Page 152 - Earth's Climate Past and Future

128 PART III • Orbital-Scale Climate Change

Sinω ε εsinω FIGURE 7-14 The precessional
+1 0 -1 0 0.02 0.04 +0.4 0 -0.4 index The precessional index, εsinω,
is the product of the sine wave
function (sinω) caused by precessional
motion and the eccentricity ( ) of
Earth’s orbit.

x =

Angular Eccentricity Eccentricity-modulated
motion of (100,000 years) precession
precession (23,000 years)
(23,000 years)

Precessional index (εsinω)
The two solstice positions shown in Figure 7-13 are
0.04 0 –0.04
extreme points in a continuously changing orbit. Pre- 0
cession also moves the solstices through orbital posi-
tions with intermediate Earth-Sun distances like those
shown in Figure 7-11. In the next 11,000 years, the sol- 23,000
years
stices will move from their present positions back to
those shown at the bottom of Figure 7-13.
Eccentricity plays an important role in the effect of
precession on the amount of solar radiation received on
Earth. The full expression for this impact is sinω, the 0.5
precessional index (Figure 7-14). The sinε part of this
term is the sine wave representation of the movement
of the equinoxes and solstices around the orbit (see
Box 7-2). The eccentricity (ε) acts as a multiplier of the Myr ago 413,000
sinω term.
years
As noted earlier, the present value of is 0.0167. If
this value remained constant through time, the sinω
1.0
index would cycle smoothly between values of +0.0167
and –0.0167 over each precession cycle of ~23,000 years.
As shown in Section 7-4, however, the eccentricity of
Earth’s orbit varies through time, ranging between 0.005
and 0.06 (see Figure 7-7). These changes in cause the
sinω term to vary in amplitude (see Figure 7-14).
100,000
Long-term variations in the precessional index have years
two major characteristics (Figure 7-15). First, they
1.5
occur at a cycle with a period near 23,000 years because
of the regular angular motion of precession at that cycle
(see Figure 7-14). Second, the individual cycles vary
widely in amplitude because changes in eccentricity
modulate the 23,000-year signal (see Box 7-1). At times FIGURE 7-15 Long-term changes in precession The
the 23,000-year cycle swings back and forth between precessional index ( sinω) changes mainly at a cycle of 23,000
extreme maxima and minima; at other times the ampli- years. The amplitude of this cycle is modulated at the
tude of the changes is small. eccentricity periods of 100,000 and 413,000 years.