Page 224 - Earth's Climate Past and Future

200 PART III • Orbital-Scale Climate Change

BOX 11-1 LOOKING DEEPER INTO CLIMATE SCIENCE

The Link between Forcing and the Time Constants of Ice Response

he relationship between the forcing of ice sheets and years. If we assume a mid-range value of 10,000 years for
Ttheir response can be quantified by the following T, and we use f = 1/41,000 years (= 0.000024), then
equation, provided that the variations under investigation
ϕ = arctan 2 × 3.14 × 0.000024 × 10,000
are sine waves:
ϕ = arctan 1.51
ϕ = arctan 2πfT
Geometry tables tell us that the angle whose tangent is
where arctan means “the angle whose tangent is . . .,” ϕ is
1.51 is 56.5°. This angle, expressed as a portion of a full
the lag of the ice response behind the forcing in degrees
360° circle, needs to be converted to the number of years
(out of a full 360° circle), f is the frequency under investiga-
as a portion of a full 41,000-year cycle:
tion in 1/year (f is the inverse of the period), and T is the
56.5°/360° × 41,000 = 6,400 years
response time (the time constant) of the ice sheets in years.
If ϕ is known, the equation can be used to solve for T The estimated lag of ice sheets with a 10,000-year time con-
and conversely. For example, consider the case of summer stant behind summer insolation forcing at the 41,000-year
insolation forcing of ice sheets at the 41,000-year tilt cycle is thus 6,400 years. This value is close to the observed
18
cycle. Ice sheets are thought to have a time constant of lag of the 41,000-year component of the δ O (“ice volume”)
response somewhere in the range of 5,000 to 15,000 signal behind the summer insolation forcing at 41,000 years.

Ice sheets could have controlled CO by any or all of One factor that was probably involved in the shift
2
several mechanisms (Chapter 10). If strong winds from the 41,000-year glacial world to the ~100,000-year
picked up dust formed along the ice margins or in glacial world was the slow cooling that had been
regions of cold dry ice-driven climates and blew it out underway for millions of years, as shown by δ O
18
to the ocean, fertilization by iron or other trace ele- records from the Pacific Ocean (Figure 11–14). This
ments could have strengthened the carbon pump mech- gradual polar cooling would have slowly reduced abla-
anism and reduced atmospheric CO concentrations. If tion in high northern latitudes to the point that some
2
ice sheets caused the decrease in depth of sinking of ice began to survive during relatively weak insolation
North Atlantic Deep Water, the resulting drop in the maxima. This residual ice would then form a base for
CO –2 ion concentration in south polar waters could additional ice growth, as proposed for the “large glacia-
3
have caused a CO decrease. And if ice sheet growth tion” phase in Chapter 9.
2
helped to cool deep-water temperatures, the CO solu- A likely reason for the spacing of these larger glacia-
2
bility mechanism would have reduced atmospheric CO tions at approximately 100,000 years is evident in the
2
concentrations. The evidence examined to this point summer insolation trends in (Figure 11–15). Although
suggests that ice sheets did drive dust concentrations in these insolation changes are dominated by changes at
the northern hemisphere (see Figure 11–10) and also the 23,000-year precession cycle, modulation of the
affected the flow of North Atlantic Deep Water (see precession signal by eccentricity at a period near
Figure 10–15). 100,000 years is also obvious. This modulation pro-
duces clusters of unusually high insolation maxima at
Why Did the Northern Ice Sheets Vary at intervals of approximately 100,000 years. If ice sheets
were able to grow to a relatively large size during inter-
100,000 Years?
vals when insolation maxima were smaller, they could
This investigation has now led us full circle back to have been vulnerable to rapid melting when insolation
where we started—with the northern ice sheets. The ice maxima grew larger, at intervals of ~100,000 years.
sheets clearly fluctuated at a period near 100,000 years, This response is possible because ice melting is
and they probably sent this signal south by means of sensitive only to the “upper side” of the envelope of mod-
their control of the greenhouse-gas concentrations at ulation by eccentricity. Insolation minima are equally
~100,000 years. But a major question remains unre- prominent on the opposite side of this envelope, but they
solved: Why did the ice sheets fluctuate at a period near are irrelevant to ice melting, which occurs only during
100,000 years in the first place? insolation maxima. In this way, major deglaciations could