Author’s reply to reviewer 1

ence carry a huge uncertainty that cannot be properly constrained by evidence. The Paleocene–Eocene Thermal Maximum is usually cited as precedent; however, its isotopic carbon excursion took place so long ago that our poor knowledge of its source, amount, and release timescale precludes any meaningful estimation of its decay.

IPCC confidence comes essentially from David Archer's studies, that since 1997 has become the authority of reference. It is clear that the unburial and release of huge carbon fossil stores constitutes a long-term perturbation of the carbon cycle. Since carbon only permanently exits the carbon cycle very slowly through calcium carbonate sea-bottom burial, and silicate rock weathering, the different compartments of the carbon cycle will have to deal with excess carbon for a very long time and this should necessarily lead to an equilibration between compartments at higher levels than prior to the perturbation. At present the complexity of the effects involved is being studied with box-modeling, but every step in the process requires taking assumptions. It is assumed that the land biosphere, that is currently a sink due to an increase in photosynthesis over respiration, should reach equilibrium within decades after the end of anthropogenic emissions and then become a net source as atmospheric levels decrease. The reduction in atmospheric CO2 is then assumed to occur mainly through ocean uptake on a timescale of centuries, driven by changes in oceanic chemistry and ocean mixing. It is assumed that as more carbon dioxide dissolves in the ocean, it will compromise the ocean's buffering capacity and that ocean acidification will increase the Revelle factor (dissolved CO2 to dissolved inorganic carbon). This is then expected to reduce the efficiency of the ocean carbon sink until it stops taking CO2 after about 1000 years, when 14–30% of the maximum level reached remains in the atmosphere (Archer & Ganopolski 2005). Higher temperature is also expected to contribute to a decrease in the ocean carbon sink efficiency.

Archer's (2005) worst case scenario involves anthropogenic emissions of 1600 GtC by 2100 (545 GtC emitted 1870–2014) and increasing afterwards. Up to 1000 GtC should be contributed by a reversal of the land biosphere and soils sinks, and the rest to 5000 GtC total contributed by permafrost and marine methane clathrate deposits. A more realistic scenario considering fossil fuel supply-side constrains and extrapolating observed warming leads to only 500–1000 GtC addition at most. But this amount disregards any effort to reduce emissions. It is to be expected that a higher certainty on CO2 climatic effects should lead to more intense efforts to curtail emissions.

It is impossible to have a high confidence that 14–30% of the carbon emitted will remain in the atmosphere 1000 years from now. That number comes from a set of assumptions made using a poor understanding of the carbon cycle, and it could be much lower. Those models are unable to reproduce or explain the significant increase of 20 ppm in CO2 that took place between 6,000 and 600 yr BP. Initializing the models at 6,000 yr BP doesn't produce the pre-industrial CO2 levels of 280 ppm, unless ad hoc assumptions are introduced, indicating models cannot be trusted to project atmospheric CO2 levels thousands of years into the future.

The National Research Council set in 2008 the Committee on the Importance of Deep-Time Geologic Records for Understanding Climate Change. This body produced a 2011 report: Understanding Earth's Deep Past: Lessons for Our Climate Future (National Research Council 2011). This expert committee fully acknowledges the uncertainty present in CO2 adjustment time estimates from boxmodels:

“Although box-model calculations should not be considered definitive, they do suggest that the fossil-fuel perturbation may interfere with the natural glacial–interglacial oscillation driven by predictable changes in Earth’s orbit, perhaps forestalling the onset of the next Northern Hemisphere ‘ice age’ by tens of thousands of years. A more convincing exposition of the central question of “how long” requires more comprehensive models. Scientific confidence in those models will only be high if they can be evaluated against observation. The historical record, and even the expanse of the Quaternary climate record, contains nothing comparable.”

The proposed fat-tail of anthropogenic CO2 adjustment time should be taken as a possible scenario if certain assumptions are correct, and not as what is expected to happen.

14.7 Glacial inception in the Holocene

Glacial inception is the transition from interglacial climate to glaciation, a process characterized by ice-sheet build up and falling sea-levels. However, there is no unambiguous definition of glacial inception that allows it to be placed at a specific point in time for each interglacial. In the excitation/relaxation dynamic model of glaciations discussed in chapter 2 (see Sect. 2.9, Fig. 2.15), and illustrated in Fig. 14.3, glacial inception can be understood as an irreversible commitment from a quasi-stable interglacial state into a relaxation process towards a stable glacial state, taking place once the conditions that made the interglacial possible have disappeared, and once the downward drift in temperature allows the boundary crossing at the commitment point (Fig. 14.3, unstable point).

