Outline

Earth Sun Geometry

Solar Insolation Effects

• Obliquity

• Eccentricity

• Precession

• Putting it all together: Insolation

Obliquity

Obliquity refers to the tilt of the Earth's axis. Over time, the angle of Earth's tilt varies between 22.2 and 24.5 degrees (currently the tilt is 23.5 and decreasing). These variations, discovered by French astronomer Urbain Leverrier in the 1840s, are caused by the gravitational pull of large planets, including Jupiter. Earth's obliquity varies cyclically with a period of 41,000 years.

See the obliquity cycle animated! The tilt is exaggerated by about 10x in this animation. However, the phasing is accurate.

What is the effect of variations in obliquity? Changes in obliquity amplify or suppress the seasons. A larger tilt means that the summer hemisphere will receive more solar radiation, while the winter hemisphere will receive less.

Eccentricity

The Earth's orbit around the Sun is described by its eccentricity. Eccentricity is expressed mathematically as:

e = (a2 - b2)1/2  / a

where a and b are the major and minor axes of the ellipse, respectively. What is the eccentricity of a circular orbit? Earth's eccentricity has varied over time between values of 0.005 and 0.0607 (currently the eccentricity is 0.0167). Eccentricity has a period of about 100,000 years (see below).

Changes in insolation due to the eccentricity cycle are very slight, at most 0.2%. Eccentricity is important because it modulates the amplitude of the precession cycle (see below).

See the eccentricity cycle animated! The eccentricity is exaggerated. Without this exaggeration, the changes would be nearly imperceptible.

Precession of the equinoxes

The position of the solstices and equinoxes are not fixed. Instead, they shift with respect to Earth's eccentric orbit and with respect to aphelion (point in Earth's orbit farthest from Sun) and perihelion (point in Earth's orbit closest to the Sun).

The best way to imagine the axial precession is to think of the Earth as a spinning top. As a spinning top slows, it begins to wobble. Similarly, the Earth has a slow wobbling motion, called the axial precession. This wobbling motion does not affect the tilt angle of the Earth, but the direction in which the Earth is tilting (see the diagram above). The axial precession is caused by the gravitational pull of the Sun and the Moon on the Earth's equatorial bulge.

The axial precession causes the solstices and equinoxes to move around Earth's orbit, completing a full orbit around the Sun every 25,700.

A second motion also affects the position of the equinoxes and solstices and is known as the precession of the ellipse. This motion describes the rotation of the Earth's elliptical orbit (see below). This motion is even slower than the wobbling motion of the axial precession.

The combined effect of the axial precession and precession of the ellipse is referred to as the precessional cycle with a cyclicity of 3,000 and 19,000 years (for an average of 21,700 years). See the precessional cycle animated! This animation demonstrates the changing winter time position of the Earth in its orbit around the Sun.

(above figure from http://en.wikipedia.org/wiki/Precession)

The complete effect of the precession on solar radiation must take into account both the eccentricity of the Earth's orbit and the precession. Compare the unmodulated (above) and modulated (below) precessional cycles.

What is the effect of the precessional cycle? The precession cycle modifies where the equinoxes and solstices occur in the Earth's, influencing the seasonal cycle. Currently, the Earth's axis points toward Polaris. In 12,000 years, the axis will be tilted toward Vega, and the orbital positions at which winter and summer solstices occur will be reversed. Consequently, the Northern hemisphere will experience winter near aphelion and summer will occur near perihelion. Thus, seasonal contrasts will be greater than they are today.

Insolation changes on Earth

The diagram below shows the long-term June and December insolation variations. Changes in low- and middle-latitude insolation are the result of precession. Solar insolation changes at high middle-latitudes are due predominantly to the obliquity cycle.

Figure. June and December insolation at various latitudes (from Earth's Climate Past and Future by W.F. Ruddiman).

Also note that the phasing of the insolation maxima and minima differ for the obliquity and precession cycles. The tilt causes in-phase changes in insolation. If the tilt increases, both hemispheres receives more insolation during summer and less during winter (see the top panel below). In contrast, precession causes out-of-phase changes in insolation. When the Northern Hemisphere summer solstice is at aphelion (as it is now), the summer insolation is at a minima. On the other hand, the Southern Hemisphere summer solistice is at perihelion and summer insolation is at a maxima (see the bottom panel).