English is not bound by rules, Jeff. It is bound only by how people use it, and often, that is not logically at all.

I so love it when people defend how wrong they are. It’s not an English rule, it’s a logical statement. “Could care less” is logically different from “couldn’t care less”. There was nothing wrong with the grammar, just with your logic. But if you want to just be like the rest who say the opposite of what they mean, so be it, you’re well on your way to being a world-class Climate Scientist (TM). I can still point it out. Me, I prefer to say what I mean.

Curt
February 10, 2014 10:40 pm

Jeff – You really need to learn about irony, and of the Yiddish contribution to American English (which is where the ironic “I could care less” comes from).

Greg
February 10, 2014 11:46 pm

Willis: “And in any case, your claim that it should be abs() is just plain wrong … check any text on vector addition. However, my guess is you’ll never admit you are wrong …”
No Willis, you’re missing the point. While you picked up the factor or two error you did not comment on abs() except to say “we’re both wrong” without explaining why you thought Clive was wrong.
Your vector calculation is spot on and no-one is saying otherwise. The point is that because the gravity gradient causes TWO “bulges” that are diametrically opposed you need to ADD new moon orientations AND full moon orientations in the same way.
The simplist way to do that would be to do abs(cosines) instead of using its signed value.

Greg
February 11, 2014 12:01 am

“Is the effect large? Probably not, or we’d have seen the evidence.”
http://climategrog.wordpress.com/?attachment_id=774
This is why the direction of the vector you calculated is important.
Greg:” Willis , are you able to provide a precise value for the peaks in fig2 ?
In particular the ones that look to be circa 27, 29 days and 13 months.”
Willis: “Yes.”
Very amusing! Please do so then. To two decimal places if that is possible. And please add the 8.x year peak to the shopping list. 😉

Greg
February 11, 2014 12:21 am

Willis: “Say what? That makes no sense at all. I have not calculated the “vertical component” of the tidal field. ”
Maybe Richard was not clear by what he meant but you are missing the point.
The vector you calculate is just a special case, the force along the line between the Earth and moon centres. That only has a vertical component and you are plotting its scalar magnitude. Fine.so far.
However, it should be noted the gravity acts at all points on the ocean not just along the axis between the two. Water is not ‘sucked up ‘ by this straight line force as much as it is drawn in from all sides by the tangential force. This is what Richard is trying to say.
Your calculation is probably sufficient to look at timing ,so it’s not a problem, but Richard’s point is a key to understanding tidal forces and their effects.
You noted from your fishing experience that there is huge horizontal displacement of water in tides. This is why, it’s the horizontal component. Though we usually measure the height, the main effect of tides is horizontal movement.
It is important to realise that water does not come up, it comes in from all sides. It is primarily a surface effect. And that is all important if we want to consider its effect on SST and energy transportation.

Greg
February 11, 2014 12:49 am

W. Clive, I fear I don’t know what you mean by the “eccentricity values of the moon relative to the earth-moon barycentre”. As far as I know, the eccentricity of the moon stands on its own, it’s not “relative” to anything.”
Since the moon revolves around the barycentre that would be the most suitable choice of coordinate frame to select on the JPL site. You could of course use any coordinates you like and calculate the eccentricity which is still eccentric however you measure it.
What Clive is saying is that it is highly variable, not a nice stable ellipse with the barycentre at one focus of the ellipse.
Perhaps try not taking everyone’s comments as an attack that has to be fended off. It was a great idea to post this article, there is a lot of cyclomania going about so taking a critical look is a very good idea. But you admit you’re learning some of this as you go along and others are trying add to that process.
I’m going to try to get the R code to run but what would be informative is to plot the N/S component of the force vector. That should give some indication of the force likely to cause horizontal transport of surface water in and out of the tropics.
This can be done by the vector “dot product” with (0,0,1) , the unit vector towards the north pole, basically the sine of its angle with respect to the equator.

