Guest Post by Willis Eschenbach
I’ve been listening to lots of stuff lately about tidal cycles. These exist, to be sure. However, they are fairly complex, and they only repeat (and even then only approximately) every 54 years 34 days. They also repeat (even more approximately) every 1/3 of that 54+ year cycle, which is 18 years 11 days 8 hours. This is called a “Saros cycle”. So folks talk about those cycles, and the 9 year half-Saros-cycle, and the like. The 54+ year cycle gets a lot of airtime, because people claim it is reflected in a sinusoidal approximately 54-year cycle in the for example the HadCRUT temperature records.
Now, I originally approached this tidal question from the other end. I used to run a shipyard in the Solomon Islands. The Government there was the only source of tide tables at the time, and they didn’t get around to printing them until late in the year, September or so. As a result, I had to make my own. The only thing I had for data was a printed version of the tide tables for the previous year.
What I found out then was that for any location, the tides can be calculated as a combination of “tidal constituents” of varying periods. As you might imagine, the strongest tidal constituents are half-daily, daily, monthly, and yearly. These represent the rotations of the earth, sun, and moon. There’s a list of the various tidal constituents here, none of which are longer than a year.
Figure 1. Total tidal force exerted on the Earth by the combination of the sun and the moon.
So what puzzled me even back then was, why are there no longer-period cycles used to predict the tides? Why don’t we use cycles of 18+ and 54.1 years to predict the tides?
Being a back to basics, start-from-the-start kind of guy, I reckoned that I’d just get the astronomical data, figure out the tidal force myself, and see what cycles it contains. It’s not all that complex, and the good folks at the Jet Propulsion Lab have done all the hard work with calculating the positions of the sun and moon. So off I went to JPL to get a couple hundred years data, and I calculated the tidal forces day by day. Figure 1 above shows a look at a section of my results:
These results were quite interesting to me, because they clearly show the two main influences (solar and lunar). Figure 1 also shows that the variations do not have a cycle of exactly a year—the high and low spots shift over time with respect to the years. Also, the maximum amplitude varies year to year.
For ease of calculation, I used geocentric (Earth centered) coordinates. I got the positions of the sun and moon for the same time each day from 1 January 2000 for the next 200 years, out to 1 Jan 2200. Then I calculated the tidal force for each of those days (math in the appendix). That gave me the result you see in Figure 1.
However, what I was interested in was the decomposition of the tidal force into its component cycles. In particular, I was looking for any 9 year, 18+ year, or 54.1 year cycles. So I did what you might expect. I did a Fourier analysis of the tidal cycles. Figure 2 shows those results at increasingly longer scales from top to bottom.
Figure 2. Fourier analysis of the tidal forces acting on the earth. Each succeeding graph shows a longer time period. Note the increasing scale.
The top panel shows the short-term components. These are strongest at one day, and at 29.5 days, with side peaks near the 29.5 day lunar cycle, and with weaker half-month cycles as well.
The second panel shows cycles out to 18 months. Note that the new Y-axis scale is eight times the old scale, to show the much smaller annual cycles. There are 12 month and 13.5 month cycles visible in the data, along with much smaller half-cycles (6 months and 6.75 months). You can see the difference in the scales by comparing the half-month (15 day) cycles in the top two panels.
The third panel shows cycles out to 20 years, to investigate the question of the 9 and 18+ year cycles … no joy, although there is the tiniest of cycles at about 8.75 years. Again, I’ve increased the scale, this time by 5X. You can visualize the difference by comparing the half-year (6-7 month) cycles in the second and third panels. At this scale, any 9 or 18+ year cycles would be very visible … bad news. There are no such cycles in decomposition of the data.
Finally, the fourth panel is the longest, to look for the 54 year cycle. Again, there is no such underlying sine-wave cycle.
Now, those last two panels were a surprise to me. Why are we not finding any 9, 18+, or 54 year cycle in the Fourier transform? Well … what I realized after considering this for a while is that there is not a slow sine wave fifty-four years in length in the data. Instead, the 54 years is just the length of time that goes by before a long, complex superposition of sine waves approximately repeats itself.
