Simple rule accounts for onset of ice age deglaciations over the past three million years

The sequence of ice ages followed by warm interglacials has been the dominant force in creating, extinguishing and changing nature and life on Earth for the past three million years. Understanding what causes these climate cycles is fundamental to understanding the global climate in the past and present. A recent study has created a simple mathematical rule that can account for the timing of the onset of interglacials following ice ages over the past three million years. The rule is based on predictable long-term astronomical variations in the Earth’s orbit and tilt called Milankovitch cycles, without any knowledge of atmospheric greenhouse gas concentrations, ice sheet dynamics, volcanism, cosmic rays, dust or other climate data. This study supports the orbital theory for glacial/deglacial cycles, but still leaves many open questions regarding the underlying physical mechanism by which the great ice sheets wax and wane.


For most of the Northern Hemisphere ice ages, from 3 to 0.8 million years ago the Earth’s climate varied between cold glacial and warm interglacial periods with a 41,000 year cycle. But about 800,000 years ago the glacial/interglacial cycles changed to what is referred to as the “100,000 year cycle”. The paleoclimate record, which is comprised of data from Antarctica and Greenland ice cores, marine sediment cores, cave calcite cores, and other sources, provides information about regional surface temperature, global atmospheric greenhouse gas concentrations, primary vegetative production, and ocean current strength.

Ice age terminations and insolation 65 N Tzedakis
Ice ages and terminations (a) Temperature proxy from sea floor ice cores (b) Daily mean insolation on 21 June at 65° N. Numbers at the top denote Marine Isotope Stages (MIS). Black arrows denote interglacials. SOURCE Tzedakis et al.

This record, which stretches back 800,000 years over multiple glacial/interglacial cycles in the case of the Antarctica ice core record, shows that the “100,000 year” cycle is not constant but varies between 84,000 and 120,000 years. It also reveals that the cooling/warming cycles are asymmetric. Cold periods are longer than the warm interglacial periods which average only 20,000 years in duration. At the present there are no generally accepted physical explanations for what causes the glacial/deglacial cycles. There have been attempts to explain the cycles based on solar variability linked to sunspots, astronomical variations in the Earth’s orbit and tilt, cosmic rays, volcanism, ice sheets dynamics, greenhouse gases, atmospheric dust, and ocean currents.


In 1941 Milutin Milankovitch published a book in which he hypothesized that the cycle of glacial/interglacial periods is controlled by variations in incoming solar radiation (insolation) which are determined by small, predictable changes in the Earth’s orbit and tilt with respect to the sun. This theory is referred to as the orbital theory and the astronomical cycles that cause this effect are called Milankovitch cycles. According to the orbital theory, changes in the total amount of summer heat radiation from the Sun teaching the Earth in the high-latitudes of the Northern Hemisphere are responsible for the glacial/interglacial cycles through their warming of Northern ice-sheets.

Most of the Earth’s land mass is in the Northern Hemisphere and during ice ages great ice sheets form in high northern latitudes, growing in winter and melting in summer. Small variations in the Earth’s orbit and tilt affects the amount of heat that the Northern Hemisphere receives which can vary by as much as 25%.  Milankovitch hypothesized that variation in the total amount of solar energy received in summer in the high latitudes of the Northern Hemisphere is responsible for the sequence of glacial/deglacial cycles observed over the past 3 million years.

The Earth’s poles, which are tilted about 23° from the vertical, mark out circles over the course of about 26,000 years. This is called precession and is the reason why thousands of years from now the north pole will no longer point at the “pole star”. In addition the Earth’s orbit is not exactly circular, it actually is an ellipse, which means that the distance between the Earth and the Sun varies. Thirdly, the angle between Earth’s tilt and the vertical is not constant. This is called obliquity and varies between 22.1° and 24.5° with a period of about 41,000 years.

The ellipticity of the Earth’s orbit, the variation in the direction of its axis (precession), and its tilt (obliquity)can be calculated over the past several million years from Newton’s laws. To account for the combined effects of precession and obliquity, Milankovitch used ‘caloric summer half-year insolation’, which is a measure of the total amount of solar energy received over summer at 65° N.  Milankovitch found that near 65° N, precession and obliquity are equally important and ellipticity is less important in determining the variation in the ‘caloric summer half-year insolation’.