Greg
February 11, 2014 1:16 am

Willis, with the fix you sent me I’ve got the code running, Thanks.
tideforce=sqrt(sunforce^2 + moonforce^2 + 2*sunforce * moonforce * cosines )
You’re not actually doing the vector addition, you are (correctly) finding the magnitude of the vector addition directly without actually doing the addition. I had not dug into the code before since I don’t try modding code before I know I can run it.
I’ll see whether I can come up with a code fix (though working in R gives me a rash).
Without worrying about the implementation can you see the point of ensuring the vectors are always adding not subtracting?

Greg
February 11, 2014 1:45 am

>>
[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))”
>>
The correction was not correct. The latter term should 2 * sun_force * moon_force * cos(angle)* sin(angle) this can be simplified to :
1* sun_force * moon_force * sin(2*angle)
using the trig identities I linked for you yesterday:
http://www.trans4mind.com/personal_development/mathematics/trigonometry/sumProductCosSin.htm#Products
see eqn 6.4 and put x=y
2*cos(x)*sin(x)=sin(2x)
====
Now if my R is correct this could be corrected by
cosines=rowscalars/(sundist*moondist)
sines=sin(2*acos(cosines))
then
# MAGNITUDE OF (add forces as vectors)
tideforce=sqrt(sunforce^2 + moonforce^2 + sunforce * moonforce * sines )
The spectra come out very similar but have a little group of peaks around 13-14 days (which makes sense) and the circa 11.5 and 13.5 mo peaks are equal in size.
I’ll see if I can do a mod to get new and full moons to add in the same sense..

Greg
February 11, 2014 1:49 am

BTW the 8.x years has gone! I said that was a bit odd earlier. One mystery less.

Greg
February 11, 2014 2:01 am

modsincos= sin(acos(cosines))+cosines
main difference in spectrum is we now have 13-14 day tide variation and 27 day is now about as big as 29day.

Greg
February 11, 2014 2:07 am

Damn it, I called it modsincos and forgot to mod it !
modsincos= abs(sin(acos(cosines))+cosines)
27 day is now biggest which makes a lot more sense.

tallbloke
February 11, 2014 2:26 am

Greg says:
there is huge horizontal displacement of water in tides. This is why, it’s the horizontal component. Though we usually measure the height, the main effect of tides is horizontal movement.
It is important to realise that water does not come up, it comes in from all sides. It is primarily a surface effect. And that is all important if we want to consider its effect on SST and energy transportation.

Greg gets it. I’ve mentioned horizontal tidal components on WUWT many times to Leif, and he’s always blanked it. The vertical component of the tide on the Sun from Jupiter is around 1mm (due to the Sun’s enormous self gravity and the distance), but the horizontal component is much more extensive.
However, the tidal force is small compared to the forces passed back to the Sun from the planets via resonant harmonics carried by the interplanetary magnetic field as well as by the gravitational field. Willis seems to think the study of interplanetary harmonic resonance is ‘numerology’. But then, he doesn’t seem to be aware of the extensive literature on this subject in the astrophysics journals.

Greg
February 11, 2014 2:35 am

OK I’ve had strong coffee and hopefully have finished making typos in the equation 😕
modsincos= abs(sin(acos(cosines))*cosines)
The resulting plot and spectrum looks like this.
http://oi61.tinypic.com/2iihjkn.jpg

RichardLH
February 11, 2014 2:38 am

Willis Eschenbach says:
February 10, 2014 at 6:02 pm
“Say what? That makes no sense at all. I have not calculated the “vertical component” of the tidal field. I have calculated the SIZE, aka the AMPLITUDE, aka the STRENGTH, of the tidal force … and that is a scalar.
So it can’t be the “vertical component” of anything, it doesn’t have a direction.”
I rather do understand exactly what it is you have plotted and have equally rather obviously failed to convey the limitations of what has been done and how it can be improved.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Tidalvectors2_zpsc9b57e6a.png
The above is a plot of the ‘tide rising force’ from Wiki that will allow me to describe better what has been done and what is missing. You have plotted the magnitude of the single vector that is pointed to the ‘Satellite’ in the above diagram. That is perfect valid and correct from the data that you have obtained.
However your plot is a 1D line through the slightly more complex reality of what is going on.
I order to move to 2D (and then on to 3D) all the other vectors need to be considered. In particular the vectors in the Green and Red sections above.
These two web sites go into a lot more detail of the vectors, the changes involved and the causation of the two tides.
http://co-ops.nos.noaa.gov/restles3.html
http://www.lhup.edu/~dsimanek/scenario/tides.htm
If you now re-read what I said earlier about vertical and horizontal and consider the description as from being someone who is standing on the globe in the diagram when making the description you may better understand what I was trying to describe.

