Home > paleoclimate, Research Papers > Huybers 2006b: A Summation of Summer Days

Huybers 2006b: A Summation of Summer Days

2011 January 24

There’s wide agreement with Milankovitch that variations in total and regional insolation due to the evolution over time of Earth’s orbital parameters – eccentricity, obliquity, and precession – broadly drive the glacial and interglacial climate states of the last million years or so. But there remains considerable discussion of exactly how these mechanisms work. And, frankly, the fact that the most dramatic and obvious feature of the Earth’s climate – the advance and retreat of the glaciers of the ice ages – remains in many ways a mystery should give a pause to all who are interested in climate modeling that extends beyond a few decades.

Before going further, a quick visual guide to eccentricity, obliquity, and precession.



Huybers took a shot at the answer in Science in 2006 in Early Pleistocene Glacial Cycles and the Integrated Summer Insolation Forcing. He introduces the paper recounting Adhemar’s argument about longer Southern Hemisphere winters. (Adhemar predates Milankovitch by 60 years) Croll argued that decreased insolation leads to glaciation. But Milankovitch tagged summer insolation (the lack of it, that is) as the culprit. Huybers expands on Milankovitch.

Huybers notes that precession controls the intensity of summer insolation. But Late Pliocene and early Pleistocene glacial cycles don’t correlate well with precession – their glacial episodes correlate better with obliquity.

The Abstract

Long-term variations in Northern Hemisphere summer insolation are generally thought to control
glaciation. But the intensity of summer insolation is primarily controlled by 20,000-year cycles in the
precession of the equinoxes, whereas early Pleistocene glacial cycles occur at 40,000-year intervals,
matching the period of changes in Earth’s obliquity. The resolution of this 40,000-year problem is
that glaciers are sensitive to insolation integrated over the duration of the summer. The integrated
summer insolation is primarily controlled by obliquity and not precession because, by Kepler’s second
law, the duration of the summer is inversely proportional to Earth’s distance from the Sun.

Echoing Budyko in some ways, Huybers lays out an argument for linking TOA insolation and temperature based on modern empirical data. So how best to link insolation to the ablative process that would control the growth and retreat of glaciers?

A good measure of air temperature’s influence on annual ablation is the sum of positive
degree days (22, 23), defined as S = SUM(alphai*Ti) where Ti is mean daily temperature on day i and alphai is one when Ti >= 0C and zero otherwise

(I need latex)

In other words, only count the energy contributions from above freezing days. Those days will contribute to ablation.

A quantity analogous to S can be defined for insolation. For latitudes between 40 to 70N, the temperature is near 0C when insolation intensity is between 250 and 300 W/m2 (Fig 1C), and tau = 275 W/m2 is taken as a threshold (24).

Now that we have a method to sum summer days, we need a method to calculate changes in ice volume.

So far, only modern observations have been used to argue that summer energy is a better indicator of glacial variability than insolation intensity. It remains to test this result against past glacial variations. Changes in summer energy are expected to correspond to rates of ablation and thus are most directly compared against rates of ice volume change (27). After smoothing using an 11-ky tapered window, the time derivative of a composite d18O record is used as a proxy for ice volume change (28). Importantly, the age model for the proxy record does not rely upon orbital assumptions.

There is an excellent correspondence between summer energy at 65-N and the rate of ice volume change. …

And on the summary …

The amplitude of the summer energy and rates of ablation show less agreement during the late Pleistocene (r^2 > 0.4) than during the early Pleistocene. The most rapid ablation events, known as terminations, follow periods of greatest ice volume (32), suggesting that the sensitivity to summer energy depends on the amount of ice volume. To quantify this effect, the amount of ice volume is estimated with the use of d18O 10 ky before peak ablation, and sensitivity is defined as the ratio between the amplitude of ablation and the amplitude of the local maximum in summer energy nearest in time. A significant correlation is observed between ice volume and sensitivity (r^2 > 0.6). Perhaps large ice sheets are inherently more unstable (13), or perhaps they are more strongly forced by local insolation because they extend to lower latitudes.

I stumbled on the code behind this article some months ago looking for a way to calculate precisely what Huybers’ calculated. Unfortunately, he made use of a lookup table prepared by Berger 1991. I’ll be exploring this code a bit over the next few days.

Seals & Croft (1972)

  1. DeWitt Payne
    2011 January 24 at 7:42 pm

    The problem I have with the standard theory of a glacial period needing a trigger of low insolation is that the Vostok core records look like a series of impulse responses with the normal condition being glacial, not the other way around. I think it’s a matter of perception. Civilization started during the current interglacial and so everyone thinks the current conditions are somehow normal and won’t change unless disrupted. But the Vostok record looks more like something triggers an interglacial which then decays back to glacial. Then there’s the 100,000 year problem. Muller and MacDonald suggest there’s another contributor, orbital inclination.


    The rate of change of ice volume tracks the Milankovitch cycles quite well except for the glacial/interglacial transitions. Then the change in ice volume is much larger than expected in both directions.

    Then there’s Ruddiman, who believes that if we hadn’t invented agriculture and increased methane levels and significantly changed land use/land cover 8,000 years ago, we would already be well on our way to a glacial period.

  2. 2011 January 24 at 8:19 pm

    Cool read. Orbital inclination crossing planes of dust accretion, causing increased snowfall (or cloud cover?).

    Have to admit that the 100Kyr seems an unlikely coincidence. But the solar dust cloud (and subsequent cloud seeding) represents a big ‘maybe.’

    Agree with you that glaciation is the Quaternary baseline. Huybers is arguing from the position of ‘what causes of the melting’ not so much ‘what causes the glaciation.’

    Also agree that the interglacials look like an impulse response – quick on the upslope, slow on the decline.

    Setting the stage

    Two Tertiary tectonic events proved to have major implications for Earth’s climate. First, around six million years ago, the Panama Seaway closed, separating the Pacific and Atlantic Oceans. This increased the salinity contrast between the two oceans, which worked to strengthen the thermohaline circulation that brings warm waters and moist air masses to the higher latitudes. Second, the uplifts of the Himalayan and Rocky Mountains caused greater “meandering” of the jet stream and the midlatitude storm tracks that bring moisture to the far north (i.e. before the mountains were born, storm tracks would not go too far north or too far south).

    The increased moisture transport to the high latitudes as a result of the strengthening of the thermohaline
    circulation and more storm track meandering allowed for the continued “greening” of the higher latitudes, as well as the growth of the Greenland and Antarctic ice sheets. More high latitude vegetation, combined with the general stabilization of Earth’s ecosystems, led to a steady decline in CO2. These lower atmospheric CO2 levels worked to amplify Earth’s response to orbital cycles, and this amplification made possible the extensive glaciation events that characterized the next period, the Quaternary


  3. Tom W.
    2011 January 24 at 9:55 pm

    Might try reading Ice Ages And Astronomical Causes by Muller and MacDonald. They really expound on the glacial cycles, the traditional Milankovitch theory and all sorts of other theories.

  4. 2011 January 25 at 6:01 am

    This is getting to be spooky. Everywhere I turn, Tamino is there. 😉

  5. Steve Bloom
    2011 April 12 at 3:04 pm

    Just a quick drive-by:

    The Muller and McDonald idea has been abandoned.

    Re the Central American Seaway, such a thing was speculated about but not proven. Current thinking is that it probably wasn’t a big influence. Major factors were atmospheric circulation changes due to uplift (Andes also), Indonesian Seaway near-closure, and continued widening/deepening of the Strait of Magellan (noting that glaciations need that deep Southern Ocean reservoir for CO2), but the big one is the continuing gradual reduction of atmo CO2, without which the glacial cycles couldn’t have initiated at all. So the biggest factor is the tectonically-driven balance between CO2 emissions (via volcanism) and sequestration (via rock weathering plus biological, emphasis on the former and noting again all of those nice new mountains).

    That website is a laudable effort, but in the same article I noticed this:

    “By 1.8 million years ago (the start of the Pleistocene epoch), things had cooled to the point where the planet was waxing and waning between glacial and interglacial cycles on a period of 41,000 years, in accordance with the
    oscillations of Earth’s obliquity cycle. These glacial cycles continued until about 1.17 million years ago, when further
    intensification of the “cold tongue” in the eastern Pacific caused the birth of the modern “Walker circulation.” This
    caused even more poleward moisture transport and reinforced the positive feedbacks described above. This
    intensified glacial growth and resulted in the establishment of the modern 100,000 year glacial cycle.”

    So the MPT is down to the Walker circulation, lagged by ~300 ky? Interesting if true, but it’s the first I’ve heard of it.

    I can’t comment directly on the impulse response idea, but as a refugee from a cold climate I would just note that winter snow/ice does more or less the same thing (slow accumulation, rapid melt). The effect is most obvious in the case of lake and river ice.


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