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Friday, July 22, 2011

Chris Colose: Milankovitch Cycles

Milankovitch Cycles

by Chris Colose, Skeptical Science, July 22, 2011

This post is intended to serve as a supplement to SteveBrown’s series on the Last Interglacial, beginning here.
Changes in the Earth's orbit brought about by astronomical variations have a strong impact on Earth’s climate.  They serve as the pacemaker for the glacial-interglacial cycles over the Quaternary (roughly the last two and a half million years of Earth's history), and provide a strong framework for understanding  the evolution of the climate even over the Holocene (the last 10,000 years, beginiing near the termination of the last glacial period).   Milankovitch cycles are insufficient to explain the full range of Quaternary climate change, which also requires greenhouse gas and albedo variations, but they are a primary forcing that must be accounted for.
Orbital variations are also likely to be a generic feature of other planets, with strong implications for the fate of planetary atmospheres (for example, understanding the potential for habitability on other systems).  This post will serve as a guide to what these so-called Milankovitch cycles are, how they work, and highlight some "to-be-done" work that remains.
Milankovitch cycles are classically divided into the precession, the obliquity, and the eccentricity cycles.  These cycles modulate the solar insolation (i.e., the total energy the planet receives from the sun at the top of the atmosphere) or its geographic distribution.  For example, Figure 1 shows the solar insolation change at various latitudes in June over the last one million years.
Figure 1. June (daily averaged) insolation (W/m2) over the last 1,000,000 years (0 = 1950) at blue = 90° N, red = 60° N, green = 30° N, purple = Equator, light blue = 30° S, and orange = 60° S.  [Data from Berger, A., and Loutre, M. F. (1991). Insolation values for the climate of the last 10 million years, Quaternary Sciences Review, Vol. 10, No. 4, pp. 297-317.]
Each of the relevant Milankovitch cycles are described below: 
Eccentricity:  Eccentricity is a measure of how circular a curve is, with e=0 describing a circle, and e=1 describing a parabola. The orbital eccentricity therefore characterizes how circular or egg-shaped a planet’s orbit around the sun is (Fig. 2).  The timescale of Earth’s eccentricity variation is ~400,000 years with a superimposed 100,000 year cycle.  There is also an unimportant 2.1 million year cycle.
Figure 2. Circular and eccentric orbit.  
Because of eccentricity, the distance of the Earth at perihelion (point closest to sun) is slightly different than the distance to aphelion (point farthest from sun).  
Earth’s eccentricity is very moderate, never exceeding approximately 0.07 (almost a perfect circle).  The modern day eccentricity is 0.016, and as a result, the solar insolation that hits Earth varies by ~6.4% over the course of a year.  There are some more extreme examples: Pluto’s eccentricity is about 0.25, higher than any other planet in our solar system. HD 20782b, a newly discovered exo-planet almost 120 light years away has an eccentricity on the extreme end of ~0.97 (similar to Halley's Comet). Eccentricity can introduce very large "distance seasons" on a planet, although this also depends on the thermal inertia, which is large enough on a body with oceans (or a dense atmosphere) to moderate the changes between perihelion and aphelion.  As we will see, Earth's seasonal variations are primarily deterimined by its axial tilt rather than its eccentricity.
Eccentricity is the only Milankovitch cycle that alters the annual mean global solar insolation (i.e., the total energy the planet receives from the sun at the top of the atmosphere).  For the mathematically inclined, the annually-averaged insolation changes in proportion to 1/(1-e2)0.5, so the solar insolation increases with higher eccentricity. This is a very small effect though, amounting to less than 0.2% change in solar insolation, equivalent to a radiative forcing of ~0.45 W/m2 (assuming present-day albedo). This is much less than the total anthropogenic forcing over the 20th century. However, eccentircity does modulate the precessional cycle, as we shall see.
Obliquity:  Obliquity describes how tilted a planet’s axis is (Fig. 3 shows the obliquity of eight planets, plus Pluto which is labeled as a planet).   The tilt of the Earth is ultimately what allows for the existence of seasons, since the Northern Hemisphere is pointed toward the sun in the boreal summer and away from the sun in the boreal winter.  The tilt of Earth’s axis (in other words, the angle between the spin–axis and a line perpendicular to the orbital plane) varies between about 22° and 25° (currently 23.5°) over a period of nearly 41,000 years, driving changes in the distribution of sunlight between the equator and high latitudes (with more tilt implying more sunlight at high latitudes, and less at lower latitudes; therefore, more oblique orbits favor deglaciation on Earth). 
Uranus is at the extreme end with a tilt of ~98 degrees; this would induce a very different structure of solar heating (where at certain times the North or South pole would be receiving most of the sunlight, and allow for a large migration of the solar “hotspot” over the course of one Uranian year); this should drive a different atmospheric circulation than on Earth. For highly oblique planets outside our solar system that have a surface, continents at the polar regions would be alternatively cooked and frozen, while the tropical latitudes would have two summers and two winters. At large obliquities (greater than about 54 degrees), the poles receive more annual mean insolation than the planetary equator (Ward, 1974), and thus the annual mean energy transport by the circulation would be equatorward.
Figure 3. Obliquity of the planets and the direction of spin (note that Venus rotates clockwise, in a retrograde fashion). Taken from Click image to enlarge.
Precession: Precession does not describe how tilted the Earth’s axis is but rather the direction of its axis.  This changes what star is the “North Star” over time (today it is Polaris, but near the end of the last deglaciation it was Vega), and as described below, governs the timing of the seasons. This is illustrated in Figure 4 (a and b) below.

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