A point of inflection can be observed in the Antarctic proxy temperature record of past interglacials. In each case the slowly declining temperature of the late interglacial suddenly accelerates into a terminal decline towards glacial conditions (Fig. 14.7). In the case of the Eemian interglacial, this inflection point takes place at 120 ka, coinciding with the determination of glacial inception by different criteria (Fig. 14.4), confirming the date. It can be assumed that the inflection point in the cooling rate corresponds to glacial inception in all cases, and can be explained as a point when the intensification of positive feedbacks (like ice-albedo, vegetation changes, or changes in oceanic currents), leads to a steepening of the latitudinal temperature gradient, an intensification of meridional transport of heat towards the poles, and the consequent accelerated cooling of the planet into glaciation.

The start of an interglacial is also lacking a formal definition. In the case of the Holocene the start is formally placed 11,700 years ago (Walker et al. 2009). At that time EPICA Dome C deuterium proxy temperature record shows no anomaly with respect to current value (0°C anomaly). For a consistent comparison we can define the start of every interglacial at the time they first reach 0°C anomaly in the EPICA Dome C record. For cooler interglacials that didn't reach 0°C anomaly, picking a lower temperature would lead to overestimating their length, as a

Fig. 14.7 Interglacial length normalization

The start of an interglacial is defined, as for the Holocene, by the time EPICA Dome C temperature anomaly reaches 0°C, or by extrapolating the rate of warming to the 0°C value. The end of an interglacial is defined at the inflection point where EPICA Dome C temperature anomaly increases its rate of cooling towards glacial values.

lower temperature is reached earlier. A more correct choice, in the author's opinion, is to extrapolate the warming trend to the point where it would have reached 0°C anomaly, picking that time as the normalized start of the interglacial (Fig. 14.7; table 14.1). This choice avoids the significant bias of overestimating the length of cool interglacials. MIS 13a cannot be normalized and it is not analyzed under the criteria chosen here.

Normalized in this way interglacials are between 10 and 16 kyr in length, with an average of 13 kyr, with two exceptions: MIS 7e and MIS 11c. Orbital configuration explains MIS 7e and MIS 11c anomalous length (Fig. 14.8, see also Fig. 2.16). A consistent rule is that all interglacials end when obliquity is low. No interglacial of the past 800 ka has gone beyond 15.5 kyr from the obliquity maximum (Fig. 14.8a). Since MIS 7e had a late start with respect to the obliquity cycle it became a very short interglacial. Since MIS 11c started early in the obliquity cycle due to its unusual precessional insolation, it became a very long interglacial. Low eccentricity allows long interglacials when other conditions are present, but it does not cause them to be long.

The other orbital rule is that interglacials of the past 800 ka start when the combination of obliquity and precessional insolation is high enough (high summer energy). Precessional insolation is irrelevant for glacial inception, as three interglacials (MIS 7c–a, MIS 11c, and MIS 17) were capable of surviving through an insolation minimum, yet they suffered glacial inception close to the next maximum, when obliquity dropped. A typical interglacial (Fig. 14.8, line between circles) starts 2000 years before obliquity maximum, and 1000 years before insolation maximum, and lasts 13,000 years. So far, the Holocene is extraordinarily close to a typical interglacial in astronomical terms and length.

Orbital configuration alone can explain when interglacials start and end, while changes in CO2 levels cannot. Interglacial temperature is inversely correlated to the amount of ice-volume before deglaciation starts (see Fig.

Interglacial Start End Length

MIS 1 11,700

MIS 5e 131,400 120,000 11,400 MIS 7c–a (-214,200) 198,200 16,000

MIS 7e 243,800 236,000 7,800

MIS 9e 335,500 324,800 10,700

MIS 11c 424,800 401,000 23,800

MIS 15a (-579,100) 564,800 14,300

MIS 15c (-623,800) 609,200 14,600

MIS 17 (-707,400) 693,100 14,300

MIS 19c (-786,300) 776,200 10,100

Table 14.1 Normalized interglacial length

Dates in yr BP for the start, end, and length, of normalized interglacials. Dates between parenthesis are extrapolated from the rate of warming. These dates and lengths are used to compare interglacial orbital conditions for the rest of the chapter.

Fig. 14.8 Interglacial orbital configuration

a) Interglacial start and end dates (triangles in arrows) relative to the obliquity maximum. Light grey area indicates interglacial start for all interglacials except MIS 7e and MIS 11c that had an anomalous length due to starting too late and too early respectively in the obliquity cycle. Dark grey area indicates interglacial end for all interglacials. Circles indicate start and end of a typical interglacial with average 13 kyr length. Interglacials start when obliquity is high and end when obliquity is low. b) Interglacial start and end dates (triangles in arrows) relative to northern summer insolation maximum. Light grey area indicates interglacial start for all interglacials. Dark grey area indicates interglacial end for all interglacials. Circles indicate start and end of a typical interglacial with average 13 kyr length. Interglacials start when insolation is high but can end at any time in the insolation cycle.