And the same thing is true about the 18-year Saros cycle. It’s not a gradual nine-year increase and subsequent nine-year decrease in the tidal force, as I had imagined it. Instead, it’s just the (approximate) repeat period of a complex waveform.
As a result, I fear that the common idea that the apparent ~60 year cycle in the HadCRUT temperatures is related to the 54-year tidal cycles simply isn’t true … because that 54 year repeating cycle is not a sine wave. Instead, looks like this:
Figure 3. The 54 year 34 day repetitive tidal cycle. This is the average of the 54-year 34-day cycles over the 200 years of data 2000-2200.
Now, as you can see, that is hardly the nice sine wave that folks would like to think modulates the HadCRUT4 temperatures …
This exemplifies a huge problem that I see happening. People say “OK, there’s an 18+ year Saros cycle, so I can divide that by 2. Then I’ll figure the beat frequency of that 9+ year cycle with the 8.55 year cycle of the precession of the lunar apsides, and then apply that to the temperature data …”
I’m sure that you can see the problems with that approach. You can’t take the Saros cycle, or the 54+ year cycle, and cut it in half and get a beat frequency against something else, because it’s not a sine wave, as people think.
Look, folks, with all the planets and moons up there, we can find literally hundreds and hundreds of varying length astronomical cycles. But the reality, as we see above, is not as simple as just grabbing frequencies that fit our theory, or making a beat frequency from two astronomical cycles.
So let me suggest that people who want to use astronomical cycles do what I did—plot out the real-life, actual cycle that you’re talking about. Don’t just grab the period of a couple of cycles, take the beat frequency, and call it good …
For example, if you want to claim that the combined tidal forces of Jupiter and Saturn on the sun have an effect on the climate, you can’t just grab the periods and fit the phase and amplitude to the HadCRUT data. Instead, you need to do the hard lifting, calculate the actual Jupiter-Saturn tidal forces on the sun, and see if it still makes sense.
Best regards to everyone, it’s still raining here. Last week, people were claiming that the existence of the California drought “proved” that global warming was real … this week, to hear them talk, the existence of the California floods proves the same thing.
In other words … buckle down, it’s gonna be a long fight for climate sanity, Godot’s not likely to show up for a while …
w.
THE USUAL: If you disagree with something that I or someone else said, please quote the exact words you disagree with, and tell us why. That way, we can all understand what you object to, and the exact nature of your objection.
CALCULATIONS: For ease of calculations, I downloaded the data for the sun and moon in the form of cartesian geocentric (Earth-centered) coordinates. This gave me the x, y, and z values for the moon and sun at each instant. I then calculated the distances as the square root of the sum of the squares of the xyz coordinates. The cosine of the angle between them at any instant is
(sun_x * moon_x + sun_y * moon_y + sun_z * moon_z) / (sun_distance * moon_distance)
and the combined tidal force is then
sqrt( sun_force^2 + moon_force^2 + 2* sun_force * moon_force * cos(angle))
DATA AND CODE: The original sun and moon data from JPL are here (moon) and here (sun), 20 Mb text files. The relevant data from those two files, in the form of a 13 Mb R “save()” file, is here and the R code is here.
EQUATIONS: The tidal force is equal to 2 * G * m1 * m2 * r / d^3, where G is the gravitational constant, m1 and m2 are the masses of the two objects, d is the distance between them, and r is the radius of the object where we’re calculating the tides (assuming that r is much, much smaller than d).
A good derivation of the equation for tidal force is given here.
Willis:
“Whether a quantity is a “scalar” or a “vector” (or something more exotic) is a question of what representation of the group of isometries it resides in. For n-dimensional Euclidean space, this is the group O(n). For n=1, O(n) has just the elements 1 and -1. A vector acts nontrivially under -1, while a scalar is unchanged.”
is obviously beyond you then.
RichardLH:
I take severe exception [to] your post at February 13, 2014 at 9:57 am which suggests I made “prejudicial, racial, comments”. I DID NOT!
