Huybers 2006b: A Summation of Summer Days
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.
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.