Milankovitch cycles

Earth’s movements

The Earth's rotation around its axis, and revolution around the Sun, evolve over time due to gravitational interactions with other bodies in the solar system. The variations are complex, but a few cycles are dominant. Milankovitch studied changes in the orbital eccentricity, obliquity, and precession of the Earth's movements. These changes alter the amount and location of solar radiation reaching the Earth. This is known as solar forcing (an example of radiative forcing). Milankovitch emphasized the changes experienced at 65° north due to the great amount of land at that latitude. Land masses change temperature more quickly than oceans, even though water is easier to heat (has a higher heat capacity) because of the mixing of surface and deep water.

Orbital shape (eccentricity)

The Earth's orbit is an ellipse. Eccentricity measures the departure of this ellipse from circularity. The shape of the Earth's orbit varies between nearly circular (with the lowest eccentricity of 0.000055) and mildly elliptical (highest eccentricity of 0.0679) Its geometric or logarithmic mean is 0.0019. The major component of these variations occurs with a period of 413,000 years (eccentricity variation of ±0.012). Other components have 95,000-year and 125,000-year cycles (with a beat period of 400,000 years). They loosely combine into a 100,000-year cycle (variation of −0.03 to +0.02). The present eccentricity is 0.017 and decreasing.

Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn. However, the semi-major axis of the orbital ellipse remains unchanged; according to perturbation theory, which computes the evolution of the orbit, the semi-major axis is invariant. The orbital period (the length of a sidereal year) is also invariant, because according to Kepler's third law, it is determined by the semi-major axis.

The semi-major axis is a constant. Therefore, when Earth's orbit becomes more eccentric, the semi-minor axis shortens. This increases the magnitude of seasonal changes.

The relative increase in solar irradiation at closest approach to the Sun (perihelion) compared to the irradiation at the furthest distance (aphelion) is slightly larger than four times the eccentricity. For Earth's current orbital eccentricity, incoming solar radiation varies by about 6.8%, while the distance from the Sun currently varies by only 3.4% (5.1 million km). Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its most eccentric, the amount of solar radiation at perihelion will be about 23% more than at aphelion. However, the Earth's eccentricity is always so small that the variation in solar irradiation is a minor factor in seasonal climate variation, compared to axial tilt and even compared to the relative ease of heating the larger land masses of the northern hemisphere.

The seasons are quadrants of the Earth's orbit, marked by the two solstices and the two equinoxes. Kepler's second law states that a body in orbit traces equal areas over equal times; its orbital velocity is highest around perihelion and lowest around aphelion. The Earth spends less time near perihelion and more time near aphelion. This means that the lengths of the seasons vary.

Perihelion currently occurs around January 3, so the Earth's greater velocity shortens winter and autumn in the northern hemisphere. Summer in the northern hemisphere is 4.66 days longer than winter, and spring is 2.9 days longer than autumn.

Greater eccentricity increases the variation in the Earth's orbital velocity. However, currently, the Earth's orbit is becoming less eccentric (more nearly circular). This will make the seasons more similar in length.

Axial tilt (obliquity)

The angle of the Earth's axial tilt with respect to the orbital plane (the obliquity of the ecliptic) varies between 22.1° and 24.5°, over a cycle of about 41,000 years. The current tilt is 23.44°, roughly halfway between its extreme values. The tilt last reached its maximum in 8,700 BCE. It is now in the decreasing phase of its cycle, and will reach its minimum around the year 11,800 CE.

Increased tilt increases the amplitude of the seasonal cycle in insolation, providing more solar radiation in each hemisphere's summer and less in winter. However, these effects are not uniform everywhere on the Earth's surface. Increased tilt increases the total annual solar radiation at higher latitudes, and decreases the total closer to the equator.

The current trend of decreasing tilt, by itself, will promote milder seasons (warmer winters and colder summers), as well as an overall cooling trend. Because most of the planet's snow and ice lies at high latitude, decreasing tilt may encourage the onset of an ice age for two reasons: There is less overall summer insolation, and also less insolation at higher latitudes, which melts less of the previous winter's snow and ice.

Axial precession

Axial precession is the trend in the direction of the Earth's axis of rotation relative to the fixed stars, with a period of 25,771.5 years. This motion means that eventually Polaris will no longer be the north pole star. It is caused by the tidal forces exerted by the Sun and the Moon on the solid Earth; both contribute roughly equally to this effect.

