... ice age theories
... spectra
Beginning in the early 1900s, the climate of the world began to warm. This is evident in Figure 1-1, which shows the average Earth surface temperature from 1880 through 1999. The temperature is an area-weighted average over the land and ocean compiled by the National Oceanographic and Atmospheric Administration, using an averaging technique devised by Quayle et al. ; see also . In the plot, "zero" temperature is defined as the temperature in 1950. The fine line shows the monthly temperatures; the thicker line shows the 12 month yearly averages.
The figure shows that the 20th century had a temperature rise of nearly one degree Celsius. That may not sound like a lot, but its effects are quite noticeable. In Europe, the great glaciers of the Alps, such as the Mer de Glace near Chamonix, have been in retreat, and the canals of Holland almost never freeze over, as they did in an earlier era to allow Hans Brinker to silver skate into legend. The effects elsewhere on the globe are more severe, with large areas of Central Africa, once fertile, becoming arid and no longer capable of supporting a large population. Although the reason for this warming is not fully understood, many climate scientists think it is the result of the addition of carbon dioxide and other greenhouse gases into the atmosphere by humans.
As we go back in time in search of earlier records, the historical record becomes less reliable. Fortunately, Nature has provided its own recording mechanism. As we will explain in Chapter 4, measurements of oxygen isotopes yield an estimate of ancient temperatures combined with total global ice volume — a combination which is just as interesting as temperature alone, if not more so. Data from a kilometer long core taken from the Greenland glacier, as part of the Greenland Ice Sheet Project "GISP2" , are shown in Figure 1-2. For comparison purposes, the zero of temperature scale for this plot was set to match that of the previous plot. For historical interest, we marked some events from European history.
Figure 1-2 Climate of the last 2400 years
The cool period preceding the 20th century warming is now seen as a dip that lasted 700 years. This period is now referred to as "the little ice age." (The coldest periods, near 1400 and 1700, are sometimes called the two little ice ages.) In her popular account of the history of the 14th century, historian Barbara W. Tuchman, argues that the low temperatures triggered social conflict and poor food production, and was thus responsible for hunger, war, and possibly even pestilence . Just a few centuries prior, at the beginning of the second millennium, Europe had experienced the "medieval warm period" . It was a time when civilization emerged from the Dark Ages, art and painting flourished, and the wealth and new productivity of Europe allowed it to build the great cathedrals. Some historians will attribute this flowering to great leaders, or to great ideas, or to great inventions, but it is foolish to ignore the changes in climate. Just prior to that, in the 900s, the Vikings were invading France, possibly driven from the more northern latitudes by the cold temperatures of that century. The height of the Roman republic and empire was reached during another time of unusual warmth — even higher than the warm period of today, if the ice-reckoned temperature scale is accurate.
The next plot (Figure 1-3) shows the data from the Greenland ice core back to 10,000 BC. Near the right hand side of this plot, the little dip of the little ice age is clear. Some scientists argue that global warming is not human caused, but is simply a natural return to the normal temperature of the previous 8,000 years. In fact, no one knows for sure if this is right or not. But the foundation for thinking that human effects will cause warming is substantial. Even if the recent rise in temperature is natural, human caused effects have a high probability of dominating in the near future, and within our lifetimes the temperature of the Earth could go higher than has ever seen previously by Homo sapiens.
Figure 1-3 Climate of the last 12,000 years
The dip near 6000 BC is not understood. It actually appears to be coincident with a short term increase in temperature that took place in Antarctica! So we can’t easily interpret everything in these plots, at least not without studying other records. Fluctuations are evident all over the plot, and crying to be understood.
Agriculture began about 7,000 BCE, as marked on the plot. All of civilization was based on this invention. Agriculture allows large groups of people to live in the same location. It allows a small number of people to feed others, so that the others can become craftsmen, artists, historians, inventors, and scientists.
The sudden rise at the left side of the plot, at about 9,000 BCE (i.e. 11,000 years ago), was the end of the last ice age. The abruptness of the termination is startling. Agriculture, and all of our civilization, developed since this termination. The enormous glacier, several kilometers thick, covering much of North America and Eurasia, rapidly melted. Only small parts of this glacier survived, in Greenland and Antarctica, where they exist to this day. The melting caused a series of worldwide floods unlike anything previously experienced by Homo sapiens. (There had been a previous flood at about 120 kyr, but that was before Homo sapiens had moved to Europe or North America.) The flood dumped enough water into the oceans to cause the average sea level to rise 110 meters, enough to inundate the coastal areas, and to cover the Bering Isthmus, and turn it into the Bering Strait. The water from melting ice probably flooded down over land in pulses, as ice-dammed lakes formed and then catastrophically released their water. These floods left many records, including remnant puddles now known as the Great Lakes, and possibly gave rise to legends that persisted for many years. As the glacier retreated, it left a piles of debris at its extremum. One such pile is now known as New York’s Long Island.
