3.6 The Bølling–Allerød and Younger Dryas as part of the Dansgaard–Oeschger cycle

duce a deglaciation before obliquity starts decreasing. In contrast, peak high-latitude summer insolation has a bigger effect when it happens close to the obliquity maximum, as then both act together. When two peaks in highlatitude summer insolation occur in the same obliquity window, as in O–18 and O–13, the obliquity peak coincides with an insolation trough, resulting in a cooler, oddly shaped, more symmetrical interglacial (MIS 17 and MIS 13a), similar to interglacials before the MPT.

One result from this analysis is that future interglacials should be predictable to a high degree (Fig. 2.14). Interglacials will skip one obliquity window to allow for sufficient ice build up, unless insolation is very high. The simple flow chart in Fig. 2.14 only fails to hindcast the highly unusual MIS 13a interglacial (that without its temperature spike it might not be considered an interglacial), but correctly hindcasts the outcome of the other 23 cases, including the very infrequent occurrence of two consecutive missing interglacials at O–2 (MIS 3). There was no interglacial at MIS 3 despite sufficient global ice-volume because high-latitude summer insolation was not high enough due to the low eccentricity at the time.

The global ice-volume requirement is surprising because global temperature correlates well with global icevolume, and therefore the planet is in a colder state when there is a very high ice-volume, as it happened during the LGM. It is likely a proxy for strong feedback factors that operate more strongly when temperatures are very low and ice levels very high. Among the known factors are: • Reduction of ice-albedo • Increased melting of ice • Rising sea levels • Increase in dust • Increased volcanism • Increase in greenhouse gases

The effect of the temperature decrease during a glacial period prior to the next obliquity cycle has the effect of pulling a spring. The stronger it is pulled, the stronger and faster it will go in the opposite direction when released. This spring acts as a negative feedback to further cooling, and its existence can be inferred from the narrow thermal regulation of the planet during at least the past 540 million years (see Sect. 9.3.2). It is what allows interglacials to take place during this very cold period of the planet, as otherwise for the last 1.5 million years the planet would have been locked in a permanent glacial period only interrupted by interglacials every 400 kyr, at the peak of eccentricity. It is possible that there wouldn't be humans if that had happened as conditions are already too close to CO2 starvation for plants during glacial maxima. Only the arrival of the occasional interglacial prevents further cooling.

When obliquity starts rising during a glacial period it starts moving energy little by little from tropical to polar areas. Its effect on the global average temperature is not noticeable for many thousands of years. If the planet is very cold, with a great portion of the water in huge ice sheets over continents and continental shelves then powerful feedbacks will start. Temperatures will rise after about ten thousand years of increasing energy transfer to higher latitudes and warming will accelerate. It is at about this time when rising precessional insolation during the summer in the Northern Hemisphere will start contributing to the undergoing melting of the northern ice sheets. The contribution of feedback factors and northern summer insolation is what allows the Earth, every 1.8 obliquity cycles on average, to overcome the cold inertia of the planet. It is an additive process where obliquity sets the pace, and is helped by feedback factors and northern summer insolation. If one of these two is strong enough the other might be dispensed. The result is that every interglacial is different. It is the response to forces that assemble and come apart at different times and with different intensities.

2.8 Summer energy as the relevant insolation forcing

Peter Huybers (2006) observed that the melting or growing of the ice-sheets must depend on the cumulative time spent at the ice-sheet border latitude above 0°C during a melting season. It is the same reasoning that led Milutin Milankovi# to propose his theory 86 years earlier, but in the meantime the time factor had been diluted in favor of the maximum intensity of the insolation responsible. Huybers' observation led to the proposal of a Milankovitch parameter that is close to caloric summer but accounts better for the different duration of summers. He called it summer energy and is calculated by adding the day-time insolation energy (in GJ/m2) at 65°N for every day that was above a certain insolation threshold enough for icemelting, that at 65°N was determined to be 275 W/m2 (Huybers 2006).

Didier Paillard (1998) added the last piece of the puzzle when he proposed a simple model that reproduced the glacial cycle by introducing an ice-volume factor that was needed to transition from interglacial to mild-glacial state, and from mild-glacial to full-glacial state. The model forbids the reverse transitions. In essence Paillard's model introduced the brilliant concept that ice build-up made the transitions unidirectional towards full-glacial, and when ice-volume was very high, ice-sheet instability caused a glacial termination when enough summer energy was available.

Figure 2.15 explains how the glacial cycle responds to summer energy changes (mainly due to obliquity), and to ice-volume changes, and how ice-volume responds to eccentricity. Figure 2.15a shows the ice-volume proxy (LR04 benthic !18O) for the past 340 kyr, overlain by the summer energy parameter that has been lagged by 6000 years, to account for the observed delay of the effect to the forcing (Huybers 2009; Donders et al. 2018). By plotting ice-volume versus lagged summer energy (Fig. 2.15b), it is observed that during the 41-kyr oscillations in summer energy, ice-volume starts and ends at repeatable states defined, following Paillard (1998), as interglacial, mildglacial, full-glacial, and deep-glacial.

A simple excitation/relaxation model (Fig. 2.15c) explains the timing of glaciations. During the Early Pleistocene the situation can be described by a reversible oscillation both in summer energy and ice-volume (dashed bidirectional orange arrow) between mild glacial (D) and cool interglacial (D') at a 41-kyr frequency. At the MPT the cooling of the world caused the beginning of the buildup of extensive continental ice-sheets outside the polar regions during glaciations. Now glacial periods would