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recognized the importance of feedback mechanisms (mainly the albedo-temperature feedback) to amplify the response to the astronomical forcing.

Changes in the geometry of the Earth's orbit about the Sun and in the inclination of its axis of rotation cause the amount of solar energy received on the Earth surface to vary by season and latitude. Three astronomical parameters have therefore received great attention in recent climatological studies: the eccentricity of the Earth's orbit, which varies with a mean periodicity of —100,000 years; the tilt of the Earth's rotational axis, which varies from about 21.5° to 24.5" over an average period of 41,000 years; and the climatic precession of the equinoxes, which causes the Earth-Sun distance on each equinox and solstice to change with an average period of21,000 years. Actually, the full spectra of variations of these astronomical parameters are more complex (Berger, 1978) and unstable with time (Berger et al., 1998a). It is possible to demonstrate, for example, that there is a relationship between the amplitude and the frequency modulations of these astronomical parameters. Moreover, all these properties also characterize the behavior of insolation, in which harmonics can be significantly present, such as the 10.5 kvr related to precession, in the tropics, the Sun indeed passes over each latitude twice a year, leading to a double insolation maximum. Assuming that the climate will respond systematically to the largest of them creates such a quasi-cycle of 10.5 kyr, The spectra of insolation therefore depend on which insolation parameter is considered. In particular, the daily amount of energy received from the Sun is essentially a function of precession. Rut as soon as this insolation is integrated over a season it becomes exclusively a function of obliquity, according to Kepler's second law.

At the present, the value oft1 is 0.0167 (Table 8.1) and is decreasing (we have just passed a maximum 0.0197, 14 kyr ago). Obliquity (currently 23,45 ) is decreasing from a maximum of 24.23 reached 9 kyr ago, and climatic precession is decreasing both because of e and because the longitude of the perihelion is decreasing (Figure 8.1). This means that the present-day summer solstice, which occurs at the aphelion, will be at the perihelion within 9 kyr. But more importantly, we are at the end of a 400-kyr cycle for eccentricity. One consequence is that the 100-kyr cycle we entered —50 kyr ago will be shorter and will last only 30 kyr more, leading to an absolute minimum of e at 27 kyr AP, when it will reach almost 0 (0.0027). This implies that the climatic precession parameter (e sin u>) will be very small over the next 50 kyr. At the same

Table 8.1. Astronomical Parameters and Insolation (Berger, 1978; Berger and Loutre, 1994)
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