3.8 Mechanistic explanation of the Dansgaard–Oeschger cycle

Global ice-volume is under control of eccentricity, because high eccentricity enhances the effect of precession and low eccentricity damps it. When eccentricity is very high its effect is like returning to the Early Pleistocene, facilitating an interglacial at every summer energy oscillation. Under very high eccentricity intermediate ice-volume glacials (B, C) behave as Early Pleistocene glacials (D). This can be seen very clearly at the MIS 7e interglacial 245 kyr ago (Fig. 2.15a). As the model indicates, the glacial state prior to MIS 7e was of full-glacial, with an icevolume insufficient to produce an interglacial, thus little ice was melting despite high summer energy. However, when eccentricity became very high (Fig. 2.15a, grey curve), a late interglacial suddenly took place (C & D transition) with very little time left before low obliquity put an end to it. Then, as eccentricity continued being very high, a new interglacial was produced (MIS 7c–a). Both MIS 7 interglacials happened due to high eccentricity, and they were cool interglacials of the Early Pleistocene type. The effect that high eccentricity has in promoting interglacials and low eccentricity in inhibiting them results in more ice-volume accumulating at times of lower eccentricity. The consequence is that although interglacials do not follow a 100-kyr eccentricity cycle, ice-volume does present a 100-kyr cycle (Fig. 2.15a).

2.9 Interglacials of atypical duration

Six interglacials out of the past ten during the last 800 kyr (MIS 13a not considered for the reasons stated in Sect. 2.7), display a very similar temperature profile in EPICA Antarctic records (MIS 5e, 7c–a, 9e, 15a, 15c, 19c). They show a fast increase in temperatures for 5–7,000 years, followed by a temperature stabilization for about 5,000 more years, and then a slow temperature decline that accelerates over time for the next 10–12,000 years during which they lose two thirds or more of the temperature gained from the glacial maximum before the interglacial start. During the period of high temperature (above –2 °C anomaly), that lasts about 15,000 years, each interglacial presents a different temperature profile, highlighting interglacial uniqueness.

An average interglacial was constructed from those six interglacials by aligning them and obtaining their average and standard deviation temperature, average obliquity profile, and the average 65°N summer insolation profile for five of them. MIS 7c presents a very deviant insolation profile that would significantly alter the average of the rest, so its insolation was not included. We can compare this average interglacial to the two interglacials that display a very different duration, the short interglacial MIS 7e at 244 ka, and the long interglacial MIS 11c at 425 ka (Fig. 2.16).

MIS 7e started very late in the obliquity cycle because when obliquity increased above 23°, northern summer

Fig. 2.16 Comparison of atypical interglacials to the average interglacial

An average interglacial (black curve and 1' grey bands) was constructed from interglacials MIS 5e, 7c–a, 9e, 15a, 15c and 19c, after aligning them at the date specified in table 2.1. The obliquity for all of them (black sinusoid continuous line) and the insolation curves at 65°N 21st June for all but MIS 7c–a (black dotted line) were also averaged. MIS 7e temperature, obliquity and insolation data are similarly plotted in blue, and MIS 11 in dark red. Temperature data from EPICA Dome C, after Jouzel et al. (2007). Astronomical data after Laskar et al. (2004).

insolation was decreasing (Fig. 2.16), and ice-volume was below the threshold (Fig. 2.13). Under normal circumstances MIS 7e would have been a cycle without interglacial, however at 250 ka eccentricity was very high and rising quickly (Fig. 2.15), and ice-volume surpassed the threshold. At 248 ka, with obliquity still above 24°, and insolation at 515 W/m2 and increasing rapidly, a delayed interglacial was triggered. But as soon as insolation peaked at 242 ka, the simultaneous falling of obliquity and insolation could not sustain the interglacial. MIS 7e started late because it was triggered by precessional-linked insolation due to high eccentricity, but ended on schedule for the obliquity cycle becoming a short interglacial.