I am willing to accept your withdrawal of your offensive remark and your apology for it.
Richard
Wllis:
In case you missed it
Cartesian coordinate systems and Rotating reference frames just about covers it 🙂
richardscourtney says:
February 13, 2014 at 10:08 am
“I take severe exception ti your post at February 13, 2014 at 9:57 am which suggests I made “prejudicial, racial, comments”. I DID NOT!
I am willing to accept your withdrawal of your offensive remark and your apology for it.”
I apologise if I gave you any offense. None was intended at all.
I believe that suggesting, even indirectly, that because someone who is American and therefore would not have heard of someone who is British has the characteristics of a racial slur. That is, American’s have in the past been observed, incorrectly, to have a very parochial view of the world.
I try very hard never to use such constructs when making my arguments.
Again, sorry if I offended in any way.
RichardLH says:
February 13, 2014 at 9:51 am
So you say there are “deficiencies”, but not mathematical errors, in my calculation of the tidal force? Well, that’s a step. In other words, you’re admitting all your claims about my not understanding Cartesian math were just unbridled nastiness with no factual basis.
However, since you haven’t pointed out what those “deficiencies” might be, I fear I’m in mystery here.
I’ve calculated the magnitude of the 3-D vector sum of the two significant tidal forces at work on the earth. I haven’t calculated the tides in the Straits of Borneo. Is that a “deficiency” in my work?
Or perhaps the “deficiency” is that I have discussed the magnitude, but not the 3D direction, of those tidal forces.
In any case, I haven’t solved the Dirac Conjecture in the head post, so is that a “deficiency” as well?
The world wonders … look, Richard, I set out with a limited objective in mind. I wanted to understand the variations in the magnitude of the tidal force. I did so.
Now, you want to claim that my work is “deficient” … but I did what I set out to do.
However, if you think I should have done more, then how about you get up off your dead ass and do whatever you think I missed, so we can all see how brilliant you are.
And if you’re not willing to do the hard work to do that … then what are you whining about?
w.
Willis:
From the Wiki link I posted.
“which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were rotating in step with the moon’s orbit.”
Your calculation is the magnitude that would apply under the above statement – ALONE. That is its deficiency.
To get a real world implementation of the effect of the forces so generated I will add the ret of the WIkI entry.
“Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also because wave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if there were no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along the equator halfway around the Earth (by comparison, the Earth’s lithosphere has a natural period of about 57 minutes). Earth tides, which raise and lower the bottom of the ocean, and the tide’s own gravitational self attraction are both significant and further complicate the ocean’s response to tidal forces.”
RichardLH says:
February 13, 2014 at 10:02 am
Richard, I don’t have a clue why you think that discussing the magnitude of a 3D vector force somehow magically converts it from a 3D vector force to a 1D vector … nor do I care.
My calculations have nothing to do with 1D vectors, so someone’s technical opinion on whether a scalar is a 1D vector is immaterial to the discussion. It is, as I said before, just a red herring … and no, Richard, I’m not going to go on that snipe hunt for you or anyone else.
w.
Willis Eschenbach says:
February 13, 2014 at 10:14 am
“So you say there are “deficiencies”, but not mathematical errors, in my calculation of the tidal force? ”
You created the straw man of mathematical errors which I never posted about.
Willis:
“Whether a quantity is a “scalar” or a “vector” (or something more exotic) is a question of what representation of the group of isometries it resides in. For n-dimensional Euclidean space, this is the group O(n). For n=1, O(n) has just the elements 1 and -1. A vector acts nontrivially under -1, while a scalar is unchanged.”
The 3 dimension Euclidean space can be reduced to a 1 dimension Euclidean space and converted to a rotating reference frame as you have done. The scalar so produced is then the magnitude of the forces involved, the vector is the line along which those forces react. Can I get it any clearer?
Willis Eschenbach says:
February 13, 2014 at 10:14 am
“In any case, I haven’t solved the Dirac Conjecture in the head post, so is that a “deficiency” as well?”
