Glacial Cycles, part 2

In the previous post (also this) we established that without doubt, astronomical cycles — in particular, changes of obliquity (earth’s axial tilt) and precession (the relationship between the seasons and closest approach to the sun) — are related to the growth and decay of glacial ice. The question remains, why?

Neither of those factors affects the total energy the planet receives from the sun, either over an entire year, or over a season (seasons being defined by the progress of earth along its orbit). But they do affect how the solar energy we receive is distributed throughout the year — whether the summer/winter contrast is more or less extreme — and how the solar energy is distributed over the globe — whether the equatorial-polar contrast is more or less extreme, and whether the north-south contrast is more or less extreme.

Incidentally, there is one astronomical cycle which does affect the total energy we receive from the sun, averaged over the whole year and over the whole globe: the cycle of eccentricity of the earth’s orbit. If the solar constant is S, and orbital eccentricity is e, then the annual average insolation over the entire globe is

E = S/(4 \sqrt{1-e^2}).

For zero eccentricity, insolation is S/4, which is about 340 W/m^2 (for a solar constant of about 1360 W/m^2). A change in eccentricity causes a change in global annual average climate forcing (through a change in solar insolation), with increasing eccentricity leading to increased climate forcing.

But the eccentricity effect is small. Eccentricity varies between a minimum of near zero, and a maximum of slightly less than 0.06. If eccentricity is as high as 0.06 and the solar constant is 1360 W/m^2, then eccentricity enhancement inflates insolation from 340 W/m^2 to 340.61 W/m^2. But even that insolation increase of 0.61 W/m^2 is reduced by the albedo of the earth, to about 0.43 W/m^2 climate forcing. If climate sensitivity is 0.75 deg.C/(W/m^2), that would cause global warming of a mere 0.32 deg.C, not enough to trigger either glaciation or deglaciation.

Nonetheless, eccentricity has been proposed as the reason behind the roughly 100,000-year cycle of glaciations since the mid-Pleistocene transition (MPT, about 800,000 years ago) — it may be a driver of those cycles, or just a pacemaker. The idea has been around for quite a while, see e.g. Imbrie & Imbrie (1979, Ice Ages, Solving the Mystery, Harvard Univ. Press, Cambridge, MA).

But there are some difficulties with the attribution to eccentricity. For one thing, the physical mechanism for such an influence is unclear, the direct forcing of less than 0.4 W/m^2 (since eccentricity hasn’t been as high as 0.06 for at least five million years) isn’t enough to do the job. Also, eccentricity variations show an even stronger 400,000-year cycle which has not been detected in paleoclimate data (the “stage-11 problem”). And, there is uncomfortable mismatch between the phases of the glacial and eccentricity cycles, glacial cycles peaking before the peak in the eccentricity cycle (the “causality problem”).

Ridgwell et al. (1999, Paleoceanography, 14, 437-440) suggest that recent deglacial terminations may be principally due to precession, with nonlinear response leading to terminations every fourth or fifth cycle. Wunsch (2003, Climate Dynamics, 20, 353-363; and 2004, Quaternary Science Reviews, 23, 1001-1012) has suggested that the phenomenon is not a cycle at all, but a characteristic timescale due to stochastic behavior of the climate system. Meanwhile, Huybers & Wunsch (2005, Nature, 434, 491-494) have established rigorously a relationship between the timing of recent deglaciations and the obliquity cycle, but did not find a similar relationship for either the precession or eccentricity cycles.

So, one puzzle about glacial cycles is why, around the MPT, did the cycles change from a predominant 41,000-year cycle to around a 100,000-year cycle? Also, what’s the root cause of the roughly 100,000-year cycle? If it’s eccentricity, what mechanism is in play and why doesn’t the 400,000-year cycle show in glacial cycles? If it’s not eccentricity, what is it?

Although obliquity and precession changes don’t influence global insolation, they can have a profound impact on local insolation. Precession causes major changes (up to 100 W/m^2) in the amount of insolation at various times of year, depending on the latitude of the observer. It doesn’t change the annual average for any location, but it strongly impacts the winter/summer contrast. Hotter summers lead to more ice melt, colder winters lead to less snowfall, both of which tend to waste ice sheets. It’s worth noting that precession influences the two hemispheres oppositely: when we’re closest to the sun in northern hemisphere summer, it’s southern hemisphere winter, leading to more extreme northern seasons but less extreme southern seasons.

Obliquity actually does affect the annual average insolation at a specific location. Higher obliquity brings more energy to the poles and less to the equator, in addition to making the seasons more extreme. And, obliquity affects both hemispheres the same way — greater obliquity brings more total heat, and more extreme seasons, to both poles at the same time.

The most prominent theory about how astronomical cycles affect the growth and decay of ice sheets is through insolation at high northern latitude around midsummer (usually taken to be June 21st at 65N latitude). There’s considerable observational evidence of a powerful impact of summer heating on ice sheet mass balance from more than a century of glaciological field studies (summarized in Denton et al. 2005, Quaternary Science Reviews, 24, 1159). Yet midsummer (or most times of year) insolation at high latitudes (in fact at most latitudes) is dominated by the precession rather than obliquity cycle, while obliquity dominates global ice volume changes.

This leads to another major puzzle: why are cycles in global ice volume dominated by the 41,000-year obliquity cycle (especially prior to the MPT) with very little influence of the precession cycle, when midsummer insolation is dominated by precession with far less influence of obliquity?

I’d like to mention two prominent ideas about these questions. One is that of Huybers, that the driver for glacial changes isn’t midsummer insolation, but “summer heat,” defined as the integrated insolation during the time of year that insolation exceeds a critical threshold value. For many choices of threshold value, this is more influenced by obliquity than precession. In fact for the right threshold value, it much more closely mimics annual average insolation, which isn’t affected by precession at all.

This might explain more than just the dominance of obliquity over precession in global ice volume, it may also explain (in part) the change in the character of glacial variations since the MPT. Annual average insolation varies strongly with the obliquity cycle at high latitudes (with increased obliquity increasing insolation), and near the equator (where increased obliquity decreases insolation). Here’s the latitude-dependent change in annual average insolation for an obliquity increase from 22 deg. to 24.5 deg. (about its range of variation over the last five million years):

At about latitude 44N, the change in annual average insolation due to obliquity is zero. For a range of threshold values, the variations in “summer heat” show a similar decline as one gets farther from the pole.

Because of the gradual overall cooling over the last five million years, during recent (since the MPT) glaciations the northern hemisphere ice sheets have been much more extensive than before. Most ice ablation occurs near the edge of the ice sheet; since the larger ice sheets post-MPT extend so much further south, they suffer far less increased insolation due to obliquity (or summer heat), which significantly mutes its influence. Thus the strict obliquity control pre-MPT has given way to more influence of other factors, including precession.

Another fascinating idea is related to the fact that, while obliquity affects both hemispheres synchronously, precession affects the hemispheres oppositely. This motivated Raymo et al. (2006, Science, 313, 492-495) to suggest that precession does affect glacial cycles significantly, but prior to the MPT it affected the two hemispheres oppositely so to a large degree they cancel each other out in influencing global ice mass — the gains or losses of one hemisphere offset the losses or gains of the other.

For the southern hemisphere (in particular, Antarctica) to respond strongly enough to counteract a significant part of northern-hemisphere changes, requires greater fluctuation in Antarctic ice. Raymo et al. suggest that prior to the MPT, the East Antarctic ice sheet didn’t always extend all the way to the coast, so the “ablation zone” was land-based rather than ocean-based. This allows for much more variation in Antarctic ice in response to insolation, which allows for strong precession influence on ice sheets but with opposite signs in opposing hemispheres, so global ice volume shows far less precession influence.

Since the MPT, they suggest, the ablation zone of the East Antarctic ice sheet has been ocean-based rather than land-based. Therefore it’s less affected by insolation changes, and far more affected by sea level changes — rising sea levels can “unpin” the ice and contribute to its decline, while falling sea levels extend the land area and the ice sheets expand to reach the (more distant) sea. Hence the northern hemisphere fluctuations, by altering sea level, are a primary driver of southern glacial ice, so the two hemispheres response to precessional changes in synch rather than out of.

I’ll close with one final idea. When obliquity increases, and the poles tilt more toward the sun, more of the incoming sunlight strikes polar regions, which is where we find most of earth’s ice and snow. Ice and snow are highly reflective, so increasing the insolation in polar regions increases earth’s albedo (net reflectivity of incoming solar radiation). This decreases climate forcing even when insolation is unchanged, in fact increased obliquity reduces climate forcing. I’ve calculated, using seasonal and geographical albedo data from ERBE (Barkstrom et al. 1990, EOS Transactions, American Geophysical Union, 71, February 27) that an increase in obliquity from 22 to 24.5 degrees changes albedo enough to change climate forcing by about -0.83 W/m^2. Of course, this is under present albedo conditions, it doesn’t account for changes in the cryosphere which lead to albedo feedback.

That’s not a lot — it’s less change than present greenhouse-gas forcing — but it’s not zero either.


18 responses to “Glacial Cycles, part 2

  1. Didn’t jim hansen have a paper that discussed N. Hemis. insolation and glacial advance and retreat ?

  2. I think something key to consider with the ice albedo feedback is where the tilt progressively moves tilting the earth it melts ice at the fringes first and the potential glacierized zone moves northward thereby reducing the potential for the ice albedo forcing.

  3. Figure 2 doesn’t appear, only an “x” sign instead…

    [Response: ??? There’s only one figure, and it shows for me. Do others see the figure? Do others see an “x” sign?]

    [Response 2: I found the problem. I had left a “placemarker” image tag in the post, which doesn’t show on my browser. It should be fixed now.]

  4. Quite interesting. Takes me back to a meeting in 1987 I had with George Denton, Terry Hughes and Sykuro Manabe. The topic of the latitudinal variation of the solar forcing was the focus. To test the resultant latitudinal impact I proposed we examine the snowline from Alaska to Patagonia today versus the late Wisconsin. The result showed a rather uniform shift in snowline elevation for glaciers regardless of latitude. This was not in agreement with the CLIMAP reconststrucitons of limited tropical latitude warming. Five years later updated tropical temperature reconstructions were completed that showed a relatively consistent temperature change with latitude in the late Wisconsin. The work was then published in Paleo3

  5. Horatio Algeranon

    What’s the status of the idea that the change of the earth’s orbital inclination might be involved?

    Muller and MacDonald surmise that when Earth’s orbit reaches a certain plane, the planet plows through an extra-thick cloud of interplanetary dust. These small particles drift through the upper atmosphere and set in motion a series of climatic effects, perhaps blocking out sunlight, stimulating cloud growth, or weakening Earth’s ozone layer. Such factors cool the planet enough to produce an ice age. Later, as the planet’s orbit pulls out of the dust, the climate warms enough to fight back the ice.

    Ice ages and astronomical causes: data, spectral analysis and mechanisms (Richard Muller, Richard A. Muller, Gordon James MacDonald) develops this idea.

    [Response: It never gained much traction. It has several problems, especially that it requires an unrealistic lag (over 30,000 years) between the supposed driving cycle and the response. Berger (1999, International Journal of Earth Sciences, 88, 305-316) had this to say:

    The ice-age hypothesis of Muller and MacDonald (1995, 1997a, 1997b) has two parts: (a) The 100-kyr cycle does not owe its existence to Milankovitch forcing; and (b) variations in inclination of Earth’s orbit (i.e., the orbit’s angle with the solar system invariable plane) provide the mechanism sought. In support of the first proposition, Muller and MacDonald point to the paradox that the spectrum of oxygen isotope series from deep-sea sediments contains no power for two prominent eccentricity cycles, 125 and 400kyr. In support of the second proposition, they offer a match between the SPECMAP record (Imbrie et al. 1984) and a plot of the amplitude of orbital inclination, shifted by 33kyr. The hypothesis of Muller and MacDonald is rejected in both parts, although an influence of inclination forcing is not precluded entirely. The paradox of the missing eccentricity cycles (125 and 400kyr) is explained by suppression of the two longer cycles, and enhancement of the one near 96kyr, as a result of internal oscillation. A Muller-MacDonald machine for making the 100-kyr ice-age cycles, however conceived, would have to have a memory near 30kyr to provide for phase shift between input and output. Precisely this amount of memory is sufficient to produce the needed oscillation in Milankovitch machine here applied; thus, there is no advantage, from the point of view of either necessity or simplicity, in replacing Milankovitch forcing, with its precise phasing (despite the fuzzy physics), with inclination forcing, and with its severe problems in phasing (and, thus far, no physics at all).

    Also, I have some doubts about Muller & McDonald’s spectral analysis of the SPECMAP stack.]

  6. tamino –

    Many thanks for these posts. As usual, your expositon is wonderfully clear and a delight to read.

    Do you have any comments on the idea that the 100,000 year feature is set by a phase locking mechanism, a la Tziperman et al.? If I understand this concept correctly, such a mechanism would require that there be a ‘natural frequency’ of the Earth system near the weakly forcing orbital frequencies. What might be the essential processes that would set such a natural frequency?

    [Response: I’m definitely out of my depth here, but I’ll speculate anyway.

    Wunsch (possibly also with Huybers?) has constructed models in which post-MPT deglaciation requires a sufficient buildup of ice mass to be triggered. This happens on a roughly 100,000-year timescale, but the *trigger* mechanism is still obliquity/precession forcing. This explains both the timescale, and the correlation of the timing of deglaciations with obliquity and precession cycles (the obliquity correlation is firmly established, the precession correlation isn’t).

    Meanwhile, Raymo & Lisiecki have done a time-frequency analysis of the LR04 stack (using windowed Fourier analysis, and I’ve reproduced their results with wavelet analysis) which shows that prior to the MPT, the amplitude of the obliquity/precession *response* increases and decreases with the amplitude of the obliquity/precession *forcing*. This argues strongly that pre-MPT, these cycles weren’t just pacemakers but actual drivers of glacial cycles. However, the forcing/response amplitude correlation breaks down post-MPT, which suggests that they may be acting more as pacemakers than drivers.

    What I haven’t seen (but my knowledge of the literature is limited) is a physical mechanism behind all this — which is kind of what you really asked about! It all seems highly speculative to me.]

    • David B. Benson

      Palliard, D. (1998) The timing of Pleistocene glaciations from a simple multiple-state climate model, Nature, 391, 378–381 offers a hypothesis, the one used in Archer & Ganopolski (2005).
      The idea is that there are threshold values in summer insolation and also in ice volume which trigger changes between the three states, interglacial, moderate ice and maximum ice.

  7. But the eccentricity cycle hasn’t also (in addition to global annual insolation) an influence on regional/seasonal insolation, because in a more eccentric orbit the seasons are more extreme than in a circular orbit?

    [response: Indeed, but that influence is taken into account in the definition of the precession factor. It’s defined as

    p = e \sin(\bar \omega),

    where e is the eccentricity and \bar \omega is the angle between the astronomer’s definition of precession and the longitude of perihelion. Hence changes in e surely affect climate, but this is called part of the “precession” influence in the literature. The possibility of eccentricity control on the 100,000-year cycle of recent glaciations are hypotheses about the impact of eccentricity alone (apart from its influence on the precession factor).]

    • Tamino, the eccentricity has a 100 ooo year period and the more eccentric is the orbit, seasons are more extreme.

      Even if eccentricity is included in the definition of the precession factor, the 100 000 year cycle still has an influence on seasonal insolation, independent of the precession cycle.

      The question is: how significant is the influence of the 100 000 year eccentricity cycle on seasonal insolation?

  8. One thing you didn’t mention was any climate effects of the whole solar system’s passage about the milky way.

    I found one article that says that this cannot explain some long term climate cycles (they are not talking about the apparent shorter-term cycle of ice ages).

    It’s something worth mentioning in the post, since many people know that the solar system moves through the milky way, and that different areas of the milky way might have different characteristics that would affect earth’s climate. But at the same time, they might not know the timescales involved, and whether it bears upon the cycle of ice ages. I didn’t know, so I just googled a bit.

  9. “Precession” in the Solar system can refer to 1) the wobble of Earth’s rotational axis, or 2) the advance of its perihelion point around the sun. Or the same for another planet. The Milankovic cycle analyses I’ve seen attribute climate effects to the first, but you seem to have the second in mind. Could you clarify what’s going on here?

    [Response: The climatological definition of precession involves both. It’s the difference between the longitude of the rotational axis and the longitude of perihelion. That’s why its dominant periodicity (~22000 yr) is different from that of the “precession of the equinoxes” (~26000 yr).]

  10. Every now and then, I get hit with the “CO2 lags temperature” talking-point.

    Wonder if this explanation makes sense.

    During the depths of a glacial period, ice covers a greater fraction of the NH than the SH (due to the fact that it’s easier for ice-sheets to grow over land than open water).

    That means that as the Earth’s tilt increases (increasing summer insolation at the higher latitudes), the SH will absorb more of the solar energy during summertime than the NH will (due to the fact that open water has a much lower albedo than ice/snow).

    Thus, the SH will start warming earlier/faster than the NH. The SH warming causes the Southern Ocean to warm and outgas CO2 (as well as other dissolved gases) into the atmosphere. The additional CO2 spreads the warming to the NH, helping to melt the great NH ice-sheets. Without the additional CO2, it might be difficult for the additional summer insolation alone to melt the ice-sheets (because so much of the solar energy gets reflected away when the ice-sheets are at their maximum extent).

    So you have SH warming first, followed by increased atmospheric CO2 levels, and then NH warming.

    This seems consistent with what I’ve read about the NH lagging the SH during glacial to interglacial warming phases.

    To those out there who know a lot more about paleoclimatology than I do, does this make sense?

    [Response: It seems to me that warming of the oceans in either hemisphere will lead to outgassing of CO2. Also, if I recall correctly there’s a nontrivial amount of CO2 trapped in air bubbles in the ice sheets, and as they disintegrate that too is released to the atmosphere. There’s also permafrost, and as the permafrost line moves poleward considerable CO2 can be released. I guess there’s no shortage of ways that warming can cause CO2 increase. I like to emphasize that in this case of CO2 and temperature, causation goes both ways.]

    • David B. Benson

      Makes sense.

      What is well established comes from benthic cores in the Pacfic Warm Pool: at the end of LGM first the deep ocean warmed, followed by the shallow ocean; CO2 started upwards ~700 years later.

  11. Pete Dunkelberg

    Orbital forcing of methane too?

    “Critically, our simulations capture the declining trend in methane concentrations at the end of the last interglacial period (115,000–130,000 years ago) that was used to diagnose the Holocene methane rise as unique. The difference between the two time periods results from differences in the size and rate of regional insolation changes and the lack of glacial inception in the Holocene. Our findings also suggest that no early agricultural sources are required to account for the increase in methane concentrations in the 5,000 years before the industrial era.”

  12. Halldór Björnsson

    Thanks for a very good sequence of posts on this. For a long time my feeling has been that the simplest explanation for the mid pleistocene transition (to 100Kyr cycle) is the background cooling, ongoing throughout the pleistocene (The obvious explanation for which is a steady decrease in atmospheric CO2). Andre Berger and coworkers did some nice work in the late 1990s showing that a model of theirs was able to reproduce the 41K to 100K switch as the background CO2 concentration was lowered. The 100K frequency came about as a combination of precession and obliquity frequencies. Their 1999 Quat. Sci. Rev. paper (Berger, Modelling northern hemisphere ice volume over the last 3 Ma) can be downloaded from science direct. Hezi Gildor and Eli Tzipperman have also published similar ideas. -The detailed mechanisms in these models vary, but the crux of these ideas is that given enough cooling sufficient ice mass can be built up fast enough for the ice sheets to loose phaselocking to 41K.
    There is a readable review paper on the 100K transition by Ridgewell and Maslin published in 2005 (Mid-Pleistocene revolution and the ‘eccentricity myth’; the preprint can be found here:

    I still haven’t seen a study that examines these models and finds the simplest physical model that will produce the 100K transition as a result of background cooling.

    [Response: Thanks for an interesting reference.]

    • David B. Benson

      Halldór Björnsson | February 5, 2011 at 11:55 pm — Exactly what Tamino responded.

    • I found these two articles helpful (traced from David B. Benson’s tip, above):
      GLACIAL CYCLES: TOWARD A NEW PARADIGM (the basics of Paillard’s model, plus a nice historical perspective)

      in which the authors conclude: “…that in spite of the importance of understanding the natural carbon cycle, the solution to the mystery of the glacial/interglacial CO2 cycles still eludes us.” This article was published in 2000; I’m still looking updates. (By the way, the article contains a nice section called “A MODEL OF THE OCEAN CARBON CYCLE: A GEOCHEMICAL PRIMER”.)