# Astronomical influence on climate

1. Jun 29, 2008

### giann_tee

I've been working on a task in the area of astronomy, regarding influence on climate by astronomical factors. However, the work is rather tough and I have a problem on wording of "amplitude of precession".

You definitely know about the precession of Earth's axis, once in 25 765 years. It is also called precession of equinoxes, because the Equator and the Ecliptic will intersect at points that are moving against background stars (at some speed). All clear so far.

There is another kind of precession that is simply speaking, the rotation of the Earth's orbit once in 112 000 years relative to background stars which doesn't seem to matter much to the climate, because it is all relative and only Sun matters.

1. according to the position of the equinox relative to the Sun on ecliptic we measure tropical year, SEASONS and calendar.

2. according to the position of the equinox relative to the perihelion (closest point to the Sun on orbit) we determine where on the Earth's orbit is the equinox. When we know that, we know what SEASON it is when the Earth is closest to the Sun. The cycle takes 21 000 years to repeat the event of equinox and perihelion happening on the same day.

Now I don't know why I had to say all that when it is on the internet, here
http://en.wikipedia.org/wiki/Precession_(astronomy)

I call this cycle the cycle of climatic precession.

According to eccentricity, the orbit may be more elongated or more round like a circle. If it is more elongated, the AMPLITUDE of precession is greater. It is further said that eccentricity modulates precession. You can review this greatly chaotic presentation:
http://www.soest.hawaii.edu/GG/FACULTY/POPP/Lecture12.ppt

I am trying to find a simple passage of text to properly define the "amplitude of precession". Slides 23, 24, 25... are about that topic.

Precession index p = eccentricity sin(omega) somehow includes two kinds of precession. Not clear.

Precession index turns precession into sine wave, and eccentricity stands for amplitude. All clear.

Precession index is 23 000 years cycle. Not clear.

Possible solution: ignore the number and continue. Any ideas?

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Part II

I am using the following statements. The axial tilt and precession for that matter, are not expected to change the GLOBAL insolation because the distance to the Sun is always the same.

The tilt says how much sun is there at the poles or at some latitude at what angle.

Climatic precession modulates seasonal cycle.
http://www.people.fas.harvard.edu/~phuybers/Doc/HuybersThesis.pdf

Only eccentricity changes GLOBAL insolation because of the different distances at which Earth is passing by Sun.
http://en.wikipedia.org/wiki/Milankovitch_cycles

However, if we pretend that eccentricity is really high value. Planet could be so far out of sunlight once a year that it would get cooler a lot. Does it take away the heat and returns the ONE YEAR AVERAGE to standard value as for circular orbit? In this question I disregard the nonlinear domain where on some other planet the heat may be stored for long time so it doesn't matter and so on.

These are my thoughts, thanks for reading, if you have some idea about precession I would appreciate it.

2. Jun 29, 2008

### tony873004

In an eccentric orbit, the planet spends more time at aphelion, where it will receive less sunlight. And it speeds through its perihelion, where its insolation is greatest. But the insolation is much stronger at perihelion due to the inverse square relationship. But it does not average out. A planet in a more eccentric orbit will receive more insolation during the course of a single orbit than a planet in a less eccentric or circular orbit with the same semi-major axis. The power point presentation says for Earth it is about 0.2% about a mean. I think they meant to say about 0.2% peak to peak, as Earth's average insolation at high noon when its orbit is closest to round (e=0.005) is about 1367.5 watts / square meter, and when its orbit is at its most elliptical (e=0.067) is about 1370.3 watts / square meter, which is a 0.2% difference between minimum and maximum.

3. Jul 4, 2008

### giann_tee

Yes, you're right the eccentricity changes the global, yearly average. Formulas for insolation that appear here and there are clones from Huybers 2006.
http://www.people.fas.harvard.edu/~phuybers/Doc/HuybersThesis.pdf
(page 48).

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*Eccentricity*

Models appear to differ. Wikipedia seems to be based on a model of Imbrie&Imbrie and it says eccentricity has cycles 413ky, 136ky, 95ky. Even though by just looking the graph is the same, Andre Berger says 400ky, 125ky, 95ky in which case I ... think they all wrongly copied from one another. Laskar 2004 says 405ky cycle here:
http://www.imcce.fr/Equipes/ASD/insola/earth/earth.html
There's a new model http://astrobiology.ucla.edu/OTHER/SSO/SolarSysInt.pdf
but I don't see nice orderly data anywhere.

If Fourier analysis gives different frequencies for these models of motion, how big is the error?

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*New definition for solar constant? or insolation?*

Total solar irradiance just seems to miss me on what the difference is.

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*More precession*

Whether justified or not, I am using
"precession of the axis" 25765y due to which we experience precession of equinoxes in the relative way
"anomalistic precession" 112ky due to which we experience precession of perihelion in the absolute way

The conflicting definitions. Inclination is traditionally defined as angle between the earth's orbital axis and sun's axis. The angle is 7.25 degrees. Defined against invariable plane the angle is up to 3 degrees.
http://en.wikipedia.org/wiki/Earth
http://en.wikipedia.org/wiki/Invariable_plane

If we take the traditional definition of measuring against "plane of sun's equator" then the truth would be that the orbital plane is precessing and due to this we have a 70ky cycle of inclination. Measuring against invariable plane it would be a 100ky quasi-period.
http://muller.lbl.gov/papers/nature.html

The period 112ky for anomalistic precession doesn't relate in obvious way to the 70ky period of yet another precession of orbital plane. For example, according to Huybers, frequencies 1/25765 (precession of Earth's axis of rotation) - 1/70000 = 1/41000 frequency of the change of axial tilt (obliquity). Apparently the numbers are not the problem, but rather witchcraft.

