The 100-kyr periodicity, the sawtooth pattern and the timing of the terminations are reproduced with constant CO2 levels 20,24 (for example 220 p.p.m.; Fig. 1e), and are robust for a range of model parameters (Supplementary Fig. 4).
By contrast, the spectral peak of ,100-kyr cycles is greatly reduced, and permanent large ice sheets remain, with the imposition of instantaneous isostatic rebound (Fig. 1f). This result supports the idea that the crucial mechanism for the 100-kyr cycles is the delayed glacial isostatic rebound 14,15, which keeps the ice elevation low, and, therefore, the ice ablation high, while the ice sheet retreats. We note, however, that CO2 variations can result in amplification of the full magnitude of ice-volume changes during the 100-kyr cycles, but do not drive the cycles. Ice-sheet changes may induce variations in CO2 through changing sea surface temperature, affecting the solubility of CO2 (ref. 25), and through changing sea level, affecting the stratification of and CO2 storage in the Southern Ocean18. During deglaciation, the melt water may affect ocean circulation, leading to an increase in atmospheric CO2 (refs 23, 26, 27).
A remarkable conclusion from our model results is therefore that the 100,000 year glacial cycle exists only because of the unique geographic and climatological setting of the North American ice sheet with respect to received insolation. Only for the North American ice sheet is the upper hysteresis branch moderately inclined; that is, there is a gradual change between large and small equilibrium ice-sheet volumes over a large range of insolation forcings. For this reason, as demonstrated in Fig. 2b, the amplitude modulation of summer insolation variation in the precessional cycle, due primarily to eccentricity, is able to generate the 100-kyr cycles with large amplitude, gradual growth and rapid terminations.