Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing
Abstract
Long-term variations in Northern Hemisphere summer insolation are generally thought to control glaciation. But the intensity of summer insolation is primarily controlled by 20,000-year cycles in the precession of the equinoxes, whereas early Pleistocene glacial cycles occur at 40,000-year intervals, matching the period of changes in Earth's obliquity. The resolution of this 40,000-year problem is that glaciers are sensitive to insolation integrated over the duration of the summer. The integrated summer insolation is primarily controlled by obliquity and not precession because, by Kepler's second law, the duration of the summer is inversely proportional to Earth's distance from the Sun.
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References and Notes
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The use of a constant value for τ illustrates the concept of summer energy. A more detailed description would take into account that τ is expected to be spatially and temporally variable, depending on factors such as elevation, albedo, clouds, heat transport, and greenhouse gas concentrations. Note, however, that results are not sensitive to plausible choices of τ and that values less than 325 W/m2 yield broadly consistent summer energies (fig. S1). Summer energy values at 65°N are given in table S1.
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The relationship between insolation intensity and insolation energy is more precisely illustrated by noting that I ∝ 1/r2, where I is insolation intensity and r is the distance from the Earth to the Sun. Conservation of angular momentum (or, equivalently, Kepler's second law) dictates that dt ∝ r2dλ, where dt is an infinitesimal change in time and dλ the corresponding change in solar longitude. The energy received by the Earth is then J = Idt ∝ dλ. In contrast with I, the J between any two solar longitudes is independent of r and, thus, independent of the precession of the equinoxes.
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Are past changes in summer energy sufficient to cause the waxing and waning of ice sheets? Although a full answer requires a realistic model of Pleistocene climate, some indication is provided by modern glacial changes: A 2.4 W/m2 global average increase in radiative forcing caused by greenhouse gases (34) has apparently led to a general decrease in glacial mass (35), suggesting that glaciers are sensitive to relatively small changes in the radiation budget.
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Amplitude cross correlation was computed by pairing local maxima in insolation with the nearest (in time) maximum in the rate of change of ice volume. Before identifying maxima, both the δ18O record and the summer energy were smoothed by using an 11-ky tapered window. There are 34 local maxima in summer energy at 65°N between 2 and 1 My ago and another 34 between 1 My ago and the present. Squared cross correlations of 0.4 and higher have P values of less than 0.01. Spectral and coherence analysis is performed by using Thomson's multitaper method (36).
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This paper benefited from discussion with E. Boyle, B. Curry, M. Raymo, P. Stone, E. Tziperman, and C. Wunsch. J. Levine provided valuable assistance in calculating the insolation. The NSF paleoclimate program supported this work under grant no. ATM-0455470.
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Volume 313 | Issue 5786
28 July 2006
28 July 2006
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American Association for the Advancement of Science.
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Received: 23 January 2006
Accepted: 9 June 2006
Published in print: 28 July 2006
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