In another thread, Vukcevic posted a question about lunar months. Despite my being a Master Druid, I have to protest that I’m not an expert on tides. Just an informed Druid ;-) More a broad generalist than expert in any one thing. So, in response to:
27 June 2014 at 3:35 pm (Edit)
Hi Mr. Smith
You are known as the expert on the tides I’ll have to go back to your main article on the subject, but for the moment I have a short question :
Wikipedia: article http://en.wikipedia.org/wiki/Lunar_month
lists 5 different numbers for the lunar month Odd one out is the synodic month quoted as ~29.53, while the other four are all with periods closely spaced between 27.2 and 27.55 days
How do you rate significance of the synodic month’s period in relations to ‘climate change’ compared to any of the rest?
We have this posting.
The short form is “it is the beat frequency between them, not any one month”.
The long answer follows…
Tides depend on gravity, and in particular to weather and climate, IMHO, the tractional force pulling ocean waters away from the poles and toward the equator. That is most strong under certain alignments of sun, moon, and earth; with certain orbital conditions of closest approach and straightest alignment. The closer, straighter, and most synchronized with each other, the stronger the tides and the stronger the tractional force pulling cold polar water away toward the equator. Also the shallower or deeper channels such as Drake Passage so the more or less deflection of currents such as the Circumpolar Current up the spine of South America toward the equator. https://chiefio.wordpress.com/2010/12/22/drakes-passage/
So when does what happen?
First up, the 5 months:
A synodic month is the most familiar lunar cycle, defined as the time interval between two consecutive occurrences of a particular phase (such as new moon or full moon) as seen by an observer on Earth. The mean length of the synodic month is 29.53059 days (29 days, 12 hours, 44 minutes, 2.8 seconds). Due to the eccentric orbit of the lunar orbit around Earth (and to a lesser degree, the Earth’s elliptical orbit around the Sun), the length of a synodic month can vary by up to seven hours.
The draconic month or nodal month is the period in which the Moon returns to the same node of its orbit; the nodes are the two points where the Moon’s orbit crosses the plane of the Earth’s orbit. Its duration is about 27.21222 days on average.
The tropical month is the average time for the Moon to pass twice through the same equinox point of the sky. It is 27.32158 days, very slightly shorter than the sidereal month (27.32166) days, because of precession of the equinoxes. Unlike the sidereal month, it can be measured precisely.
The sidereal month is defined as the Moon’s orbital period in a non-rotating frame of reference (which on average is equal to its rotation period in the same frame). It is about 27.32166 days (27 days, 7 hours, 43 minutes, 11.6 seconds). The exact duration of the orbital period cannot be easily determined, because the ‘non-rotating frame of reference’ cannot be observed directly. However, it is approximately equal to the time it takes the Moon to pass twice a “fixed” star (different stars give different results because all have proper motions and are not really fixed in position).
An anomalistic month is the average time the Moon takes to go from perigee to perigee – the point in the Moon’s orbit when it is closest to Earth. An anomalistic month is about 27.55455 days on average.
The different months tell us different things about the orbital status and alignments. Lets take them in reverse order and start with the “Anomalistic month”. When the moon is at perigee, it is closest to the Earth so tides are stronger. That matters. So this month length matters. But other things matter too. When that perigee point comes on top of a moon-sun alignment, the forces on tides are even stronger. So it is the interaction of the two that makes the total tide cycle. (Actually the interaction of even more than the two, but for now we are just using two to show the process).
So if the moon is closest to the earth, and the moon and sun are both lined up, we get even stronger tides. That ‘moon and sun line up’ is easiest to see, literally. When lined up with the moon on the far side of the Earth from the sun we get a full moon. When lined up on the side toward the sun we get a new moon. Both are strong tides. When directly over head, the gravitational pull is slightly stronger than when it is on the other side of the planet, so you get the stronger tides when the moon and sun are both overhead during a New Moon and weaker tides (though still strong) when at the full moon. That is the Synodic Month (first on the list above).
As the Synodic and Anomalist months move into an alignment, with perigee at the moment of the moon aligned with the sun, we get Perigean Spring Tides. Some of the strongest. The wiki on tides puts it at 7 1/2 lunations:
The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, at perigee, the range increases, and when it is at apogee, the range shrinks. Every 7½ lunations (the full cycles from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range. Even at its most powerful this force is still weak causing tidal differences of inches at most
Oh, and note in passing that the orbit of the Earth around the sun has a perihelion point where solar tide force is stronger, so that ‘beats’ against these other cycles too. But the solar tide force is smaller than the lunar, so that effect is an addition on top of the lunar cycle, not a dominant force variation. But longer term, it adds to the ‘cycles in cycles’.