RichardLH
February 11, 2014 2:42 am

Willis Eschenbach says:
February 10, 2014 at 6:18 pm
“…
This is just simple ‘Gaussian’ low pass filter stuff but it independently confirms at least part of his case.
Since he has not revealed his data or code, we have no clue what “his case” might actually contain once it is opened … so far he has no case, he just has advertising materials.”
He himself acknowledged here on WUWT that my independent discovery of an ~60 year cycle in the temperature data was one of the results that he had concluded was present by a different route.
I have no knowledge as to if his claim of attribution is valid but to would appear that a simple ‘Gaussian’ treatment of the temperature data confirms his figure as being present.

RichardLH
February 11, 2014 2:45 am

Gail Combs says:
February 10, 2014 at 6:33 pm
“I did reference Fig 1….
>>>>>>>>>>>>>
I saw your figure 1 but wanted to make sure the link to the whole paper was available. (It is a long thread)”
No problem. It is a very important point and I have asked on a couple of occasions now if Willis is attempting to refute it, in whole or in part.

RichardLH
February 11, 2014 2:49 am

Willis Eschenbach says:
February 10, 2014 at 7:55 pm
“What I have plotted is the tidal force, the actual amount of combined tidal pull exerted by the sun and moon.”
You have plotted a single vector from the full set as described by the “Tide Generating Force” as it is more normally called in scientific literature. c.f. Wiki and the urls I have quoted previously.

RichardLH
February 11, 2014 2:52 am

Willis Eschenbach says:
February 10, 2014 at 8:22 pm
“because the relationship above means that at the poles, when the sun never rises, the full moon never sets …”
Now stop for just a moment and consider how this relates to the tides raised by the bodies in question at the points you stand on the Earth. Light and Gravity do follow similar paths you know 🙂
You own words this time.

RichardLH
February 11, 2014 3:02 am

Greg says:
February 11, 2014 at 2:35 am
“modsincos= abs(sin(acos(cosines))*cosines)
The resulting plot and spectrum looks like this.
http://oi61.tinypic.com/2iihjkn.jpg
Is the R too long to post here? Or would dropbox and the like be a better place to share it from (if you wish to share).

RichardLH
February 11, 2014 3:05 am

Climate Scientist: I want a tool to examine Climate Temperatures.
Geek: How do you define Climate?
Climate Scientist: Longer than 30 years.
Geek: So you want a tool that will show how the planet’s temperature responds in periods of more than 30 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: ??????????

RichardLH
February 11, 2014 3:06 am

Oops – sorry wrong thread 🙂

Greg
February 11, 2014 3:45 am

“Is the R too long to post here? ”
Willis already provided his code at the top. I just added a couple of lines.

Gail Combs
February 11, 2014 4:21 am

RichardLH says: @ February 11, 2014 at 2:45 am
In response to: Gail Combs says: @ February 10, 2014 at 6:33 pm
>>>>>>>>>>>>
I am ‘computer challenged’ so all I can do is read and try to follow what is said.
For the others who might be following this thread still, this is another visual aid:
https://en.wikipedia.org/wiki/File:Moon_trajectory1.svg
It helps to not think of the moon as ‘circling the earth’ but as following in a slightly different orbit around the sun compared to earth and the two planets as ‘dancing’.