Add all the straw man you like. I will not get cross – or distracted.
RichardLH says:
February 13, 2014 at 10:19 am
Richard, what on earth are you talking about? That wiki quote is about the AMPLITUDE OF THE TIDES, and what I wrote this post about was the MAGNITUDE OF THE TIDAL FORCE.
Claiming that a discussion of the magnitude of the tidal force is somehow “deficient” because it doesn’t discuss the amplitude of the resulting tides on Earth is … well, I don’t have words for it, but it’s nuts.
I didn’t set out to discuss the amplitude of the tides, I didn’t want to discuss the amplitude of the tides, and I didn’t discuss the amplitude of the tides.
That is not a “deficiency” in my discussion. The discussion of the tides resulting from the tidal forces I calculate above is an entirely different discussion. It is a valid discussion, and a fascinating discussion to a seaman like myself … but it’s a different discussion.. If you want to have that discussion, fine … but don’t come around here whining that my discussion is “deficient” because it didn’t discuss what Richard thought I should discuss.
You want to expose your brilliance on the subject? Anthony is more than happy to publish such discussions. Put your money where your mouth is—you write about the stuff you want to write about, and we can have that discussion about scalars versus 1D vectors ….
But bitching at me because I didn’t do it the Richard way, claiming it’s “deficient” because Richard’s pet topics got short shrift? Sorry, that’s not what this post is about. The head post is about the TIDAL FORCE, and not about the resulting TIDES. Please contemplate the difference before sending me wiki quotes about the TIDES.
w.
PS—as a point of logic, you say:
In fact, my calculation of the tidal forces is the magnitude that applies whether the ocean possesses a uniform depth or not. My calculation applies whether there are or are not landmasses. It applies whether the Earth is rotating in step with the moons orbit, out of step with it, or not rotating at all.
In other words, your statement, that my calculations of the magnitude of the tidal force only apply under the conditions listed, is simply not true. My calculations apply regardless of those conditions, because they are calculations of the FORCES involved, and not calculations of the resulting TIDES.
Willis Eschenbach says:
February 13, 2014 at 10:37 am
The Wiki is about the outcome (i.e. amplitude) of the effect of the magnitude of the tidal force as it applies to the Oceans.
Indeed if we are only discussing the abstract quantity of magnitude without relating to the outcome on the Earth’s oceans then what are we talking about?
Surely is the possible effects on Climate that this is all about, isn’t it?
Richard, in an attempt to defuse the situation, let me try this a different way by asking you a question—what is your objection to my head post about tidal forces?
You agree that the math is correct. And yes, it doesn’t discuss the resulting tides, but then it never was about the tides. It was an examination of the tidal forces. So lack of discussion of actual earthly tides is not the problem.
So what is it that I said about the tidal forces that has you so upset? If you could let me know exactly what I said in the head post that has you so incensed, that would be useful.
Thanks,
w.
“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.”
In order to understand how the long term deltas in the tidal forces may, or may not, effect the “HadCRUT temperature records” then consideration has to be made how such changes in the forces play out on the worlds oceans (and possibly atmosphere). This is a complex subject involving as it does geographical restrictions and fluidic flows that will be difficult to determine from just a simple treatment of the changes themselves. [The fact that Earth’s rotational period, spin axis, and the orbital periods and planes are not aligned but] are elliptical and precessing makes this even more complicated.
Small orbital changes may also be brought about by other planetary influences that may amplify such tiny factors when applied here on Earth in the longer term.
Edit:
…The fact that Earth’s rotational period, spin axis, and the orbital planes are not aligned…
ReEdit: Damn it.
…The fact that Earth’s rotational period, spin axis, and the orbital periods and planes are not aligned…
RichardLH says:
February 13, 2014 at 10:43 am
Possible effects on climate are indeed the context of the discussion. However, we cannot discuss all of the climate issues, or even many of those issues, in every post. For example, political actions regarding climate policies are also the context of the discussion, as is the effect of those policies on the poor … but this post is not about those aspect of the context either. Like most of my posts, I pick one subject, and talk about that.
Now, I’ve spent a good chunk of my life at sea. Like most seamen, I’m fascinated by the tides. I fished night-times for some years, and there’s nothing like working outside on the ocean all night every night to put a man in touch with moon and the tides. I’ve watched the tidal winds roll in the mouth of the bay and up the river, and I’ve calculated my fishing times to take advantage of that wind. And as I said, I was forced by circumstances to generate my own tide tables …
So I’m keenly aware of the larger contexts you raise—of the tides resulting from the tidal forces discussed above, and of the effects of the tides on the climate. I’ve written entire posts on those subjects.
However, this is not one of those posts about the tides, or about tidal effects on the climate. This post reflects my ongoing struggles to understand those underlying tidal forces that create the tides. How are the variations in those tidal forces not a legitimate subject, and indeed a fascinating subject, for discussion in and of itself?
For example, as I said above, I had thought that the 54-year repeating tidal cycle was a long, slow sine wave of the amplitudes of the tides. And as a result, I had thought such a cycle might be related to inter-decadal changes in the global surface temperatures.
But that turned out not to be the case at all, as Figure 3 makes clear. There is no long, slow 54-year sine wave in the tidal data, that was just my misunderstanding.
Now, I’ve been a seaman all my life, and I know a lot about tides. I’ve studied them a lot. I know where the amphidromic point in the Pacific is, for example … can you tell me where, or even what, that point is without google? Perhaps you can, and if so I tip my hat to you, but my point is, I’m not a layman on tidal matters.
So when I find I’m harboring a misconception like the idea that the 54-year tidal cycle is a long slow sine wave, I figure I’m likely not the only person holding that incorrect view. You might not be one of the folks thinking that, but if I have that misconception, I’m not the only one … and so I write about it.
And indeed, that fact alone is of great interest in the larger context of climate and the effects of tides on climate … it means that next time someone tries to relate the 54-year tidal cycle to the some “around 60 year” purported cyclical variations in surface temperature, I can say “Well, there may or may not be a cycle there, but it’s not related to the 54-year tidal cycle.”
Best regards,
w.
Willis Eschenbach says:
February 13, 2014 at 11:15 am
“Now, I’ve spent a good chunk of my life at sea. Like most seamen, I’m fascinated by the tides. I fished night-times for some years, and there’s nothing like working outside on the ocean all night every night to put a man in touch with moon and the tides. I’ve watched the tidal winds roll in the mouth of the bay and up the river, and I’ve calculated my fishing times to take advantage of that wind. And as I said, I was forced by circumstances to generate my own tide tables ”
I am a sailor as well. Sailed a lot along the South Coast of England in everything from Enterprise Dingy to 34ft deep sea craft. In all sorts of tides and weather..
“So I’m keenly aware of the larger contexts you raise—of the tides resulting from the tidal forces discussed above, and of the effects of the tides on the climate. I’ve written entire posts on those subjects.”
Me too. (though I’ve written no posts 🙂 )
“However, this is not one of those posts about the tides, or about tidal effects on the climate. This post reflects my ongoing struggles to understand those underlying tidal forces that create the tides. How are the variations in those tidal forces not a legitimate subject, and indeed a fascinating subject, for discussion in and of itself?”
It is, but without the context of how this relates to the effects of those forces on the climate kinda abstract.
“For example, as I said above, I had thought that the 54-year repeating tidal cycle was a long, slow sine wave of the amplitudes of the tides. And as a result, I had thought such a cycle might be related to inter-decadal changes in the global surface temperatures.
But that turned out not to be the case at all, as Figure 3 makes clear. There is no long, slow 54-year sine wave in the tidal data, that was just my misunderstanding.”
If looked at from the aspect of low latitudes only, sure.
Consider your own observation about the Sun and the Poles. Up there things are a bit different. Tides, like daylight, are on a much longer period. 6 monthly in fact. A world away from stuff at the Equator. (or should that be half a world 🙂
There, given the non-alignment of spin axis to Moon orbit. things may well change in the 54 year cycle you seek.
