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.
Greg Goodman says:
February 10, 2014 at 3:06 am
Yes.
w.
RichardLH says:
February 10, 2014 at 3:31 am
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.
w.
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
Greg Goodman says:
February 10, 2014 at 3:42 am
One thing you may not be realizing, Greg, is that your choice, to refuse to explain your claims and to answer simple questions with insults in this thread, has burned your bridges with me. I will not respond further to your gibberish, which you have refused over and over to either cite, support, or explain.
w.
So you DO care then.
Henry Bowman says:
February 10, 2014 at 5:54 am
Without further details, that’s like saying “I don’t like the way you dress.” So is it my tie you don’t like, or what?
In this case, you’ve quoted me saying:
• Longman’s paper contains a host of empirical formulas for the solution of the n-body problem.
• His values are quite close to the real values.
• However, they are approximations and not solutions of the underlying equation.
My conclusion was that it would be useless to do e.g. a Fourier analysis on such results, because there would be a host of spurious cycles … I mean, his formulas use things like time squared, and time cubed … hardly physics.
So … which of those do you think are wrong? The part about time cubed? The part about empirical formulas?
Thanks for an interesting link. I’d love to, but I’m on a Mac, and sadly, TSoft is PC only …
w.
RichardLH says: @ur momisugly 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)
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?
richard telford says:
February 10, 2014 at 6:42 am
Thanks, Richard, I’d seen that. Their abstract says (emphasis mine):
Here’s my thinking. Is it possible that there is a tidal effect on the climate? Sure, although there’s much more likely to be an affect on the weather.
Is it likely to be global? Perhaps, but less likely.
Is the effect large? Probably not, or we’d have seen the evidence.
w.
clivebest says:
February 10, 2014 at 7:00 am
No, I haven’t plotted the tides in any way, shape, or form, either sub-lunar or antipodal.
What I have plotted is the tidal force, the actual amount of combined tidal pull exerted by the sun and moon.
This is separate and distinct from the tides themselves, which are the two bulges in the ocean on opposite sides of the earth. I have not measured their magnitude in any manner.
w.
David L. Hagen says:
February 10, 2014 at 8:01 am
That’s the same BS excuse that all the climate alarmists push. It’s exactly what Michael Mann and Phil Jones said, and it’s just as pathetic and unconvincing when you and Scafetta try it on.
This is 2013, David. If a description in English could serve to give instructions to a computer, we’d program in English. But English is far too vague and imprecise for the purpose. Plus you ignore the reality of bugs and errors in your code. You are claiming that if there are bugs in Scafetta’s code, that his English language description of the code is sufficient to allow others to find those bugs … you sure that’s your final answer?
For example, in this very post, I put up the exact formulas I used … and one of them was wrong. This was discovered and fixed immediately.
Now, suppose I’d just given a description of what I’d done and not shown the equations. It could have taken weeks to discover the error in my code.
Now, suppose further that after oddities were discovered in my work, I had flat-out refused to show you all how I did the calculations … what would you say then?
Because that kind of malfeasance is what you are defending, David. You are allying yourself with Mann and Jones, and I’m sick of fighting this particular fight.
For me, it’s no code, no data, no science, not because I say so, but for a simple reason:
SCIENCE DEPENDS ON TOTAL TRANSPARENCY
And as a result, those like Scafetta that refuse to practice that are not scientists in any sense. As Mosher said, that’s not science … that’s advertising.
Why is this so hard to understand? No, David, Scafetta doesn’t get to hide his code and data and call himself a scientist.
I mean, that doesn’t even pass the smell test. Surely you must know that if a man is hiding something … it’s because he has something to hide.
w.
dan says:
February 10, 2014 at 9:54 am
Since you haven’t included either the link in question or mosher’s comment, you’re just wasting electrons and expressing your unpleasant opinions. What the hell are you referring to? What link? What comment?
w.
clivebest says:
February 10, 2014 at 10:23 am
Here’s an odd fact I learned back in the Cenozoic, when I was studying celestial navigation. The path the full moon takes in the sky is the path the sun will take in six months. Oh, don’t jump up and say “but Willis, it’s not the exact same path”. It’s not … but it is close enough for practical purposes.
In particular, it helps us to make better sense of Clive’s comment, because the relationship above means that at the poles, when the sun never rises, the full moon never sets …
Which of course intensifies the effect Clive describes above.
w.
Greg Goodman says:
February 10, 2014 at 3:32 pm
Just more of your usual bovine byproducts, Greg. I commented on it here, shortly after it was posted, so people reading through wouldn’t be misled.