MIS 11c is a very exceptional interglacial. As figure 2.13 shows it was triggered by its extraordinary icevolume values under very modest insolation as soon as increasing obliquity and increasing insolation indicated the feedbacks the right direction. Ice-volume at 433 ka was the highest for the past 5.3 Myr (tied with 630 ka; Lisiecki & Raymo 2005). MIS 11c jumped the gun and obviated the c. 6 kyr delay between forcing and effect. It is unknown how it did it, but it got a 6 kyr lead over the rest of the interglacials. Then MIS 11c proceeded to increase its temperature in three steps. The first step, triggered by rising insolation and a strong feedback response, ended early when insolation peaked at 424 ka. But then rising obliquity provided the impetus for a second warming period (as insolation did not decrease much) that ended at 235 ka when obliquity peaked. Then a third warming step took place caused by a second insolation peak at 226 ka. The three warming steps responsible for the extraordinary duration of MIS 11c are clearly detected in the temperature record (see Figs. 2.11 and 2.16) and give MIS 11c the opposite temperature profile to most interglacials since it evolves from lower to higher temperature. It is the interglacial with highest temperature for the longest time despite occurring at a time of low eccentricity. Given the high increase in energy and the normal thermal inertia of the planet, its decline was also a very long one, despite being more pronounced than the average decline (Fig. 2.16). Due to the confluence of all these unlikely circumstances, MIS 11c is simply unrepeatable. The Holocene has absolutely nothing in common with MIS 11c except taking place at a time of low eccentricity.

2.10 Role of obliquity in the glacial cycle

Most scholars publishing on the glacial cycle have focused on local conditions to try to explain terminations. Insolation, changes in albedo, and dust deposition are supposed to act maximally at a certain latitude at the edge of the ice sheet to melt it. However, the evidence that obliquity plays an important role poses a significant problem, as obliquity's effect on insolation decreases very fast as the distance from the pole increases (Fig. 2.8). Solving the glacial cycle, therefore, may require out of the box thinking. Such thinking has been provided by researchers focusing on a very little studied property of solar insolation, the latitudinal insolation gradient (LIG). Moisture delivery to Antarctica (Vimeux et al. 1999) and Greenland (Masson–Delmotte et al. 2005) has been shown to strongly correlate with obliquity and interpreted as resulting from changes in LIG affecting the hydrological cycle. LIG differences arise from differences in the angle of incidence of solar rays resulting from seasonal changes in the orientation of the Earth. At any time the amount of insolation at a certain latitude depends mainly on precession, but the summer pole points towards the Sun, and on summers the amount of insolation at high latitudes changes significantly with obliquity. When obliquity is high the summer LIG flattens and when it is low the summer LIG steepens. Changes in summer LIG follow almost exactly changes in obliquity at both hemispheres (Fig. 2.17). By contrast winter LIG changes do not depend on obliquity, as the winter pole is in the dark, and depends almost exclusively

Fig. 2.17 Changes in the summer latitudinal insolation gradient depend on obliquity

a) Mean summer insolation depends mainly on precession. Northern Hemisphere in dark red. 60°N (solid curve) and 30°N (dotted curve) are for the month of July (21st June–21st July). Southern Hemisphere in light blue 60°S (solid curve) and 30°S (dotted curve) are for the month of January (21st December–21st January). Observe how insolation in both hemispheres is in anti-phase, largely cancelling its net effect. b) The summer latitudinal insolation gradient is similar and in phase in both hemispheres, and depends mainly on the obliquity cycle. Dark red solid curve is the result of subtracting the 60°N minus the 30°N mean insolation. When obliquity is high both are similar and the gradient is flatter. When obliquity is low the gradient becomes steeper (more negative value). A steeper gradient drives more energy and moisture towards the poles, favoring planetary cooling and ice growth, leading to glacial inception. Light blue solid curve is the same for the Southern Hemisphere. Black dotted curve corresponds to obliquity. Data from Laskar et al. (2004) analyzed with AnalySeries (Paillard et al. 1996).

on precession. On summers polar energy budget depends mostly on insolation and is very much affected by obliquity, while on winters poles get most of their energy from winter energy transport from lower latitudes. But as we have seen it is the summer conditions that are critical for terminations and glacial inceptions.