Which is why I suggested that you plot this from the North Pole as well.
In between we will get a mix of 6 month and daily in greater and greater proportions as we head South.
Things also change at 60 degrees to the orbital plane. Here the resultant vector is all tangential to the surface. No vertical component at all.
This all mixes together to make the outcome a lot less simple than I think you see.
“Well, there may or may not be a cycle there, but it’s not related to the 54-year tidal cycle.”
I do wish I had your easy outlook on life. I see a much more complex and possibly interesting picture, that’s all.
See my other post for why.
Willis
Ignorance? Embarrassing myself – that really is sweet. I’m not the guy trying to decompose an amplitude modulated signal using a Fourier Transform and then embarrassingly trying to state the law.
I generally try to speak to those in the manner they speak to me. A 1D vector – which you haven’t heard of HAS magnitude and direction +/-!!!! If it isn’t direction then it isn’t a vector. Pick up a math dictionary before spouting nonsense. If your vector is always +ve then it is only ever in one direction with a given magnitude. If you want to know what a 1D, 2D, 3D, 4D vector is do a search on elementary kinematics.
On a general point there seems very little point in empty gestures such as providing links to code and data if you just shout everyone down every time they try to explain something to you.
Some inks for those who like to understand the complexities on things in general. BBC Science so not just some random urls 🙂
BBC Science of ‘The Code’ aka Mathematics as applied to the World around us
Numbers
Shapes
Predictions
RichardLH
Willis has form in this. As far as I can tell he learns a new type of analytical method and then – and hats of to him – he quickly grasps a working knowledge of it and then applies it to just about anything he can get his hands on. We all do this but whereas most of us might temper our enthusiasm by accepting that these are typically highly nuanced areas of science/maths, Willis takes to his word processor writes an article based on this shallow knowledge proclaiming some new insight (I’m sure sometimes he does find some) while dictating how it should’ve been done by all those who went before. Anyone to suggest that he might be wrong are not tolerated – see his reaction on 1D vectors.
cd says:
February 13, 2014 at 12:30 pm
“Anyone to suggest that he might be wrong are not tolerated – see his reaction on 1D vectors.”
I come not to criticise – but to explore. Curiosity, always curiosity.
RichardLH
Don’t take this the wrong way but your posts can be a little “smarter-than-thou” – probably because you are to most ;). I enjoy WUWT, not out of curiosity but rather sincere interest in what information is provided. But it gets a bit out of hand some times as blogs do and you sometimes get a lot of flack. For example, I think my post touched a nerve as Willis clearly thinks he is above me. He seems unaware that the type of operation he is doing between two vectors produces another vector with magnitude and direction and just because he choose not to express it in one or more Cartesian coords he sees it as just a number, but of course it’s still a vector (+ve going one way and -ve going another way relative to fixed point; akin to displacement in kinematics). But again it’s all rather academic.
I watched your piece on Tommy Flowers. Very interesting. Many an unsung hero. I wonder if he has failed to get the recognition because he didn’t go through the academic route. Obviously brilliant man. How did you hear about him?
Out of interest, feel free not to reply, but are you in industry/academia?
Oops should have been “…distance of motion in 1D kinematics”
cd says:
February 13, 2014 at 12:52 pm
“Don’t take this the wrong way but your posts can be a little “smarter-than-thou” – probably because you are to most ;).”
I am sorry. I never try to be cleverer than anyone else. Everybody has insights that others miss. Happens to me all the time. I can overlook the most obvious of conclusions. Always curious about what I DON’T see.
“I watched your piece on Tommy Flowers. Very interesting. Many an unsung hero. I wonder if he has failed to get the recognition because he didn’t go through the academic route. Obviously brilliant man. How did you hear about him?”
Well I just may have had a hand in producing the next generation of some of the stuff he did for blank spaces on the map……
“Out of interest, feel free not to reply, but are you in industry/academia?”
Retired from both at present. Not likely to stay that way for long 🙂