That difference in height that is called “weak” does not mean “has little effect”, IMHO. It still amounts to huge quantities of water moved via the tractional forces away from the poles, and significant changes in quantity of water that goes through Drake Passage vs deflection up the coast as a current. What does moving 1/2 foot depth of water over the whole Southern Ocean from Antarctica to the Equator have as an effect on, say, ENSO?
Their use of 7 1/2 lunations is an interesting number. At 29.53059 days per lunation that is 221.479425 days. The beat between anomalistic and synodic months is 29.53059 – 27.55455 = 1.97064 difference. Dividing synodic by that gives 14.9852788941 which needs to be divided by 2 (as they are counting both new and full moon tides) for that 7 1/2 (that is closer to 7.49263). So about every 221 days a major tide, and about every 442 days has one just a tiny bit stronger (new vs full moon). Perhaps a time period useful for weather, but climate not so much…
Next up is the Draconian month. That is when the moon crosses the ‘node’ line. It is in the plane of the Earth / Sun orbit exactly. When that coincides with a perigean spring tide, it makes them just a bit stronger. So yet another beat frequency to factor into the mix. When the moon is high over the North, water flows toward the north pole. When below the ecliptic, more water flows toward the south pole. That cycle too likely matters. Both “strongest” and “which pole” will matter to weather and climate.
IMHO the Sidereal month is not relevant to tides nor climate. The alignment with a star far far away does not influence the solar / lunar alignment nor the lunar Earth distance, so ought to have no effect. It might have a correlation with precession, and that precession can have some climate correlations, but it is more a correlation than a causation, so I’d look for longer term causality in precession interactions with seasons and not with a lunar stellar interaction.
That leaves the Tropical month. When the moon passes through the same equinox point in the sky. This is simply the same as the Sidereal month adjusted for precession of the Earth axis, so again, IMHO, is an unphysical thing in terms of tides.
So that’s the ‘big lumps’ on lunar month vs tides, IMHO. The Synodic and Anomalistic month beat frequency, with a minor Draconian beat overlay longer term.
IMHO, there are longer tide cycles that are driven by other changes than those months. The circularity of both the Luna and Earth orbits changes over time. That will change the distance between us, and thus the tides. The orbital tilt can also change over time for both the lunar orbit and the Earth orbit vs the sun and vs each other. Similarly there are interactions of tides with the surface structures, so another ‘beat frequency’ as the rotation rate of the earth aligns given surface features with the Perigean tides. I looked at that here:
In that posting it goes over things like the Saros Cycle
The eclipse calendar tends to be set by the Saros Cycle that’s a bit over 18 years.
Fortunately for early astronomers lunar and solar eclipses repeat every 18 years 11 days and 8 hours in a “Saros” cycle.
That bit about eclipses matters. That is when the moon is crossing the ecliptic. Other than that time, it is above or below the ecliptic and pulling water more north or south.
So lunar alignments suited to an eclipse (Synodic, Draconian in sync) have a cycle of variation that repeats every 18 (ish) years AND that resyncs with the topology of the land every third one of those (so the same land or ocean under the same repeat frequency of eclipses / tide forces at the same times) for a (roughly) 54 year repeat. Sort of close to the (roughly) 60 year PDO cycle (that has large error bands on the estimate of the cycle…)
That brings together the more important lunar month beat cycles with the eclipse cycle and the Earth rotation repeat beat.
Is there more?
Even longer term you can get changes in the inclination of the Earth polar tilt. Obliquity.
The Earth currently has an axial tilt of about 23.4°. This value remains approximately the same relative to a stationary orbital plane throughout the cycles of precession. However, because the ecliptic (i.e. the Earth’s orbit) moves due to planetary perturbations, the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47″ per century (see below).
Note that the pole does not bob up and down so much as the Earth bobs up and down and the measure is relative to the ecliptic, so the axial tilt is described as changing due to the ecliptic changing. Yet for practical purposes, that apparent change is what matters as that determines where the tidal force aligns.