The first experimental support for the Milankovitch hypothesis was a 1976 article by Hays, Imbrie and Shackleton. From an analysis of deep sea sediment cores it found evidence of the 41,000 and 26,000 year cycles in the marine sediment record. However, it concluded that orbital forcing theory was not able, by itself ,to explain the observed dominant 100,000-year glacial/deglacial cycle.

In 1997 a paper by Raymo et al. was the first to provide broad empirical support for the orbital forcing hypothesis. In this study the temperature record estimated from temperature proxies in deep sea sediment cores from eleven sites, from three oceans in both high and low latitudes and including eastern and western equatorial regions was analyzed. By comparing the temperature proxy record from the ocean sediment cores with the calculated summer insolation at 65° N for six of the glacial terminations, Raymo et al. concluded that all the terminations correlated with periods of increased summer solar radiation calculated from orbital theory. But it was also found that deglacial warming did not always correlate with a period of greatest increased northern solar radiation. The researchers concluded that other factors must be taken into account to explain the dominant glacial/deglacial cycle. It was suggested that once large ice sheets had developed, as a result of low temperatures for about 100,000 years, the first warming of any note caused the ice mass to melt catastrophically, triggering global warming and deglaciation. In other words the interaction between orbital variations and the extent of northern ice sheets was responsible for the pattern of ice growth and decay over the last 800,000 years.

Accounting for the onset of interglacials

Once it was clear that orbital theory by itself was unable to account for the observed glacial/deglacial cycles, researchers proposed rules that take into account other variables besides the astronomical variations in the Earth’s orbit. For example, following up on Raymo’s suggestion, in 2004 Parrenin and Paillard formulated an empirical rule based on the premise that ice volume and increased solar raditation together trigger deglaciations. Parrenin and Paillard’s rule requires as input the variation in the June solstice insolation at 65° N and the growth in the global ice volume computed from a simple model. The rule predicts that a deglaciation occurs when solar radiation is moderately warming if the ice volume is very large, or reciprocally when the ice volume is moderate if warming from solar radiation is very large. Parrenin and Paillard reported that their rule not only reproduces sea level transitions at the correct time, but also sea level minima and maxima with the right amplitude. A disadvantage of the Parrenin and Paillard rule is that it requires some way of modeling ice sheet growth.

Recently Tzedakis et al have formulated an empirical rule that requires no input data other than ‘caloric summer half-year insolation’ which can be calculated from astronomical theory. Their analysis found that before about one million years ago interglacials occurred when the energy from summer solar radiation exceeded a simple threshold, which occurred about every 41,000 years. But over the past one million years, the record shows that fewer of these insolation peaks resulted in deglaciation. This suggested to the researchers that the energy threshold for deglaciation had risen. In addition as the ice sheets grew the threshold for a complete deglaciation decreased. They modeled this as the elapsed time since the onset of the previous interglacial. Tzedakis et al. formulated this in a simple rule that only requires as input the ‘caloric summer half-year insolation’ peaks. The parameters of the rule, the insolation threshold and the rate this threshold decays with time since the last deglaciation, were determined using a statistical algorithm.

The rule is able to account for the onset of all deglaciations over the past three million years. The Tzedakis rule accounts for the dominance of glacial–interglacial cycles with a period of 41,000 years early in the Quaternary and for the change to the “100,000-year cycle” about one million years ago. It suggests that the appearance of larger ice sheets over the past million years was a consequence of an increase in the energy threshold required to initiate deglaciation.

It must be borne in mind that this is a purely statistical rule and does not explain the physical mechanism by which the ice sheets grow and contract. Whatever the underlying causes, the study suggest that a climate transition and a gradual rise in the deglaciation threshold led to longer glacial/deglacial cycles. The emergence of longer glacials then allowed the accumulation of larger and increasingly unstable ice sheets that required lower summer insolation peaks to initiate rapid, catastropic deglaciation.


A simple rule to determine which insolation cycles lead to interglacials, P. C. Tzedakis, M. Crucifix, T. Mitsui & E. W. Wolff, Nature 542, pp427–432 (23 February 2017) doi:10.1038/nature21364

A. Berger, M.F. Loutre, Insolation values for the climate of the last 10 million years, Quaternary Science Reviews Volume 10, Issue 4, 1991, Pages 297-317,

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