Over at WUWT, Willis has a “proof” that there is no periodic cycle in tides. He does this via an analysis of the tidal force, and shows that the size of it does not change in any repeating periodic way that provides an 18.6 or ‘near 60’ year period. Substantially his argument is of the form “the force does not change enough to matter”. My assertion is that this conclusion is based on an error of ‘kind’ in his analysis.
He is looking at a vector quantity and only addressing the scalar portion of it. That is too narrow an analysis to find what, IMHO, matters. A scalar quantity has a size. That’s it. No direction. A vector quantity has both a size, and a direction.
I go 20 miles per hour. That’s a scalar.
I go 20 miles per hour due north.
That’s a vector. Both size “20” and direction “north”.
My assertion is that while “size doesn’t matter” in the tidal force scalar, direction does matter as it is a tidal forcing vector. It is the “direction” portion that makes the difference, and that “direction” does in fact have periods of 18.6 (ish) years and about 3 times that ( or about 55.6 years, though other physics will modulate that somewhat once land and topology are added in).
First up, the prior postings: I have looked at other bits of lunar / tidal “stuff” in several postings.
This is the background:
https://chiefio.wordpress.com/2011/11/03/lunar-resonance-and-taurid-storms/ is the first time I pointed at the Keeling and Whorf paper here: http://www.pnas.org/content/97/8/3814.full
Also, there’s a very nice readable page on all the ways folks get tides wrong (including the text books) here:
If you have any notion that centrifugal “force” is involved in the tides, or that rotation really is what matters, please read that link. All that really matters is the gravity vector and how it diminishes with distance.
Rotation does have an impact once continents are involved (in that the oceanic ‘tidal bulge’ can’t just run through them) but it does not have anything to do with generating the tidal force.
OK, with that preamble, on to the “why the vector part matters”.
Which Way The Tidal Force Points, Changes Over Time
Even in that excellent link on “misconceptions about tides”, they show a simplified picture of the tidal force on the planet. This is the net-net force acting on water after all the Earth gravity, Luna gravity, etc. etc. are netted out. This is what actually moves the water.
They show this image from the wiki:
The basic notion being presented is that gravity pulls the side closest to the satellite toward it, and as gravity falls off with distance, the net gravity is lower on the far side. There is also a ‘tractional’ force pulling sideways at the poles. This tractional force pulls water away from the poles, toward the two bulges. The one toward the satellite from more gravitational pull, and the one away from the satellite due to lower gravitational pull.
So far, so good. At least it avoids the mistaken notions that anything other than gravity is at work. (Be it “inertia” or “centrifugal force” or any other kind of red herring.) BUT, it ignores the fact that the satellite, in the case of the Earth / Moon system, is NOT stuck in the equatorial plane.
For almost all other systems of moons and large planets, the moons ARE stuck in the equatorial plane, and this simplification is just fine. For the Earth / Luna system, we are a binary planet and Luna orbits the Sun, not us. It has an orbit tilted about 5.5 degrees to our orbit around the Sun (ecliptic) and as our Earth axis is tilted, it has an added +/- 23.5 degrees of variation relative to our equator. (Even that is a bit of simplification, since as our axial tilt shifts, that range gets even larger or lesser, so over 41,000 or so years it has another modulation of a few degrees. Since we’re looking at cycles less than 5000 years, I think, it is OK to ignore that drift for now; though it likely matters to when interglacials happen.)
So, in reality, lunar tidal force wanders about 37 degrees back and forth on a N/S line at low times and up to 57 at times of large variation. (That is, 23.5 – 5 = 18.5, then 18.5 x 2 = 37 for the full range. Similarly, 23.5 + 5 = 28.5 when Lunar Declination to the ecliptic adds to our ’tilt’ for 57 degrees total range). This cycle of a 37 degree wobble happens each lunar month (one cycle of the moon ‘around’ the earth). Same thing for the 57 degree range when things align the other way. This change from 37 to 57 takes about one Earth year (as the Moon orbits the sun at the same pace we do, but goes above / below the ecliptic).
So on a yearly period, we have a “delta” of 20 degrees in the “alignment” of our moon with the Earth axis. In the following two images, I’ve taken that simple image above and tilted it by +/- 18.5 and then +/- 28.5 degrees. That’s what the Earth really sees in term of ‘tidal force’ on a monthly cycle during the two ranges of alignment of lunar ecliptic displacement and our polar axis alignment.
