The orbital and spin motions of the earth can be summarized by several numbers called orbital parameters. The values of the orbital parameters vary at the time scale of one thousand to ten thousand years due to gravity of other planets such as Jupiter. Accordingly, the amount and distribution of solar radiation arriving at the earth (here denoted as insolation) varies. By theoretical calculation based on celestial mechanics, past variation of orbital parameters are precisely known, at least within the Quaternary time period. Therefore, this is the most well known external factor of climatic variation in the Quaternary. The variation of orbital parameters that is relevant to insolation can be sorted into the following three components. Milankovitch (1930) computed variation of insolation including all of the three factors, and discussed it as a causative factor of glacial cycles. To commemorate his achievement, this type of variation of insolation as an external factor of climatic variation is called Milankovitch forcing.
Variation of the eccentricity of the orbit
Eccentricity is one of the measures of how different the shape of an ellipse is from a circle.
In the Quaternary times,
the eccentricity of the orbit of the earth varies between 0 and 0.07
with periods of 100 thousand years and 410 thousand years
(Fig. 4.2-2a).
When the eccentricity is larger, the global annual mean insolation is smaller,
as if solar luminosity decreased.
This effect, however, is merely of the order of one thousands of insolation itself, because it is proportional to the square of the eccentricity.
Eccentricity plays a larger role as the envelope of the effect of the season of perihelion (to be discussed below).
Variation of the season of perihelion
The direction to which the spin axis is tilted with respect to the axis of orbital motion (the line normal to the orbital plane) changes by an effect called precession.
On the other hand, the direction of perihelion (the point on the orbit where the earth is nearest to the sun) also changes.
As the combination of these, the season of perihelion varies with a period
approximately twenty thousand years.
Though the season of perihelion does not affect annual mean insolation,
it changes seasonal insolation.
For example, the perihelion exists in the northern hemisphere winter at present.
Accordingly, the summer insolation of the northern hemisphere is smaller than its long-term mean, and that of the southern hemisphere is larger
(Fig. 4.2-3a).
The situation was opposite ten thousand years ago.
The time series of a quantity representing this effect (Fig. 4.2-2b) shows,
not only the periodicity of approximately twenty thousand years,
but also its amplitude modulation like that of AM radio.
The envelope of the curve (corresponding to the voice signal in AM radio)
is the curve of eccentricity.
By power spectral analysis,
the periodicity at twenty thousand years is decomposed into two peaks
at 23 and 19 thousand years.
Variation of the tilt of the axis of rotation
The obliquity, or the tilt angle, is the angle between the spin axis and the axis of orbital motion.
It varies between 22o and 24.5o with a periodicity of 41 thousand years (Fig. 4.2-2c).
Its effect to insolation vanishes when spatially averaged over the globe,
but it does not vanish when annually averaged at each latitude.
By latitudes, insolation is larger in high latitudes and smaller in low latitudes when obliquity is larger.
By seasons, summer insolation is larger and winter insolation is smaller in both hemispheres when obliquity is larger (Fig. 4.2-3b).
Time series of insolation
Fig. 4.2-4 shows time series of insolation at summer and winter solstices at four latitudes.
Insolation at summer solstice near the tropic (the second panel)
reflects the twenty thousand year cycle of the season of perihelion,
and winter insolation in high latitudes (the bottom panel)
reflects the forty thousand year cycle of the tilting angle,
respectively, almost purely.
Time series of other latitudes and seasons show various combinations of the two effects.