Currently, perihelion occurs during the southern hemisphere's summer. This means that solar radiation due to (1) axial tilt aiming the southern hemisphere toward the Sun and (2) the Earth's proximity to the Sun, both reach maximum during the summer and both reach minimum during the winter. Their effects on heating are additive, which means that seasonal variation in irradiation of the southern hemisphere is more extreme. In the northern hemisphere, these two factors reach maximum at opposite times of the year: The north is tilted toward the Sun when the Earth is furthest from the Sun. The two forces work in opposite directions, resulting in less extreme variation.

In about 13,000 years, the north pole will be tilted toward the Sun when the Earth is at perihelion. Axial tilt and orbital eccentricity will both contribute their maximum increase in solar radiation during the northern hemisphere's summer. Axial precession will promote more extreme variation in irradiation of the northern hemisphere and less extreme variation in the south.

When the Earth's axis is aligned such that aphelion and perihelion occur near the equinoxes, axial tilt will not be aligned with or against eccentricity.

Apsidal precession

In addition, the orbital ellipse itself precesses in space, in an irregular fashion, completing a full cycle every 112,000 years relative to the fixed stars. Apsidal precession occurs in the plane of the ecliptic and alters the orientation of the Earth's orbit relative to the ecliptic. This happens primarily as a result of interactions with Jupiter and Saturn. Smaller contributions are also made by the sun's oblateness and by the effects of general relativity that are well known for Mercury.

Apsidal precession combines with the 25,771.5-year cycle of axial precession (see above) to vary the position in the year that the Earth reaches perihelion. Apsidal precession shortens this period to 23,000 years on average (varying between 20,800 and 29,000 years).

As the orientation of Earth's orbit changes, each season will gradually start earlier in the year. Precession means the Earth's nonuniform motion (see above) will affect different seasons. Winter, for instance, will be in a different section of the orbit. When the Earth's apsides are aligned with the equinoxes, the length of spring and summer combined will equal that of autumn and winter. When they are aligned with the solstices, the difference in the length of these seasons will be greatest.

Orbital inclination

The inclination of Earth's orbit drifts up and down relative to its present orbit. This three-dimensional movement is known as "precession of the ecliptic" or "planetary precession". Earth's current inclination is 1.57°.

Milankovitch did not study precession. It was discovered more recently and measured, relative to Earth's orbit, to have a period of about 70,000 years.

However, when measured independently of Earth's orbit, but relative to the invariable plane (the plane that represents the angular momentum of the Solar System, approximately the orbital plane of Jupiter), precession has a period of about 100,000 years. This period is very similar to the 100,000-year eccentricity period. Both periods closely match the 100,000-year pattern of glacial events.

Problems

Artifacts taken from the Earth have been studied to infer the cycles of past climate. These fit so well with the orbital periods that they support Milankovitch's hypothesis that variations in the Earth's orbit influence climate. However, the fit is not perfect, and problems remain reconciling theory with observations.

100,000-year problem

Of all the orbital cycles, Milankovitch believed that obliquity had the greatest effect on climate, and that it did so by varying the summer insolation in northern high latitudes. Therefore, he deduced a 41,000-year period for ice ages. However, subsequent research has shown that ice age cycles of the Quaternary glaciation over the last million years have been at a 100,000-year period, which matches the eccentricity cycle.

Various explanations for this discrepancy have been proposed, including frequency modulation or various feedbacks (from carbon dioxide, cosmic rays, or from ice sheet dynamics). Some models can 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.

Jung-Eun Lee of Brown University proposes that precession changes the amount of energy that Earth absorbs, because the southern hemisphere's greater ability to grow sea ice reflects more energy away from Earth. Moreover, Lee says, "Precession only matters when eccentricity is large. That's why we see a stronger 100,000-year pace than a 21,000-year pace."

Some have argued that the length of the climate record is insufficient to establish a statistically significant relationship between climate and eccentricity variations.

The transition problem

In fact, from 1–3 million years ago, climate cycles did match the 41,000-year cycle in obliquity. After 1 million years ago, this switched to the 100,000-year cycle matching eccentricity. The transition problem refers to the need to explain what changed 1 million years ago.

