1. Objective This paper presents a statistical test of the orbital forcing of glacial terminations. Main Result Glacial periods terminated every two or third obliquity cycle at times of high obliquity. Obliquity pacing of the late Pleistocene glacial terminations P. Huybers, C. Wunsch

2. Data: Uses the EOF1 of 10 marine del 18 O records, which is a proxy for ice volume and ocean temperature. It's on a depth-derived age- model that has no orbital information built into the model. Null Hypothesis (H0): glacial terminations independent of an orbital period. Alternative hypothesis (H1): glacial terminations are paced by a certain orbital period. Orbital periods: obliquity, precession, eccentricity

3. To apply the test it is necessary to determine the PDF of H0 and H1. Model: Ice volume variability is represented by a random walk with terminations: V(t+1)=V(t)+n(t) if V(t) >= T0(=90 kyr) => terminate, and ice volume is linearly reset to 0 in 10kyr. n(t)~N(mean=1,std=2) I.C. V(t=-700kyr) between [0,T0] Note that if n(t)=1, cycles would last 100kyr (no need for oscillator).

4. Do 10000 realizations of the random walk. A PDF for H0 is constructed as follows: for each realization we consider 8 consecutive terminations and calculate where Ө is the phase between termination initiations and the orbital period. The PDF of H1 is estimated using R and considering that glacial terminations always occur at the same phase of the orbital period, but that phase observations are subject to identification (+-1kyr) and age-model (+-9kr) error.

5. ObliquityPrecessionEccentricity Phase Test Critical value of R (H0) Max likelihood of H1 Rejects H0 age-model uncertainty ~1/2 cycle H0 is not rejected

6. “Model” of del 18 O variations based on obliquity forcing. V(t+1)=V(t)+n(t) if V(t) >= T0-a*Obl(t) => terminate (the larger the obliquity, the easier) Adjustable parameters: a, T0, I.C. Set to a=15, T0=105, V(t=-700)=30 n(t) can be deterministic (=1) or stochastic (~N(1,2))

7. Deterministic periods at 70, 29 and 23 are combinations of 41 and 100 kyr. wide narrow Stochastic Times between terminations averages 100kr, but has a tri-modal distribution with peaks at 2, 3 and 4 obliquity cycles. Triang: obs duration between terminations. One realization

8. Speculation about cycle-skipping: Increased obliquity increases high latitude insolation and causes heating of ice-sheets, eventually warming the ice-bedrock interface (~10kyr). => If ice is thin, obliquity has small effect. => If ice is thick basal melting provides lubrication of the ice-bedrock interface and increases ice flux into ocean.