The role of moisture transport in glaciations is rarely considered. In 1872 John Tyndall argued: “So natural was the association of ice and cold that even celebrated men assumed that all that is needed to produce a great extension of our glaciers is a diminution of the sun’s temperature. Had they gone through the foregoing reflections and calculations, they would probably have demanded more heat instead of less for the production of a ‘glacial epoch’.” (cited by Kukla & Gavin 2004). Indeed such is the role of obliquity, which increases insolation in the tropics as it decreases it at the poles and at the same time steepens the LIG during the summers bringing the necessary moisture that will remain locked there as ice until the process reverses (Kukla & Gavin 2004). And it is not only moisture transport what depends on the LIG, the latitudinal temperature gradient (LTG) also depends on the LIG (Davis & Brewer 2009).

The LTG is a central property of Earth's climatic system at all time scales. It drives the atmospheric-oceanic circulation and helps explain the propagation of orbital signatures through the climatic system, including the Monsoon, Arctic Oscillation, and ocean circulation (Davis & Brewer 2009). Scotese (2016) has shown that one of the main differences between a hothouse and an icehouse planet is in the LTG. The same applies to the difference between glacial and interglacial periods.

Polar amplification of global average temperature changes is prominently displayed as one of the main features of Modern Global Warming, yet polar amplification is the result of changes in the LTG. Climate models treat LTG as an emergent feature and underestimate its sensitivity to changes in LIG, probably overestimating the role of non-condensing greenhouse gases in driving polar amplification (Davis & Brewer 2009).

The interpretation of the glacial cycle in terms of LTG emphasizes summer enthalpy and moisture transport from the tropics to the poles as the decisive factor under obliquity control. Within this hypothesis the tropics, with their huge thermal and moisture capacity, become principal agents in the formation and waning of ice sheets, orchestrated by obliquity changes, while local factors like latitudinal insolation, albedo, and dust are important secondary players that sometimes become decisive.

2.11 Role of CO2 in the glacial cycle

There is no doubt that CO2 is one of several feedbacks that must act on the glacial cycle, as CO2 levels increase with glacial terminations and decrease with the cooling of glacial inceptions. Its exact role remains controversial. About half of the CO2 increase at terminations comes from increased volcanic activity, probably stimulated by load changes effected by ice sheet melting (Maclennan et al. 2002; Huybers & Langmuir 2009), highlighting its feedback role. Being a positive feedback implies that the signal output is amplified, and it is generally accepted that the CO2 increase must contribute to the warming at glacial terminations. There is an objection to a more substantive role for CO2 on glacial terminations. We have reviewed in sections 2.7 to 2.9 (Figs. 2.12 to 2.15) the important role that global ice-volume plays in determining interglacial temperature. Interglacials preceded by very high global ice-volumes are warmer than interglacials preceded by lower global ice-volumes. It means that we can predict, to a certain point, how warm an interglacial is going to be from the amount of ice accumulated before it starts. And therefore we can predict how much CO2 it is going to have (absent an anthropogenic contribution), given the clear correlation between CO2 and temperature. Factors that can be predicted from causative agents in highly variable phenomena cannot be in control. The issue is even worse at glacial inceptions when the correlation between temperature and CO2 is lost, and temperature decrease leads by several millennia the CO2 decrease. At the end of MIS 5e temperature decreased by 4 °C in Antarctica in 8,000 years, without any decrease in CO2 (Fig. 2.18). Further, the rate of temperature decrease between 120.5 and 111 ka was fairly uniform at the resolution of the EPICA Dome C

Fig. 2.18 No role for CO2 at glacial inceptions

EPICA Dome C deuterium proxy for Antarctic temperature (black curve) shows a cooling of 4 °C between 123.5 and 115 ka (black arrow), when Antarctic CO2 levels (red curve) showed no change (red arrow). The rate of cooling between 120.5 and 111 ka (black dotted line) is nearly linear, with a trend of approximately –0.72 °C/kyr, that shows no response to the important differences in CO2 rate of change. Temperature data averaged with a 1,000-year running window. Epica Dome C temperature data after Jouzel et al. (2007); CO2 data after Bereiter et al. (2015).