Greg
February 11, 2014 4:24 am

BTW there was a stray line in Willis’ code. The fix is to comment it out.
# oldmai=par(“mai”)
thanks , Willis.
In resumé. sines below corrects the maths of what Willis intended to plot, modsincos accounts for the fact there are two tidal bulges and new moons need to produce the same effect as full moon.
cosines=rowscalars/(sundist*moondist)
sines=sin(2*acos(cosines))
modsincos= abs(sin(acos(cosines))*cosines)
then
# MAGNITUDE OF ( forces added as vectors) per Willis post , but with correction
tideforce=sqrt(sunforce^2 + moonforce^2 + sunforce * moonforce * sines )
# MAGNITUDE OF ( forces added as vectors, accounting for “opposite bulge”)
tideforce=sqrt(sunforce^2 + moonforce^2 + 1*sunforce * moonforce * modsincos )
The resulting plot and spectrum for latter case looks like this.
http://oi61.tinypic.com/2iihjkn.jpg

RichardLH
February 11, 2014 4:26 am

Gail Combs says:
February 11, 2014 at 4:21 am
“It helps to not think of the moon as ‘circling the earth’ but as following in a slightly different orbit around the sun compared to earth and the two planets as ‘dancing’.”
And, having once collided, are now very slowly drawing themselves apart to eventually resume their independent paths 🙂

RichardLH
February 11, 2014 4:28 am

Greg says:
February 11, 2014 at 4:24 am
“The resulting plot and spectrum for latter case looks like this.”
For the single vector as described in my posts above, that is correct. Hardly the whole picture is it? What about the Poles?

Gail Combs
February 11, 2014 4:31 am

RichardLH says: @ February 11, 2014 at 3:05 am
I am sure HarryReadMe would fully appreciate that.

RichardLH
February 11, 2014 4:34 am

Gail Combs says:
February 11, 2014 at 4:31 am
“I am sure HarryReadMe would fully appreciate that.”
Well when I came to look at the BEST database I began to understand the frustrations he felt 🙂

Greg
February 11, 2014 4:55 am

New plot looks to be the same as CliveBest’s one.

Greg
February 11, 2014 5:02 am

“For the single vector as described in my posts above, that is correct. Hardly the whole picture is it? What about the Poles?”
OH no. But one thing at a time. At least the [math] is [now] correct and the opposite bulge is take care of. Now I need to work out if the z component of this data is Earth NS or the normal to orbital or whatever ….
Then get the direction of the vector as well as its size , project the NS cmpt and we may start to see the rest of the storey.

Greg
February 11, 2014 5:05 am

maths is now correct….

RichardLH
February 11, 2014 5:20 am

Greg says:
February 11, 2014 at 5:02 am
“Then get the direction of the vector as well as its size , project the NS cmpt and we may start to see the rest of the storey.”
1D to 2D to 3D. And then time/Lat-Long three vector contour plot. And that is before we add in Geography. And fluidics!…….
Where’s that super-computer.

pochas
February 11, 2014 5:25 am

RichardLH says:
February 11, 2014 at 5:20 am
“Where’s that super-computer.”
We’ve got ’em, but they’re too busy collecting data on American citizens and running useless computer models.

RichardLH
February 11, 2014 5:33 am

pochas says:
February 11, 2014 at 5:25 am
“We’ve got ‘em, but they’re too busy collecting data on American citizens and running useless computer models.”
“Programming – Modelling the World inside a Computer” – with apologies to Larry O’Brien.

pochas
February 11, 2014 5:40 am

I wonder what shape a sphere of water would assume in orbit (assuming it could remain liquid). I would guess it would be deformed by the gravity gradient in a radial direction but also sheared in the orthogonal direction because particles further away from the sun have lower orbital velocity.

RichardLH
February 11, 2014 6:06 am

pochas says:
February 11, 2014 at 5:40 am
“I wonder what shape a sphere of water would assume in orbit”
Add together as many of these diagrams as you need for the objects concerned, scaled appropriately for masses and distances.

RichardLH
February 11, 2014 6:07 am