FWIW, I need to find another link at this point. I have it, just not sure where. That author asserts that as the various alignments change in terms of which season they are in, that is a key point. (He disparaged me for ‘not making that leap’ yet, or words to that effect; when I was simply not willing to endorse without more pondering). At any rate, having the 57 degree range arrive in winter vs summer likely has an effect. And, as we have our axial precession on a 26,000 ish range, that effect will shift which season has what tides. This, too, likely matters. Low range first, then high range:
At first blush, they don’t look all THAT different, but look a bit closer. For example, look at the North Pole. In the low range case, the vector points more ‘up and down’. Rising and falling. In the wider range, the vector goes to nearly tangential. Flushing water in and out. Think having more warm lower latitude water flushing into and out of the arctic might matter to ice melt? Think more lateral displacement might impact the Gulf Stream and just where it lands on Europe? That the wider displacement has more potential to disrupt such a flow into vortex whorls and less tendency to let it run straight? Tides in many cases drive currents (more on that later), so there ought to be wide spread changes in the size and location of currents, especially near continental shelves.
Going from yearly to 18.6 to 55.8
The cycle from minimal to maximal lunar range is an annual thing. But WHEN it happens shifts with lunar precession: It shifts with lunar apsidal precession
Precession is the rotation of a plane (or its associated perpendicular axis) with respect to a reference plane. The orbit of the Moon has two important such precessional motions. First, the long axis (line of the apsides: perigee and apogee) of the Moon’s elliptical orbit precesses eastward by one full cycle in just under 9 years. It is caused by the solar tide. This is the reason that an anomalistic month (the period of time that the Moon moves from the perigee to the apogee and to the perigee again) is longer than the sidereal month (the period of time when the Moon completes one revolution with respect to the fixed stars). This apsidal precession completes one rotation in the same time as the number of sidereal months exceeds the number of anomalistic months by exactly one, after about 3233 days (8.85 years).
Another precession is the turning of lunar orbit, the orientation of lunar orbit inclination. This motion determines the period of the lunar nodes; that is, the line along which the plane of the Moon’s orbit and that of Earth’s orbit intersect. This nodal period is about twice as long (about 18.6 years) as the apsidal precession period discussed above, and the direction of motion is Westward. This is the reason that a draconic month (the period of time that the Moon takes to return to the same node) is shorter than the sidereal month. After one nodal precession period, the number of draconic months exceeds the number of sidereal months by exactly one. This period is about 6793 days (18.60 years).
As a result of this nodal precession, the time for the Sun-Earth-Moon alignment to return to the same node, the eclipse year, is about 18.6377 days shorter than a sidereal year. The number of solar orbits during one turn of lunar orbit equals the period of orbit divided by this difference minus one.
So the season when that major vs minor tidal force arrives changes on about an 18 year cycle. That “where is the vector when?” will change what tides and currents happen, where and when. I think this matters.
More, or less, Arctic flushing in summer vs winter. Stronger, or weaker, currents in the summer vs winter taking heat toward the poles, or not.
Now notice the “bulge” part. The Earth is about 1/3 of a rotation off at each 18.6 year ‘repeat’ of the Lunar tidal force from the Saros cycle (alignments of the Sun, Moon, and Earth on the Ecliptic). That means that roughly each 55.8 years, that “bulge” arrives over the same patch of the Earth. That tidal bulge will have significantly different effects if it is over Asia than if it is over the Pacific Ocean. So that annual change might be more extreme when Asia is in winter, or when Australia is in winter, and it lands on top of them.
The 18.6 year cycle isn’t just eclipse alignments, it is also the alignment of apogee / perigee of the moon with the Earth / Sun line (just offset by part of an orbit). As that happens, both angular velocity of the moon changes, and actual tide force changes ( up to 40% per a below reference). So you can have that more / less tide force showing up over any 1/3 rotation displacement location as the 3 x cycle happens. (As it isn’t EXACTLY 1/3, even this will slowly drift as to exactly which land / sea is at the alignment over very long cycles. Yet another “dig here” to calculate; but it will be a very long cycle).
