During the last few millions of years there were many alternations of glacial and interglacial times, times of expansion and contraction of the polar ice caps. During this lecture we will not discuss how we measure past ice volume: we will get to that in the upcoming weeks. This week we will look at the pattern of fluctuations in ice volume.

The changes in ice volume were cyclical, with a rather complex periodicity. Such a periodicity can be produced by adding up three wave functions, which a wavelength of about 100,000, 41,000 and 23,000-19,000 years (as in adding up the wave functions in biorhythm analysis). These waves represent increases and decreases in solar energy as seen at a specific location on Earth.

The three periodicities are well-known to astronomers, because they describe irregularities in the pattern of the Earth's motion around the Sun (and are therefore called orbital parameters). These irregularities are caused by the gravitational effects of the other planets circling the Sun.

Such irregularities cause fluctuations not in how much solar energy is received by the whole Earth, but in how much solar energy is received at a specific latitude on Earth, or in the distribution of solar energy by latitude and by season. The three periodicities are commonly called Milankovich periodicities, after the Serbian mathematician who calculated them in the 1930s, and thought they might have caused ice ages, by causing small differences in the amount of solar energy (insolation) that reaches the Earth at the high latitudes where the ice sheets form. The idea behind this theory is that in order to form a large ice sheet much snow must accumulate in the winter, which can not melt in the summer. If we thus have a fairly cool summer, but not too cold a winter, ice sheets can be expected to grow. Winter should not be too cold, because at very low temperatures the atmosphere can not contain much water vapor, so that no snow can fall.

First, we have to know how the Earth moves around the Sun, in its elliptical orbit. The earth's axis is inclined and not at right angles with the plane through the orbit. This inclination (about 23.5^o) results in the seasons: the southern hemisphere is tiled towards the Sun during its summer which occurs during northern hemisphere winter, and the reverse. Days are longer, nights shorter on the hemisphere that is turned towards the Sun. Twice a year, in the equinoxes, day and night have the same length. During the northern hemisphere winter solstice, the shortest day occurs on the northern hemisphere and the longest day on the southern hemisphere; during the northern hemisphere summer solstice the day is longest on the northern hemisphere, shortest on the southern hemisphere. This regular patterns of motion, however, is changed because of the disturbance of gravity of the Earth by the presence of the other planets.

The three orbital parameters are:

• Variation in excentricity, or ellipticity of the Earth's orbit; periodicity about 100,000 years. The shape of the Earth's orbit around the Sun varies, from an almost exact circle (ellipticity 0) to a slightly elongated shape (eccentricity 0.06). The eccentricity influences seasonal differences: when the earth is closest to the Sun, it gets more solar radiation. If that occurs during the winter, the winter is less severe. If a hemisphere has its summer while closest to the Sun, summers are relatively warm. Nowadays, the Earth is closest to the Sun in the northern hemisphere winter (causing relatively warm winters), furthest from the Sun in northern hemisphere summer (causing relatively cool summers). Note below that excentricity and precession both influence the character of the seasons.
• Variation in obliquity, i.e., the tilt of the Earth's axis away from the orbital plane. Periodicity 41,000 years. The tilt varies between 22 and 25^o, and is on average about 23.5^o. Note that obliquity describes the tilt of the Earth's axis, but not its direction of tilt. At higher tilts, the seasonality at high latitudes becomes more extreme; changes in tilt have little effect in the tropics, maximum effect at the poles.
• Precession of the equinoxes, periodicities of about 23,000 and 19,000 years. Precession is a rather complex phenomenon, which is caused by two factors: a wobble of the Earth's axis, and a turning-around of the elliptical orbit of the Earth itself. Note that the precession affects the direction of the earth's axis, not its tilt. The combined and complex wobbly motion of the Earth has the following result: the equinoxes (days of equal length of night and day) do not keep occurring during the same day of the calendar, but slowly shift. Presently, the Earth is closest to the Sun in the northern hemisphere winter, which makes the winter there less severe. In about 11,000 years in the future the Earth will be closest to the Sun in the northern hemisphere summer, making northern hemisphere summers warmer, winters colder. The precession effect thus causes warm winters and cool summers in one hemisphere, while doing the opposite across the equator.

The Milankovich theory states that ice caps at the poles increased and decreased in size as a reflection of the solar energy received at fairly high latitudes; the insolation at 65^oN is commonly used to look at the waxing and waning of ice sheets. For a nice computer visualization of how insolation changed over the northern hemispheric polar region, click here.

We have now observed in very many different records that ice volume over the last few millions years indeed waxes and wanes on the time scales of irregularities in the Earth's orbit, and that the northern hemispheric insolation, not the insolation of the southern hemisphere, appears to drive the process. For instance, we now have relatively warm winters on the northern hemisphere (because these winters occur when the earth is close to the Sun), and our winters are colder because we arecfar away from the sun when our side of the planet is tilted away from the Sun.

The fact that the history of ice volume occurred at these orbital frequencies implicates the differences in insolation in triggering ice ages, but very many questions remain.

• The orbital fluctuations can not be the whole story: over large parts of Earth's history there were no ice sheets, and the orbital character of the Earth fluctuated in the same way. We have indeed ample evidence of climate fluctuations on Earth at times that the ice sheets were much smaller than today's ice sheets, or even absent, at Milankovich periodicities. Then why did these fluctuations not cause ice ages during these earlier periods of Earth history?
• There have been changes over time in which one of the three orbital fluctuations had the dominant effect. For the last 900 to 1200 thousand years the excentricity has been dominant, before that the 40 thousand year obliquity was dominant. Why did this dominance change?
• From the climate theoretical point of view, the differences in solar heat received are very small, much too small to explain the large differences in climate. These differences largely relate to the distribution of energy over the Earth, but we have evidence that global temperatures changed during the ice ages. We therefore think that one or more positive feedback mechanisms must have enhanced the Milankovich differences in temperature.
• One possible enhancer is the amount of CO₂ in the atmosphere, which fluctuated at the same periodicity as the ice volume, and was less by about 90 ppm (parts per million) during glacial periods, as we will discuss next week. But which was cause, which was effect?
• Other possibilities include the position of the continents: since the last few million years the northern hemispheric ice sheets grew and became smaller, and they had large continents where they could spread out. But the Antarctic ice sheet has covered the Antarctic continent and shallow seas, and can not easily grow by much.

We are therefore not sure of the exact causes of the ice ages. Milankovich differences in insolation were the trigger, but many other feedback mechanisms probably operated. Some simple ones are:

1. positive feedback. When ice caps are larger, a larger surface area of the earth is white, and reflect back much heat from the sun into space, cooling down earth further, leading to enlarge ice caps, etc.
2. positive feedback. When ocean water cools, it can dissolved more CO₂ (a gas), and thus takes up more CO₂, leading to more cooling, etc.
3. negative feedback. When sea level drops, we get more land, less ocean surface. Vegetated land reflects less solar heat into space than ocean, so lower sea levels may lead to warming. When ice caps grow, sea level drops.
4. negative feedback. When ocean waters cool, less water evaporates; that means less precipitation world wide, which means lesser ice caps (made up of snow), see further point 1.

The complexity of perceived climate change in glacial-interglacial times is increasing rapidly with more and more knowledge. A more detailed knowledge of the way in which the ocean-atmosphere system works, and of the role of the biosphere in shaping climate (by its effects on the carbon cycle) is needed before we can begin to understand even this latest, best-known part of Earth history.

Measure of ice volume on Earth. Notice the increase of ice volume staring at about 3.0 Ma, and the increase in the amplitude as well as timing of the major climate swings at about 1.2 Ma.