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Milankovitch cycles create changes in the Earth's climate.


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Milankovitch cycles are the collective effect of changes in the Earth's movements upon its climate. Milankovitch cycles are named after Serbian civil engineer and mathematician Milutin Milankovic. The eccentricity, axial tilt, and precession of the Earth's orbit vary in several patterns, resulting in 100,000 year ice age cycles of the Quaternary glaciation over the last few million years. The Earth's axis completes one full cycle of precession approximately every 26,000 years. At the same time, the elliptical orbit rotates, more slowly, leading to a 22,000 year cycle in the equinoxes. In addition, the angle between Earth's rotational axis and the normal to the plane of its orbit changes from 21.5 degrees to 24.5 degrees and back again on a 41,000 year cycle. Presently, this angle is 23.44 degrees.

Milankovitch cycles.
Milankovitch cycles.

The Milankovitch theory of climate change is not perfectly worked out; in particular, the largest response is at the 100,000 year timescale, but the forcing is apparently small at this scale, in regards to the ice ages, Various feedbacks (from carbon dioxide, or from ice sheet dynamics) are invoked to explain this discrepancy.

Milankovitch-like theories were advanced by Joseph Adhemar, James Croll, Milutin Milankovic and others, but verification was difficult due to the absence of reliably dated evidence and doubts as to exactly which periods were important. Not until the advent of deep-ocean cores and the seminal paper by Hays, Imbrie and Shackleton "Variations in the earths orbit: pacemaker of the ice ages" in Science, 1976, did the theory attain its present state.

Milankovitch cycles Earth’s movements.

As the Earth spins around its axis and orbits around the Sun, several quasi-periodic variations occur. Although the curves have a large number of sinusoidal components, a few components are dominant. Milankovitch studied changes in the eccentricity, obliquity, and precession of Earth's movements. Such changes in movement and orientation change the amount and location of solar radiation reaching the Earth. This is known as solar forcing (an example of radiative forcing). Changes near the north polar area are considered important due to the large amount of land, which reacts to such changes more quickly than the oceans do.

Milankovitch cycles on Earth's orbital shape.

Earth orbit.
Earth Circular orbit, no eccentricity.
Orbit with 0.5 eccentricity.
Orbit with 0.5 eccentricity.

The Earth's orbit is an ellipse. The eccentricity is a measure of the departure of this ellipse from circularity. The shape of the Earth's orbit varies from being nearly circular (low eccentricity of 0.005) to being mildly elliptical (high eccentricity of 0.058) and has a mean eccentricity of 0.028. The major component of these variations occurs on a period of 413,000 years (eccentricity variation of 0.012). A number of other terms vary between 95,000 and 136,000 years, and loosely combine into a 100,000 year cycle (variation of -0.03 to +0.02). The present eccentricity is 0.017.

If the Earth were the only planet orbiting our Sun, the eccentricity of its orbit would not vary in time. The Earth's eccentricity varies primarily due to interactions with the gravitational fields of Jupiter and Saturn. As the eccentricity of the orbit evolves, the Semi-major axis of the orbital ellipse remains unchanged. From the perspective of the perturbation theory used in celestial mechanics to compute the evolution of the orbit, the semi-major axis is an adiabatic invariant. Following the Third of Kepler's laws of planetary motion, the period of the orbit is determined by the semi-major axis. It follows that the Earth's orbital period, the length of a Sidereal year, also remains unchanged as the orbit evolves.

Currently the difference between closest approach to the Sun (perihelion) and furthest distance (aphelion) is only 3.4% (5.1 million km). This difference amounts to about a 6.8% increase in incoming solar radiation. Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its most highly elliptical, the amount of solar radiation at perihelion is about 23% greater than at aphelion. This difference is roughly 4 times the value of the eccentricity.

