1 The changes of orbital geometry The changes of distribution of Insolation S(latitude, time) Climate Changes Amplified or Reduced? Evidence of ice sheet evolution during last 2.5 million years. North Atlantic sediment core δ18O. The development of the ~100,000 year cycles of glaciation is a relatively recent phenomena (600,000 years). From M. E. Raymo, Ann. Rev. of Earth and Planetary Science, 22, 353, 1994. Figure from Ruddiman.23 image adopted from The Atmosphere by Lutgens and Tarbuck, © 1998 by Prentice-Hall, Inc Obliquity Precession4 INSTANTANEOUS Zachos et al., Science, 2001567 Evidence of ice sheet evolution during last 2.5 million years. North Atlantic sediment core δ18O. The development of the ~100,000 year cycles of glaciation is a relatively recent phenomena (600,000 years). From M. E. Raymo, Ann. Rev. of Earth and Planetary Science, 22, 353, 1994. Figure from Ruddiman.8 Fig. 2. Insolation forcing and Pleistocene glacial variability. (A) Number of days that insolation is above 275 W/m2 (blue) and the average insolation intensity during this interval (red). Intensity and duration are anticorrelated. (B) Spectral estimate of the duration (blue) and intensity (red), showing that the majority of the variability is at the precession periods. Shaded bands from left to right indicate the 100-ky, 41-ky (obliquity), and 21-ky (precession) bands. (C) Summer energy (red) and the time rate of change of 18O (black) for the early Pleistocene and (D) the corresponding spectral estimates. Positive rates of change indicate decreasing ice volume. Variability in both records is predominantly at the 41-ky obliquity period. (E and F) Same as (C) and (D) but for the late Pleistocene. The time rate of change of 18O has variability at the 100-ky period not present in the forcing. Huybers, Science 2006 a, 18O EOF1 normalized so that negative values indicate more ice. Dots indicate onset of a termination and horizontal bars indicate one-standard-deviation age-model uncertainties13. Termination 3 is split between events 3a and 3b. Vertical lines indicate the time of maxima in obliquity. Note that time runs from right to left in the palaeoclimate convention. b, The obliquity phase (dots) sampled at each termination and plotted on a unit circle. The vector average has a magnitude R = 0.70 (cross mark) exceeding the critical value c = 0.60 (filled circle), so that H0 is rejected. Furthermore, R is near H1's maximum-likelihood value (dashed circle). The direction is indistinguishable from maximum obliquity (top of the circle). c, d, Analogous tests are made for precession (R = 0.43, c = 0.60) (c) and eccentricity (R = 0.66, c = 0.84) (d), but in neither case can the corresponding H0 be rejected. See the Supplementary Information for more details.9 a, Deterministic model results (red) with an obliquity-dependent threshold (black) plotted over EOF1 (brown). b, Periodograms of the deterministic model results (red) and EOF1 (brown). Concentrations of energy are centred on the 1/41-kyr obliquity frequency and the 1/100-kyr glacial band; as well as combination tones at 1/70, 1/29 and 1/23!kyr. The approximate 95% confidence interval is indicated by the vertical bar on the right. c, A realization of the stochastic model. d, Histogram of the time between terminations, derived from many runs of the stochastic model. The observed duration between terminations (triangles, using termination 3a not 3b) coincide with the dominant 80- and 120-kyr modes. e, Histogram of Rayleigh's R from the stochastic model with the observed obliquity value, R = 0.70, indicated by the triangle. Obliquity pacing of the late Pleistocene glacial terminations Peter Huybers and!Carl Wunsch Nature 434, 491-494 (24 March 2005) doi: