## The Milankovitch Puzzle

The main focus in understanding Glacial cycles has been on the maximum summer insolation at 65N, yet prior to MPT (Mid Pleistocene Transition) all glaciations simply followed the obliquity cycle. To understand why obliquity is the underlying metronome, we need to consider the integrated summer insolation. Increases in the earth’s tilt boost insolation at both poles. The precession of the equinoxes only affects maximum summer insolation at one pole at a time because the earth has an elliptical orbit. Once every 23ooo years the Northern hemisphere summer coincides with perihelion and maximum insolation occurs at the summer equinox (June 21). Eccentricity of the earth’s orbit is the crucial factor in modulating just how strong this maximum value becomes, because eccentricity determines the distance at perihelion between the earth and the sun. If the earth’s orbit were circular then precession would have no effect at all. When eccentricity is low like it is today, then the effect is small , but 220,000 years ago a much larger eccentricity  increased NH summer maximum insolation by 4 times greater than today. Despite this varying precession/eccentricity effect I would argue that the underlying influence on summer insolation is still obliquity, because it affects both poles equally. If obliquity were zero there would be no seasons on earth, while larger obliquity increases the size of climate zones.

Figure 1a compares the relative strength of summer insolation at both poles with the modulating eccentricity cycle over the last 600,000 years. If you simply average the North and South maximum insolation together then you can see a perfect obliquity signal – the red dashed curve. This is what insolation would be at both poles if the earth’s orbit were perfectly circular.

Figure1. A) Calculations of insolation at both poles, their average, and the integrated insolation over a full year. B) Ice Volume data(LRO4) compared to a parameterisation of obliquity and eccentricity. Click to expand.

The solid red curve in Figure 1a is the integral of annual insolation received at the North Pole (~5GJ/m2). The precession signal now vanishes! Total summer insolation simply follows obliquity at both poles. The reason for this is because angular momentum is  conserved during an elliptical orbit. This means that the earth speeds up near perihelion and slows down at aphelion. Perihelion summers may have a high insolation on June 21st but as a result these summers can be up to 20 days shorter than aphelion summers!  Currently the SH summer is about 4 days shorter than the NH summer. The end result of this effect is that the total summer energy received from the sun in either hemisphere does not depend on precession at all. It depends only on obliquity.

The dashed red curve in Figure 1a is the average insolation over both poles. Raymo et al (1) have proposed  that prior to the MPT, the Earth was warm enough that cycles in ice volume for the Northern and the Southern hemisphere were out of phase and acted independently, depending only on local solar input. So the global effect on ice volume was the average of the two hemispheres and this caused ice volume to follows obliquity (Figure 2). This was possible before MPT because the East Antarctic Ice sheet melted back to land each cycle and so contributing to global ice volume.  As the earth cooled beyond MPT so  Antarctic Ice permanently saturated the continent shelf, breaking the N-S symmetry and Ice ages then became dominated by  NH insolation alone. Another possibility proposed by Huybers (2) is simply that total summer insolation has always driven glacial cycles before MTP and even today is the dominant term.

Figure 2: Obliquity dominated glacial cycles before MPT: 900-1500 ya

Figure 1a shows that eccentricity modulates the NH summer maximum. Figure 1b shows the Ice Volume data LRO4 from 600,000 years ago. Can eccentricity and obliquity alone describe post MTP ice ages, or is 65N insolation now the driver? The blue curve in figure 1B is simply a combination of eccentricity and obliquity, both inverted to match ice volume. The curve is not based on any physics, but is simply chosen ad hoc. Here it is.

$y = (23.35 + (0.044 - \epsilon ) \times 34.5) + (2.325 -\frac{\phi}{10}) + 2.325$

Surprisingly the main features of the last 6 glacial cycles in Figure 1b are reasonably well reproduced by this simple formula. This demonstrates how eccentricity still plays the hidden role after MPT by modulating the NH summer maximum insolation. Yet mysteriously only some NH summer maxima significantly reduce ice volume.

However, none of this yet explains why the deepest glaciations, which always occur at low eccentricity, suddenly end with a bang, even though NH summer maximum insolation maxima remain small. The LGM is a classic example.

Figure 3. Last Glacial Cycle. Note how larger NH insolation peaks before LGM had little effect on Ice Volume, although both Antarctic temperatures and CO2 both recovered slightly. The correlation of low CO2 with dust deposits in the ice however is striking. The largest deposits are just before rising temperatures ended the last glacial cycle.

The next glaciation also looks to be even more  severe than the last one as eccentricity falls to an all time low,  last seen 2.8 million years ago! You can also see the 400 ky eccentricity cycle as well below in Figure 4.

Figure 4. LA2010 calculations of the earth’s eccentricity over a 4 million year period spanning the present day.

Glacial termination at low eccentricity

So what causes the deepest glaciations like the LGM to terminate? I think the most promising proposal so far is that increased Dust due to CO2 starvation reduces albedo and primes the ice sheets for rapid melting at the next NH summer maximum. This idea was originally proposed by Ralf Ellis(3).  As low eccentricity glaciations deepen, so sea levels drop and  CO2 levels fall below 200ppm. This CO2 starvation, combined with arid conditions causes boreal forests and vegetation to die back inducing dust storms that cover the ice sheets with dust over thousands of years. This occurs especially near their southern edges.

Figure 5. The last 800,000 years of glacial cycles. The current interglacial is most similar to that 400,000 years ago. Click to expand

During the LGM CO2 levels reached dangerously low levels of ~180 ppm causing arid desertification as temperate trees and savannah died off. The resulting dust storms then deposited huge amounts of dust onto the ice sheets increasing its albedo. The consequent NH summer insolation maximum, coinciding with maximum eccentricity, finally melted back the ice sheets through reduced albedo,  aided by increasing CO2 and H2O feedbacks.

When all else fails GAIA ends ice ages !

References

1. (Raymo, Maureen & Lisiecki, Lorraine & Nisancioglu, Kerim. (2006). Plio-Pleistocene Ice Volume, Antarctic Climate, and the Global 18O Record. Science (New York, N.Y.). 313. 492-5. 10.1126/science.1123296)
2. Peter Huybers, Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing, Science June 2006
3. Ralf Ellis, Michael Palmer, Modulation of ice ages via precession and dust-albedo feedbacks, Geoscience Frontiers, Volume 7, Issue 6, November 2016, Pages 891-909
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## Ice Age insights

The discussion on the ‘dust’ theory of ice age termination at Judith Curry brought a couple of other interesting papers to light. This has started me thinking again about how recent deep glaciations terminate. Such glacial cycles apparently now only terminate when the ice sheets reach a critical size, especially at low eccentricity. Why?

Ralf Ellis proposed the build up of dust on the ice sheets due to falling CO2 and arid desert conditions reduces albedo sufficiently for the next 65N insolation maximum to trigger an interglacial. However there are other proposals.

Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume Ayako Abe-Ouchi, Fuyuki Saito , Kenji Kawamura, Maureen E. Raymo , Jun’ichi Okuno1, Kunio Takahashi & Heinz Blatter

In summary, our model results suggest that the 100-kyr cycle is essentially produced by the eccentricity modulation of precession amplitude through the changes in summer insolation , with the support of obliquity for glacial terminations, especially when eccentricity remains small after its minimum (for example at termination I 20–10 kyr BP and at termination IV 340–330 kyr BP).

A remarkable conclusion from our model results is therefore that the 100-kyr 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.

They use a simplified climate model with an ice sheet model which can reproduce 100 ky sawtooth cycles. This result is independent of CO2 levels, dust albedo etc. all of which are considered feedbacks. The root ’cause’ of this hysteresis effect is the slow isostatic rebound of ice free land.

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 rebound14,15, which keeps the ice elevation low, and, therefore, the ice ablation high, while the ice sheet retreats.

So their key physical explanation for hysteresis is deep glacial land compression with slow rebound.

The next paper tries to explain why glacial cycles transitioned from being obliquity driven to longer cycles.

A simple rule to determine which insolation cycles lead to interglacials – P. C. Tzedakis, M. Crucifix, T. Mitsui & E. W. Wolff

Here we show that before one million years ago interglacials occurred when the energy related to summer insolation exceeded a simple threshold, about every 41,000 years. Over the past one million years, fewer of these insolation peaks resulted in deglaciation (that is, more insolation peaks were ‘skipped, implying that the energy threshold for deglaciation had risen, which lead to longer glacials. However, as a glacial lengthens, the energy needed for deglaciation decreases. A statistical model that combines these observations correctly predicts every complete deglaciation of the past million years and shows that the sequence of interglacials that has occurred is one of a small set of possibilities.

Their model is based on ‘caloric summer insolation’ or the total solar energy energy received at 65N in summer months, which must exceed a threshold value for deglaciation to start. This threshold value changed ~l million years ago as the world cooled, to become a function of elapsed time t. They define an effective energy E as I +bt and this can ‘explain’ (nearly) all interglacials for the last 2.6M years.

effective energy for each peak in caloric summer insolation as a function of age for the past 2.6 Myr. The numbers are the MIS values for each transition in LRO4 benthic fora stack.

However, the paper does not really explain why the model works, so it is more of a statistical fit rather than a physical explanation for Ice age termination.

So what causes the apparent hysteresis in the deeper glacial cycles for the last million years? Proposals are:

1. Delayed rock rebound
2. Dust albedo feedback
3. CO2 feedbacks
4. Some combination of the above

Here I want to propose another possibility

5. low sea levels/Increased land area. The transition from 41 ky cycles to ~100k cycles also corresponds to a threshold in low sea-levels.  There are 2 effects of ultra-low sea levels > 100m  below today. Firstly the global land area increases significantly by up to 30%.  Land surfaces warm far more rapidly with increasing insolation than do the oceans. Europe and Indo-China both increase in size dramatically at LGM. The Bering land bridge closes the Pacific from the Arctic, and Florida triples in size

Indo-China

Secondly, ocean circulation is dramatically changed once levels fall below 100m. For example there is now just one narrow channel entrance from the Atlantic to the Arctic. Tidal mixing also becomes stronger and is amplified by obliquity.

Bathymetry of the Arctic Ocean curtesy NOAA. The 100m contour shows the sea level 20,000y ago (essentially most of the light green area) and the 1000m contour shows the maximum depth of sea ice.

Overall the world has been cooling for the last 5 million years from a climate where sea-levels were on average 20 meters higher than now. We can see this simply by inverting the LR04 ice volume data and then calibrated it to match the LGM.

5 million years of sea-level change. The top curve is the obliquity of the earth’s orbit which was the metronome for glacial cycles until a threshold was crossed.

The threshold between the 41k world and the 100k world now appears as a minimum in sea-level rather than a maximum in ice cover, which makes more sense to me. A greater expanse of exposed land surface during a NH summer maximum leads to more absorbed energy near ice sheets and faster melting. Dust on the ice sheets then aids the melt back by increasing albedo.  We need a model to determine which picture fits best!

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## GHCN August 2018 temp = 0.69C

Global temperatures for August 2018 were 0.69C based on merging GHCNV3 and HadSST3, and using spherical triangulation. The baseline for temperature anomalies is 1961-1990.

The annual average so far (8 months) for 2018 is 0.66C. 2018 is continuing a post el Nino cooling correction.

The blue line shows a 0.125C per decade warming trend. The spatial distribution of temperature anomalies is shown below.

 a) NH b) SH
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