Season (Northern Hemisphere) Durations
data from http://aa.usno.navy.mil/data/docs/EarthSeasons.html - United States Naval Obervatory
YearDate: GMTSeason Duration
2005 Winter Solstice 12/21/2005 18:35 88.99 days
2006 Spring Equinox 3/20/2006 18:26 92.75 days
2006 Summer Solstice 6/21/2006 12:26 93.65 days
2006 Fall Equinox 9/23/2006 4:03 89.85 days
2006 Winter Solstice 12/22/2006 0:22 88.99 days
2007 Spring Equinox 3/21/2007 0:07  

Orbital mechanics require that the length of the seasons be proportional to the areas of the seasonal quadrants, so when the eccentricity is extreme, the seasons on the far side of the orbit can be substantially longer in duration. Today, when fall and winter occur at closest approach, the earth is moving at its maximum velocity and therefore fall and winter are slightly shorter than spring and summer. Today, summer on the northern hemisphere is 4.66 days longer than winter and spring is 2.9 days longer than fall.

Axial tilt.

Earth's obliquity.
22.1-24.5º range of Earth's obliquity.

The Earth's rotation axis wobbles, causing a slow 2.4º change in the tilt of the axis (obliquity) with respect to the plane of the Earth's orbit. The obliquity variations are roughly periodic, with a period of approximately 40,000 years. When the obliquity increases, the amplitude of the seasonal cycle in insolation increases, with summers in both hemispheres receiving more radiative flux from the Sun, and the winters less radiative flux. As a result, it is assumed that the winters become colder and summers warmer.

But these changes of opposite sign in the summer and winter are not of the same magnitude. The annual mean insolation increases in high latitudes with increasing obliquity, while lower latitudes experience a reduction in insolation. Cooler summers are suspected of encouraging the start of an ice age by melting less of the previous winter's ice and snow. So it can be argued that lower obliquity favors ice ages both because of the mean insolation reduction in high latitudes as well as the additional reduction in summer insolation.

Presently the Earth is tilted at 23.44 degrees from its orbital plane, roughly half way between its extreme values.

Milankovitch cycles and the Earth's axial orientation.

Precessional movement.
Precessional movement.

Precession of the equinoxes is the change in the direction of the Earth's axis of rotation relative to the Sun at the time of perihelion and aphelion. The Earth goes through one complete precession cycle in a period of approximately 20,000 years. Two effects contribute to the determination of this time scale. The axis of rotation itself rotates like a top around a line perpendicular to the orbital plane, with a period of roughly 26,000 years. This gyroscopic motion is due to the tidal forces exerted by the sun and the moon on the solid Earth, associated with the fact that the Earth is not a perfect sphere but has an equatorial bulge. The sun and moon contribute roughly equally to this effect. In addition, the orbital ellipse itself precesses in space, primarily as a result of interactions with Jupiter and Saturn. This orbital precession is in the opposite sense to the gyroscopic motion of the axis of rotation, shortening the period of the precession of the equinoxes with respect to the perihelion from 26,000 to 20,000 years.

When the axis is aligned so it points toward the Sun during perihelion, one polar hemisphere will have a greater difference between the seasons while the other hemisphere will have milder seasons. The hemisphere which is in summer at perihelion will receive much of the corresponding increase in solar radiation, but that same hemisphere will be in winter at aphelion and have a colder winter. The other hemisphere will have a relatively warmer winter and cooler summer.

When the Earth's axis is aligned such that aphelion and perihelion occur during spring and autumn, the Northern and Southern Hemispheres will have similar contrasts in the seasons.

At present perihelion occurs during the Southern Hemisphere's summer, and aphelion is reached during the southern winter. Thus the Southern Hemisphere seasons should tend to be somewhat more extreme than the Northern Hemisphere seasons.

Milankovitch cycles orbital inclination.

The inclination of Earth's orbit drifts up and down relative to its present orbit with a cycle having a period of about 70,000 years. Milankovitch did not study this three-dimensional movement.

More recent researchers noted this drift and that the orbit also moves relative to the orbits of the other planets. The invariable plane, the plane that represents the angular momentum of the solar system, is approximately the orbital plane of Jupiter. The inclination of the Earth's orbit has a 100,000 year cycle relative to the invariable plane. This 100,000 year cycle closely matches the 100,000 year pattern of ice ages.

It has been proposed that a disk of dust and other debris is in the invariable plane, and this affects the Earth's climate through several possible means. The Earth presently moves through this plane around January 9 and July 9, when there is an increase in radar-detected meteors and meteor-related noctilucent clouds.

Milankovitch cycles problems.