2.15; warmer interglacials correspond to previous higher ice-volume). Interglacial temperature is also directly correlated to CO2 (see Fig. 12.8). And ice-volume is inversely correlated to eccentricity (see Figs. 2.12 & 2.15). As it is difficult to explain why CO2 levels would inversely correlate to prior ice-volume, the most likely explanation is that CO2 levels are a consequence of temperature levels, not a cause (eccentricity & ice-volume & temperature & CO2). Eemian glacial inception and the next 5000 years of cooling took place under stable 270 ppm CO2 levels, indicating that glacial inception is responding to orbital changes, not CO2 changes. Despite this evidence IPCC expresses virtual certainty that a new glacial inception is not possible for the next 50 kyr if CO2 levels remain above 300 ppm (IPCC–AR5, Masson–Delmotte et al. 2013, pg. 435). Ice core measurements indicate CO2 levels at past glacial inceptions have always been below 300 ppm, but there is simply no evidence indicating how high CO2 levels must be to stop a glacial inception, if that is even possible.

It is widely known that there is a delay between the astronomical signal and the geological evidence of climate change. This delay, in the case of obliquity is c. 6000 years (Huybers 2009; Donders et al. 2018). The logical conclusion is that the astronomical threshold for glacial inception is crossed c. 6000 years before it takes place. This inference is supported by the presence at the end of interglacials of a period of declining temperatures before reaching the inflection point that indicates glacial inception has taken place (Fig. 14.7). In the Holocene this period is termed Neoglaciation, and it is also observed between 126–120 ka in the Eemian (Fig. 14.4).

Analysis of the orbital conditions that produce a glacial inception requires examining them 6000 years before the inflection point, in the cooling rate at the end of the interglacial. Glacial inception does not take place at 65°N, but at 70°N, where ice sheets start to grow (Birch et al. 2017). Examination of 70°N summer energy (at 250 W/m2 threshold) 6000 years before glacial inception (Fig. 14.9, diamonds) reveals a threshold at 4.96 GJ/m2 when the glacial inception orbital “decision” has already been taken for all previous interglacials (Fig. 14.9, continuous line). A maximum summer energy value prior to glacial inception

Fig. 14.9 Orbital decision to end an interglacial

Summer energy at 70°N with a 250 W/m2 threshold for the past 800 ka. Diamonds mark the position 6 kyr before glacial inception as observed (Fig. 14.7) in the EPICA Dome C temperature proxy record for each interglacial except MIS 13. Continuous line marks the lowest value observed (4.96 GJ/m2). Dashed line marks the highest value for six of the nine interglacials considered. The Holocene (MIS 1) is already below the lower threshold value as the curve ends at the present.

Fig. 14.10 The Holocene is a typical interglacial

Holocene temperature profile (black solid curve, from EPICA Dome C data), obliquity evolution (black dashed curve), and 65°N summer insolation evolution (black dotted curve), do not show a significant deviation from the respective values of an average interglacial (red curves and 1' pink bands) from MIS 5e, 7c–a, 9e, 15a, 15c and 19c, aligned at 787.0, 624.4, 579.6, 335.5, 214.7, and 131.4 ka in EDC3 dates. Interglacial average summer insolation curve does not include MIS 7c–a values. The Holocene was aligned at 11.7 ka. Data after Jouzel, et al. (2007); Laskar et al. (2004). The Holocene data closeness to that of most interglacials does not provide support for hypotheses of a long interglacial on astronomical grounds, and suggests that statistically the Holocene is close to reaching the beginning of its end.

“decision” by six of the nine interglacials is apparent at 4.99 GJ/m2 (Fig. 14.9, dashed line). This narrow window of just 0.03 GJ/m2 constitutes the range where most interglacials commit to glacial inception 6000 years later, while some interglacials appear to take the decision earlier. Two of the exceptions, MIS 9e and MIS 5e, have in common a well below average duration (10.7 and 11.4 kyr), and being very warm very early, as the only interglacials to reach +3.7 °C in the entire 800 kyr EPICA Dome C ice core (Fig. 14.7; Jouzel et al. 2007). It is possible that being very warm, very early, sets an interglacial on an early cooling trend. By contrast, the other exception, MIS 17, is the coolest interglacial of the past 800 kyr, as it is the only one that didn't reach –1.5 °C in EPICA data, and is still considered an interglacial. It is not unreasonable to assume that temperature affects interglacial duration, and thus the