To recap, so far: There’s an annual change of lunar tidal force angle of significant size, that shifts as the seasons change and with lunar precession, and that drifts with precession of the equinoxes. There is an 18 ish year change of Sun / Moon / Earth alignment. There is a 3 x that phasing with Earth rotational position. The Keeling and Whorf paper looks at the variation in angular velocity of the moon:
“Varying strength in an estimate of the tide raising forces, derived from Wood (ref. 5, Table 16). Each event, shown by a vertical line, gives a measure of the forcing in terms of the angular velocity of the moon, γ, in arc degrees per day, at the time of the event. Arcs connect events of strong 18.03-year tidal sequences.”
(Note that they use 18.03 year period. I’ve not yet worked out why some folks use 18.03 while others use 18.6 though I do know why the two periods exist. They measure slightly different things. Until it can be sorted out which alignments really are driving things, I’m basically ignoring those decimal place variations.) So is it actual position? Or the change in angular velocity? I’m leaving that as a ‘dig here’. They both come about the same time period anyway, and the .03 vs .6 is down near the error band of what timing data we have on historical climate cycles; so rather than run down that rabbit hole right now, I’m leaving it for later.
So in their paper they look at angular velocity (how fast the moon runs from one place to another) and I’m looking at where the moon is and how far it goes in a month. Not that much difference, really. For the average 1470 year cycle (that has nodes at 1800 and 1200 year ranges so the 1470 is only an average) the monthly changes or even the 18 ish year changes are not as important. My belief is that on the very long ranges, it is a ‘beat’ of some shorter cycles, or the Keeling and Whorf folks have it right that the alignments of Sun and Moon at perigee with greatest angular velocity add even more tidal force to the action. But that longer cycle is not the topic right now. We still have the 18 ish year cycle of more / less “flushing” of the Arctic and more / less ocean current creation and disruption; but it gets a ‘size kicker’ from even faster angular velocity changes and even stronger gravitational forces at closest approach of the Sun and Moon to the earth.
So we have a ‘vector metronome’ that changes size by a net 20 degrees on the angle of the Luna gravity vector. We have 9 and 18 year drift of that effect relative to the seasons. We have a 3 x that beat frequency on the continental effects on currents and tides as land masses line up, or don’t, with the peak tide bulges when the moon and sun align (ecliptic crossing), and we have a longer term interaction based on perigee alignments of Sun and Moon changing the distance.
Take all those changes, shake and mix, and the resultant sloshing is the actual tide (modified by continent profiles…) I think that is more than ‘a trivial degree of change that can be dismissed’.
It is all those vector portions that matter, not the scalar of lunar gravity variation. Add in some resonance of sloshing oceans and ground profile and you get a range of tides from near zero to near 50 feet at the Bay of Fundy. All from the same “nearly constant” tidal gravity scalar of the Moon.
Some “Odd Bits” on Tides
The Bay of Fundy site has some nice descriptions of the tides there:
100 billion tonnes of water daily interactive tide animation Try our interactive tide animations! Each day 100 billion tonnes of seawater flows in and out of the Bay of Fundy during one tide cycle — more than the combined flow of the world’s freshwater rivers!
That’s just ONE spot with tidal flow. Overall, the tides create a lot of tidal mixing (per the Keeling and Whorf paper, more than the winds) and creates many of the ocean currents. Change that, and weather will follow.
I’ve also given short shrift to the effects of the land masses on the tides. That “Misconceptions” link has this nice bit:
These bulges distort the shape of the solid Earth, and also distort the oceans. If the oceans covered the entire Earth uniformly, this would almost be the end of the story. But there are land masses, and ocean basins in which the water is mostly confined as the Earth rotates. This is where rotation does come into play, but not because of inertial effects, as textbooks would have you think. Without continents, the water in the ocean would lag behind the rotation of the Earth, due to frictional effects. But with continents the water is forced to move with them. However, the frictional drag is still important. Water in ocean basins is forced to “slosh around”, reflecting from continental shelves, setting up ocean currents and standing waves that cause water level variations to be superimposed on the tidal bulges, and in many places, these are of greater amplitude than the tidal bulge variations.
Note in particular the statement “in many places, these are of greater amplitude than the tidal bulge variations.”
Those alignments and geographical placement issues can cause reflections and standing waves that are “of greater amplitude than the tidal bulge”. Where the land is, relative to the location of the Tidal Bulge matters. That bulge can wander either 37 or 57 degrees N / S during a year and change their season of arrival of extremes with the 18 ish year cycle, and the alignment with the land surfaces at solar / lunar alignment repeats on a 3 x that cycle. That ought to have a significant modifying effect on the tides (and, in fact, we do see significant changes in tides over both short and long term cycles.)