Now realize that the moon has a similar bobbing up and down moment that also changes due to “planetary perturbations”…
Look at the graphs in that link on obliquity and notice that the very long term changes are quasi periodic, but not pure cycles. We know less about lunar obliquity changes, IMHO.
There are also potential resonances with other orbital ‘stuff’, so some of the tidal effects may arrive along with things like increases in meteor storms and dust…
also looks at this paper: http://www.pnas.org/content/97/8/3814.full that is an interesting paper in terms of tidal mixing physics. They specifically look at lunar orbital mechanics and how much that changes tidal mixing of the surface layers of the ocean. They show the expected size of each impact, and what the net forces are expected to be, but only via an estimate based on purely cyclical projections of present values for cycles (reasonable, since we can’t solve the n-body orbital mechanics issues anyway). So it is good as a place to look at tides and forces as sizes, of a sort. Just realize that very long term some of the values they assume for modeling will change…
A Proposed Tidal Mechanism for Periodic Oceanic Cooling.
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.
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.
As a measure of the global tide raising forces (ref. 5, p. 201.33), we adopt the angular velocity, γ, of the moon with respect to perigee, in degrees of arc per day, computed from the known motions of the sun, moon, and earth. This angular velocity, for strong tidal events, from A.D. 1,600 to 2,140, is listed in a treatise by Wood (ref. 5, Table 16). We extended the calculation of γ back to the glacial age by a multiple regression analysis that related Wood’s values to four factors that determine the timing of strong tides: the periods of the three lunar months (the synodic, the anomalistic, and the nodical), and the anomalistic year, defined below. Our computations of γ first assume that all four of these periods are invariant, with values appropriate to the present epoch, as shown in Table 1. We later address secular variations. Although the assumption of invariance is a simplification of the true motions of the earth and moon, we have verified that this method of computing γ (see Table 2) produces values nearly identical to those listed by Wood, the most serious shortcoming being occasional shifts of 9 or 18 years in peak values of γ.
That 6 year cycle is roughly a 10x of the 221 days above (9.9 x) while 9 years is a 14.9x of it. It is also the case that the 9 is 1/2 of a Saros while 18 is almost exactly one Saros cycle. All indications that the lunar / tidal cycles line up with climate changes.
A time-series plot of Wood’s values of γ (Fig. 1) reveals a complex cyclic pattern. On the decadal time-scale the most important periodicity is the Saros cycle, seen as sequences of events, spaced 18.03 years apart. Prominent sequences are made obvious in the plot by connected line-segments that form a series of overlapping arcs. The maxima, labeled A, B, C, D, of the most prominent sequences, all at full moon, are spaced about 180 years apart. The maxima, labeled a, b, c, of the next most prominent sequences, all at new moon, are also spaced about 180 years apart. The two sets of maxima together produce strong tidal forcing at approximately 90-year intervals.
There’s more, but just read the paper. Here’s a nice graph from it:
For your question, IMHO, that graph is the “money quote” in that it shows Syzygy vs Perihileon (so the alignment of the moon with the sun at closest approach) along with lunar nodal declination effects and the net-net of those on ‘lunar angular velocity’ as a proxy of sorts for tidal force.
So, with that, hopefully that answers your question?
Some More Lunar Links
Just for completion, here’s a few more links to things I’ve posted about lunar cycles over the years. Some show my ‘progress’ from a rough grasp toward better detail, and some have some speculative bits in them, but ‘history is what it is’ ;-)
And Vuk, you ought to especially like this one: ;-)
And my favorite speculation is that we are just trying to figure out (again) what the Ancients already knew:
So, at the end of all that, the simple fact is that if it IS Luna that does it to our climate via tides cycles, then we can not accurately predict very long term as we can not solve the n-body orbital problem. We can get “close” via a lot of calculation via brute force iterations, but that will suffer from drift over long terms, and from lack of exact numbers for initial conditions (such as just what is the mass of the Trojan asteroids?…) Likely not enough error to mess things up in a 100 year prediction, but enough to make using ancient proxy data suspect as we don’t really know what the configuration of planets and Luna (and the Earth!) was 100,000 years ago. It’s just ‘projections’ based on models… perhaps good ones, or perhaps not. Hopefully good enough for ‘all practical purposes’.
With that, hopefully the above descriptions and set of links will give you enough background to ponder so that you come up with some new and useful insight.