Because the observed periodicities of climate fit so well with the orbital periods, the orbital theory has overwhelming support. Nonetheless, there are several difficulties in reconciling theory with observations.

Milankovitch cycles 100 ky problem.

The 100,000 year problem is that the eccentricity variations have a significantly smaller impact on solar forcing than precession or obliquity and hence might be expected to produce the weakest effects. However, observations show that during the last 1 million years, the strongest climate signal is the 100,000 year cycle. In addition, despite the relatively large 100,000 year cycle, some have argued that the length of the climate record is insufficient to establish a statistically significant relationship between climate and eccentricity variations. Some models can however reproduce the 100,000 year cycles as a result of non-linear interactions between small changes in the Earth's orbit and internal oscillations of the climate system.

Milankovitch cycles 400 ky problem.

The 400,000 year problem is that the eccentricity variations have a strong 400,000 year cycle. That cycle is only clearly present in climate records older than the last million years. If the 100ky variations are having such a strong effect, the 400ky variations might also be expected to be apparent. This is also known as the stage 11 problem, after the interglacial in marine isotopic stage 11 which would be unexpected if the 400,000 year cycle has an impact on climate. The relative absence of this periodicity in the marine isotopic record may be due, at least in part, to the response times of the climate system components involved - in particular, the carbon cycle.

Milankovitch cycles stage 5 problem.

The stage 5 problem refers to the timing of the penultimate interglacial (in marine isotopic stage 5) which appears to have begun 10 thousand years in advance of the solar forcing hypothesized to have been causing it. This is also referred to as the causality problem.

Milankovitch cycles effect exceeds cause.

Antarctica research station.
420,000 years of ice core data from Vostok, Antarctica research station.

The effects of these variations are primarily believed to be due to variations in the intensity of solar radiation upon various parts of the globe. Observations show climate behaviour is much more intense than the calculated variations. Various internal characteristics of climate systems are believed to be sensitive to the insolation changes, causing amplification (positive feedback) and damping responses (negative feedback).

Milankovitch cycle and the unsplit peak problem.

The unsplit peak problem refers to the fact that eccentricity has cleanly resolved variations at both 95 and 125 ky frequencies. A sufficiently long, well-dated record of climate change should be able to resolve both frequencies, but some researchers interpret climate records of the last million years as showing only a single spectral peak at 100 kyr periodicity. It is debatable whether the quality of existing data ought to be sufficient to resolve both frequencies over the last million years.

Milankovitch cycle and the transition problem.

The transition problem refers to the change in the frequency of climate variations 1 million years ago. From 1-3 million years, climate had a dominant mode matching the 41 ky cycle in obliquity. After 1 million years ago, this changed to a 100 ky variation matching eccentricity. No reason for this change has been established.

Milankovitch cycles present conditions.

solar radiation.
solar radiation.

The amount of solar radiation (insolation) in the Northern Hemisphere at 65ºN seems to be related to occurrence of an ice age. Astronomical calculations show that 65ºN summer insolation should increase gradually over the next 25,000 years, and that no declines in 65ºN summer insolation sufficient to cause an ice age are expected in the next 50,000 - 100,000 years.

As mentioned above, at present perihelion occurs during the Southern Hemisphere's summer, and aphelion during the southern winter. Thus the Southern Hemisphere seasons should tend to be somewhat more extreme than the Northern Hemisphere seasons. The relatively low eccentricity of the present orbit results in a 6.8% difference in the amount of solar radiation during summer in the two hemispheres.

Milankovitch cycles and the future.

Since orbital variations are predictable, if one has a model that relates orbital variations to climate, it is possible to run such a model forward to "predict" future climate. Two caveats are necessary: firstly, that anthropogenic effects (global warming) are likely to exert a larger influence, at least over the short term; and secondly that since the mechanism by which orbital forcing affects climate is not well understood, there is no very good model relating climate to orbital forcing.

An often-cited 1980 study by Imbrie and Imbrie determined that "Ignoring anthropogenic and other possible sources of variation acting at frequencies higher than one cycle per 19,000 years, this model predicts that the long-term cooling trend which began some 6,000 years ago will continue for the next 23,000 years."

More recent work by Berger and Loutre suggests that the current warm climate may last another 50,000 years.




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