This link: http://stevekluge.com/geoscience/images/tides.html has a very nice exposition on some of the changes of tides with changes in the axial tilt alignment of the Earth. I’m going to paste two images from it here:
Tidal bulge when in most tilt mode at the solstice:
The second picture has this description:
In the figure to the right, the Moon and Sun are both at maximum declination, as might occur on the summer solstice. Note that there is 1 tidal bulge north of the equator, and the other is south of the equator. A mid latitude observer would still experience 2 high tides (semidiurnal tides), but they would be assymetrical – the tide at X1 would be greater in both height and range than the tide 12h 25m later at X. Note also that at higher latitudes, there is only one relatively small high tide that day. “One high tide a day” tides are called diurnal tides
Now realize that the locations / seasons where those effects will show up will change on an 18 ish year cycle as the lunar ecliptic alignment changes. I think this matters. For those wanting a more in depth view, along with a load of math, read here:
http://faculty.ifmo.ru/butikov/Oceanic_Tides.pdf It is pretty deep sledding, and I’m still working my way through it. One quote, though:
XI. REAL-WORLD COMPLICATIONS
The pattern of tide-generating forces is coupled to the position of the moon ~and the sun! with respect to the earth. For any place on the earth’s surface, the relative position of the moon has an average periodicity of 24 h 50 min. The lunar tide-generating force experienced at any location has the same periodicity.
When the moon is in the plane of the equator, the force runs through two identical cycles within this time interval because of the quadrupole symmetry of the global pattern of tidal forces. Consequently, the tidal period is 12 h 25 min in this case ~the period of the semidiurnal lunar tide!. However, the lunar orbit doesn’t lie in the plane of the equator, and the moon is alternately to the north and to the south of the equator. The daily rotation of the earth about an axis inclined to the lunar orbital plane introduces an asymmetry in the tides. This asymmetry is apparent as an inequality of the two successive cycles within 24 h 50 min. Similarly, the sun causes a semidiurnal solar tide with a 12-h period, and a diurnal solar tide with a 24-h period.
In a complete description of the local variations of the tidal forces, still other partial tides play a role because of further inequalities in the orbital motions of the moon and the earth. In particular, the elliptical shape of the moon’s orbit produces a 40% difference between the lunar tidal forces at the perigee and apogee of the orbit. Also the inclination of the moon’s orbit varies periodically in the interval 18.3° – 28.6°, causing a partial tide with a period of 18.6 yr.
The interference of the sun-induced tidal forces with the moon-induced tidal forces ~the lunar forces are about 2.2 times as strong! causes the regular variation of the tidal range between spring tide, when the range has its maximum ~occurring at a new moon and at a full moon, when the sun and moon are in the same or in the opposite directions!, and neap tide, when the range has its minimum ~which occurs at intermediate phases of the moon!.
The amplitude of a spring tide may be 2.7 times the amplitude of a neap tide. Because the earth is not surrounded by an uninterrupted water envelope of equal depth, but rather has a very irregular geographic alternation of land and seas with complex floor geometry, the actual response of the oceans and seas to the tidal forces is extremely complex.
Note that he uses more precise numbers of 18.3 and 28.6 instead of my simplified 18 1/2 and 28 1/2. Also note that the apogee / perigee change of the lunar position accounts for a 40% variation in tidal force.
Exactly how lunar orbital eccentricity changes matters a great deal, and we don’t have a good handle on it, since Luna orbits the Sun, and not us. Eccentricity relative to us depends on Luna / Solar changes, stirred by the other planets. At any rate, the alignment of apogee / perigee with particular places on the Earth surface is going to mater to total tidal force, Arctic flushing activity, and current formation.
Weather depends on all of those far more than on a trace gas of questionable effect in the air.
To dismiss all these vector effects with a scalar wave of the hand is not the path to greater understanding. To assert that the effect is non-cyclical based on a particular transform on that scalar number is simplistic, at best.
To ignore folks who clearly “have clue” stating that there is an 18.6 year minor tide cycle is being a bit intemperate at well. Clearly there IS an 18 ish year cycle detected by others. I choose not to ignore them.
I have some more work to do to get a cleaner handle on all this tidal stuff, it is rather complicated. But for now, the sun is out, and the air is warm, and the pool is calling my name ;-)
Enjoy your day, a gift of the sun.
Then enjoy this evening with a nice full moon.
And ponder what they do to our oceans.