More questions and fewer assertions would improve your truthiness ratio …
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 …
w.
Jeff Alberts says:
February 10, 2014 at 6:27 pm
I do so love grammar Nazis, they’re nothing but fun, even their jokes are pointed. They always insist that English should make literal sense, and they find it appalling that ravel and unravel mean the same thing.
Like ravel and unravel, both “I could care less” and “I couldn’t care less” have come to mean the same thing. Yes, you are 100% correct that it’s not logical at all … hey, welcome to English as it is spoken.
You likely think you’re on the forefront in making this joke, but the dispute has been going on for a half century, and the joke is quite stale at this point. There’s a good history of the debate here. It points out (emphasis mine):
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. And me, I speak it, not according to rules, but according to how it is actually spoken. I’m not fool enough to try to impose my logical rules on the English language, that’s a mug’s game. For example, as the article says,
Go figure …
w.
J. Philip Peterson says:
February 10, 2014 at 6:52 pm
Well, I have a day job to pay the bills, and my gorgeous ex-fiancee works as well … the big oil check hasn’t arrived yet, must be lost in the mail.
I posted this article mostly to bring some sanity to the idea of cycles, by pointing out that you can’t just grab celestial periods (e.g. half the period of the precession of lunar nodes), claim that it has a beat frequency with some other period (say 8.55 years) and claim success in relating the heavens to the climate …
I also did it for the best reason, which is that this is how I learn. I’d never done this kind of analysis before, so I didn’t really understand how the tidal forces vary over time. Now, I know exactly how to calculate the tidal effects of Jupiter on the Moon …
The missing link, J. Philip, is that there are a lot of people out there that I refer to as “cyclomaniacs”. These are folks who are willing to grab any two celestial cycles, calculate the beat frequency, and claim some kind of effect on the climate. I’m trying to get them to actually calculate the size of the forces involved, and to use the actual historical data rather than just picking cycle lengths because they fit their fantasy.
w.
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.
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.
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).
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.
Jeff Alberts says:
February 10, 2014 at 9:32 pm
It’s not a logical statement at all, Jeff. It is an English statement, and much of English is not logical. Are you going to complain next that “ravel” and “unravel” mean the same thing? Because that’s totally illogical … but it’s also perfect English. The part you seem to be missing is …
ENGLISH ISN’T LOGICAL
For example, we say “a hundred times smaller than” … and that makes no sense at all. A hundred times X has to be bigger than X. But despite that, people say it all the time, and since people understand it perfectly, the practice will assuredly continue … and grammar Nazis will continue to bitch about it because yes, it’s not logical. I’ve been busted for using it myself. And I made the same response I make now, which is this:
You are right, Jeff. What I said isn’t logical in the slightest. However, that also doesn’t matter in the slightest, because English isn’t logical. All that counts is, do people understand perfectly what you mean? That’s what is important to people, are they understood? And since people do understand it, that’s why you are losing the fight, as grammar Nazis almost always do—the usage of “I could care less” is increasing. Eventually, it will be like “ravel” and “unravel”, totally unremarkable despite being totally illogical
Now, you can make your perfectly logical objection for the next fifty years … me, I prefer to ride the horse in the direction it’s going. People will continue to use logically incorrect statements as long as everyone understands what they mean … and I suspect that there will be people complaining about it forever, endlessly saying correctly but vainly, It’s not logical, it’s not, it’s not …
But if you’d like something new to complain about, how about the term “dust”? What’s wrong with that? Well, “dust” as a verb means to remove dust from (“dust the furniture”), or to add dust to (“dust the cake with flour”) … how logical is that?
w.
“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. 😉
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 says:
February 10, 2014 at 11:46 pm
Does anyone understand this claim? I can’t make sense of it. I use standard vector addition to combine the forces. He proposes to calculate the combined tidal force by using
Force = sqrt( sunforce^2 + moonforce^2 + abs(2 * sunforce * moonforce * cos(theta) )
where theta is the angle between the forces.
He explains that we should do it that way because, as we all know, the tidal force causes a bulge on both sides of the earth … say what? Why should that affect the way we calculate the summation of two vector forces?
Does this make sense to anyone? Because it makes no sense to me. For example, using the normal calculation, two opposite forces of strength 1 newton cancel each other out.
In his calculation, we end up with a force of
sqrt( -12 + 12 + abs(2 * 1 * 1*cos(180°)) ) = 2 newtons … but it has no direction …
Does anyone understand his claim?
w.
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.