Ok. Now imagine the beautiful National Geographic show on general relativity. They take one curved plane and throw a ball and it circles around the dent creating some nice figure. So, hey general relativity was not divided and subdivided into components of motion (such as precession of perihelion). All is one motion, if it is possible to calculate whole solution.

The point is, why bother to find orbital signals in climate record that originate from approximations?

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*What is FORCING and is it better than voodoo?*

What is the difference between a climate record of some change and a driving cause of climate?

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Do people believe that butterfly effect really exists or is it just a matter of speech?

4. Jul 4, 2008

### giann_tee

I am sorry for bringing this again, it is not about particular author but the whole experience of learning this topic.
http://www.people.fas.harvard.edu/~phuybers/Doc/HuybersThesis.pdf
Page 51, Figure 2-2
"Each orbital parameter is shown over the last two million years (left), along with the associated periodogram (right). For eccentricity (top) variability is, primarily concentrated in bands near 1/400, 1/125, and 1/95KY; obliquity (middle)
variability is concentrated at 1/41KY; and climatic precession (bottom) variability is at 1/19, 1/22, and 1/24KY."

But to me it appears clear that "climatic precession" with one main shortest variability at 21ky is given with parameter of precession
p = e sin (omega)
And clearly it is modulated by eccentricity. Therefore other frequencies must be that of eccentricity!

5. Jul 4, 2008

### giann_tee

The best page is page 88 of the same work. It is about chaos really, how adding an experimental criterion for how to make average of insolation (eg. every other day of the summer in 3pm when energy is greater than... or else bounce) shows how cause and effect are not quite the key issue. What is nonlinear?

6. Jul 4, 2008

### giann_tee

http://syrte.obspm.fr/iau2006/cm06_94_PEWG.pdf
page 16

"The Working Group on Precession and the Ecliptic, recommends:

1. The terms lunisolar precession and planetary precession be replaced by precession of the equator and precession of the ecliptic, respectively.

2. The IAU adopt the P03 precession theory, of Capitaine et al., (2003a, Astron. Astrophys., 412, 567–586) for the precession of the equator (Equations 37) and the precession of the ecliptic (Equations 38); the same paper provides the polynomial developments for the P03 primary angles and a number of derived quantities for use in both the equinox

3. The choice of precession parameters be left to the user.

4. The recommended polynomial coefficients for a number of precession angles are given in Table I of this report, including the P03 expressions set out in Tables 3–5 of Capitaine et al. (2005, Astron. Astrophys.,
432, 355–367), and those of the alternative Fukushima (2003, Astron. J., 126, 494) parameterization; the corresponding matrix representations
are given in Equations 1, 6, 11, and 22.

5. The ecliptic pole should be explicitly defined by the mean orbital angular momentum vector of the Earth–Moon barycenter in the BCRS, and this definition should be explicitly stated to avoid confusion with older definitions.

7. Jul 5, 2008

### giann_tee

Luni-solar precession causes circling of north (and south) celestial pole in about 25765 years (50'',3/year).
Planetary precession causes that circle to be a spiral really, circling around getting little wider and little more narrow over 70000 years, according to an old textbook.

The premise of old model that planetary gravitational influence to the Earth's precession was wrong, so the new model demans terms "precession of equator" and "precession of ecliptic". I await modern document for this!

Obliquity is
1/25765 - 1/70000 = 1/40772
almost 41ky cycle from 22.1o to 24,5o
modulated in amplitude from 0.7° to 2.4°

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Problem with ORBITAL precession.

3 definitions of inclination:

1. angle between planes of orbit and ecliptic (best question for students :-)
clue:
"By definition the inclination of a planet in the solar system is the angle between its orbital plane and that of the Earth. In other cases, for instance a moon orbiting another planet, it is convenient to define the inclination of the moon's orbit as the angle between its orbital plane and the planet's equator."

2. angle between ecliptic and invariant plane
eg. http://en.wikipedia.org/wiki/Invariable_plane

3. orbit and Sun's equator
(http://en.wikipedia.org/wiki/Earth)

What is ecliptic?
http://en.wikipedia.org/wiki/Ecliptic
But look! Mean Sun doesn't even travel ecliptic but follows equator.

"We recommend that the ecliptic pole be explicitly defined by the mean orbital angular
momentum vector of the Earth–Moon barycenter in the Barycentric Celestial Reference
System (BCRS), and explicitly state that this definition is being used to avoid confusion
with previous definitions of the ecliptic."
http://syrte.obspm.fr/iau2006/cm06_94_PEWG.pdf

I would notice that precession of orbit must be an absolute motion! Any ideas?

I don't see articles that quote like wikipedia the 112ky cycle of absolute motion rotation of earth's orbit.

"Projection of inclination vector to ecliptic gives 70ky cycle"
"Projection to invariable plane is 100ky cycle"
http://muller.lbl.gov/papers/nature.html

Whats with that?