Milankovitch cycles

Milankovitch cycles are the collective effect of changes in the Earth's movements upon its climate, named after Serbian civil engineer and mathematician Milutin Milanković. 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 Earth's tilt relative to the Sun changes between 21.5 degrees to 24.5 degrees and back again on a 41,000 year cycle. The Earth's axis today is tilted 23.44 degrees relative to the normal to the plane of the ecliptic.

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 – see Ice age for more discussion. Various feedbacks (from CO₂, or from ice sheet dynamics) are invoked to explain this discrepancy.

Milankovitch-like theories were advanced by Joseph Adhemar, James Croll, Milutin Milanković 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 Hayes, Imbrie and Shackleton "Variations in the earths orbit: pacemaker of the ice ages" in Science, 1976, did the theory attain its present state.

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.

Orbital shape

The eccentricity, or 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. 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.

Axial tilt

The Earth's spin wobbles, causing a slow 2.4° change in the tilt of the axis (obliquity). This precession of the axis follows a cycle of approximately 40,000 years. When the tilt increases to 24.5 degrees, the winters become colder and summers are warmer than at 22.1 degrees, when with less tilt the winters are milder and summers are cooler.

Presently the Earth is tilted at 23.44 degrees from its orbital plane.

Cooler summers are suspected of encouraging the start of an ice age due to their melting less of the previous winter's ice and snow.

Axial orientation

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 25,800 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.

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 mesospheric clouds.

Problems

There are several difficulties in reconciling theory with observations.

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.

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.

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.

Effect exceeds cause

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).

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.

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.

Present conditions

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

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.

References

External links

Milankovitch Cycles and Glaciation
The Milankovitch band
Some history of the adoption of the Milankovitch hypothesis (and an alternative)
More detail on orbital obliquity also matching climate patterns
Graph of variation in insolation Note 20,000 year, 100,000 year, and 400,000 year cycles are clearly visible.
The Seasons
This review article discusses cycles and large-scale changes in the global climate during the Cenozoic Era.
This article shows the influence of Milankovitch cyles on climate variation during the late Oligocene and early Miocene, around 20-25 million years ago.
This thesis has a good introduction on Milankovitch cycles. It nicely describes an indirect influence of Milankovitch orbital variations on rainfall and other climate factors, using results from geological deposits as well as climate simulations. It focuses on the region around the Mediterranean Sea.
The NOAA page on Climate Forcing Data includes (calculated) data on orbital variations over the last 50 million years and for the coming 20 million years.
The orbital simulations by Varadi, Ghil and Runnegar (2003) provide another, slightly different series for orbital eccentricity, and also a series for orbital inclination

Ice ages | History of climate | Climate forcing agents

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