The unsplit peak problem

Even the well-dated climate records of the last million years do not exactly match the shape of the eccentricity curve. Eccentricity has component cycles of 95,000 and 125,000 years. However, some researchers say the records do not show these peaks, but only show a single cycle of 100,000 years.

Stage 5 problem

Deep-sea core samples show that the interglacial interval known as marine isotope stage 5 began 130,000 years ago. This is 10,000 years before the solar forcing that the Milankovitch hypothesis predicts. (This is also known as the causality problem, because the effect precedes the putative cause.)

Effect exceeds cause

Artifacts show that the variation in Earth's climate is much more extreme than the variation in the intensity of solar radiation calculated as the Earth's orbit evolves. If orbital forcing causes climate change, science needs to explain why the observed effect is amplified compared to the theoretical effect.

Some climate systems exhibit amplification (positive feedback) and damping responses (negative feedback). An example of amplification would be if, with the land masses around 65° north covered in year-round ice, solar energy were reflected away. Amplification would mean that an ice age induces changes that impede orbital forcing from ending the ice age.

The Earth's current orbital inclination is 1.57° (see above). Earth presently moves through the invariable plane around January 9 and July 9. At these times, there is an increase in meteors and noctilucent clouds. If this is because there is a disk of dust and debris in the invariable plane, then when the Earth's orbital inclination is near 0° and it is orbiting through this dust, materials could be accreted into the atmosphere. This process could explain the narrowness of the 100,000-year climate cycle.

Present and future conditions

Since orbital variations are predictable, any model that relates orbital variations to climate can be run forward to predict future climate.

Astronomical calculations show that 65° N summer insolation should increase gradually over the next 25,000 years. Earth's orbit will become less eccentric for about the next 100,000 years, so changes in 65° N summer insolation will be dominated by changes in obliquity. No declines in this insolation sufficient to cause a glacial period are expected in the next 50,000 years.

An often-cited 1980 orbital model by Imbrie and Imbrie predicted "that the long-term cooling trend that began some 6,000 years ago will continue for the next 23,000 years." More recent work suggests that the current warm climate may last another 50,000 years.

However, the mechanism by which orbital forcing influences climate is not well understood nor definitive:

1. Earth is not homogenous. Milankovitch did not relate Earth's ice ages to the total amount of solar radiation (insolation) reaching Earth but to the insolation striking 65° N in summer, due to the relative ease of heating the larger land masses of the northern hemisphere. Later studies have suggested that insolation hitting ice would simply be reflected away.
2. Earth is not inert. Geology affects climate; not just from the heat of the Earth's core, but from changes to the atmosphere caused by volcanic eruptions. Even the configuration of land masses and ice masses changes over time due to continental drift.
3. The flourishing and industrial activity of humankind may affect climate (may contribute anthropogenic effects) in ways not predicted by orbital models. Many studies have concluded that detectable increases in greenhouse gas in the 20th and 21st centuries would trap energy and result in a warmer climate. A previous theory was that industrial particulate pollution of the atmosphere would block solar radiation and result in cooling.
4. The article Future of earth presents a variety of infrequent events, such as collisions of bodies within the solar system and encounters with bodies outside the solar system, with the potential to make past or future climate deviate from a mathematical model of orbital forcing.

Effects beyond Earth

Other bodies in the Solar System undergo geological effects associated with orbital fluctuations like the Milankovitch cycles, though not as intense or complex as the Earth's cycles. These cycles cause the movement of elements in the solid state:

Mars has no moon large enough to stabilize its obliquity, which has varied from 10 to 70 degrees. This would explain recent observations of its surface compared to evidence of different conditions in its past, such as the extent of its polar caps.

Saturn's moon Titan has a ~60,000-year cycle that changes the location of the methane lakes.

Neptune's moon Triton has a similar variation to Titan with respect to migration of solid nitrogen deposits over long time scales.

Scientists using computer models to study extreme axial tilts have concluded that high obliquity would cause climate extremes that would threaten Earth-like life. They noted that high obliquity would not likely sterilize a planet completely, but would make it harder for warm-blooded, land-based life to thrive. Although the obliquity they studied is more extreme than Earth ever experiences, there are scenarios 1.5 to 4.5 billion years from now, as the Moon's stabilizing effect lessens, where obliquity could leave its current range and the poles could eventually point almost directly at the Sun.