In the next plot, Figure 1-4, we show the Greenland ice data for the last 100,000 years. The very unusual nature of the last 11,000 years stands out in striking contrast to the 90,000 years of cold that preceded it. We now refer to such an unusual warm period as an interglacial. The long preceding period of ice is a glacial. During the last glacial, humans developed elaborate tools, and Homo sapiens migrated from Africa to Europe. But they did not develop civilization until the ice age ended.
During the glacial, not only was the temperature lower by 8 Celsius (and some estimates put it at more than 12 Celsius — the record is a superposition of ice volume and temperature), but the climate was extremely irregular. The irregularities in temperature during the glacials, the wild bumps and wiggles that cover much of Figure 1-4, are real, not an artifact of poor measurement. The same bumps and wiggles are seen in two separate cores in Greenland, and in data taken from sea floor records found off the California coast. The ability to adapt quickly during this wild climate ride may have given a substantial advantage to adaptable animals, such as humans, and made it difficult for other large fauna to survive. Maybe it was these rapid changes, and not the rapaciousness of humans, that drove the mammoths, camels, giant ground sloths and giant beavers (the size of bears) of North America extinct. Recent global warming appears negligible on this plot. However, if predictions of climate modelers are correct, global warming temperature changes will be comparable those during the ice age.
Figure 1-4 Climate of the last 100,000 years
The reliable data from Greenland go back only as far as shown in Figure 1-4. We can continue the climate plot further back by using the records from Vostok, the Russian base in Antarctica, where another ice core was drilled. The last 420 thousand years of a deuterium measurement at Vostok is shown in Figure 1-5, with the most recent 100 kyr appended from the Greenland record (which is more detailed). The temperature scale was adjusted to agree with the scale on the Greenland record.
Figure 1-5 Climate for the last 420 kyr, from Vostok ice
From this plot, it is clear that most of the last 420 thousand years (420 kyr) was spent in ice age. The brief periods when the record peaks above the zero line, the interglacials, typically lasted from a few thousand to perhaps twenty thousand years.
These data should frighten you. All of civilization developed during the last interglacial, and the data show that such interglacials are very brief. Our time looks about up. Data such as these are what led us to state, in the Preface, that the next ice age is about to hit us, any millennium now. It does not take a detailed theory to make this prediction. We don’t necessarily know why the next ice age is imminent (at least on a geological time scale), but the pattern is unmistakable.
The real reason to be frightened is that we really don’t understand what causes the pattern. We don’t know why the ice ages are broken by the short interglacials. We do know something — that the driving force is astronomical. We’ll describe how we know that in Chapter 2. We have models that relate the astronomical mechanisms to changes in climate, but we don’t know which of our models are right, or if any of them are. We will discuss these models in some detail in this book. Much of the work of understanding lies in the future. It is a great field for a young student to enter.
The ice records take us back only to 420,000 years in the past. However, oxygen isotope records in sea floor cores allow us to go further. One of the best sets of data comes from a location in the northern Atlantic Ocean known as the Ocean Drilling Project Site 607 . This site has climate data going back three million years, and is shown in Figure 1-6. But before you look at the figure, let us warn you. In the paleoclimate community, there is a convention that time is shown backwards. That is, the present is plotted on the left-hand edge, and the past is towards the right. We are going to use this opportunity to change our convention, for the remainder of the book, so that you will have less trouble reading the literature. (The literature of "global warming" scientists, in contrast, follows the other convention, which we have used up until now.) We apologize for this change in convention, but we do not take blame for it.
In Figure 1-6, the 10 kyr years of agriculture and civilization appear as a sudden rise in temperature barely visible squeezed against the left hand axis of the plot. The temperature of 1950 is indicated by the horizontal line. As is evident from the data, civilization was created in an unusual time.
There are several important features to notice in these data, all of which will be discussed further in the remainder of the book. For the last million years or so (the left most third of the plot) the oscillations have had a cycle of about 100 kyr (thousand years). That is, the enduring period of ice is broken, roughly every 100 kyr, by a brief interglacial. During this time, the terminations of the ice ages appear to be particularly abrupt, as you can see from the sudden jumps that took place near 0, 120, 320, 450, and 650 thousand years ago. This has led scientists to characterize the data as shaped like a "sawtooth," although the pattern is not perfectly regular.
Figure 1-6 Climate of the last 3 million years
But as we look back beyond a 1000 kyr (1 million years), the character changes completely. The cycle is much shorter (it averages 41 kyr), the amplitude is reduced, the average value is higher (indicating that the ice ages were not as intense) and there is no evidence for the sawtooth shape. These are the features that ice age theories endeavor to explain. Why did the transition take place? What are the meanings of the frequencies? (We will show that they are well-known astronomical frequencies.) In the period immediately preceding the data shown here, older than 3 million years, the temperature didn’t drop below the 1950 value, and we believe that large glaciers didn’t form — perhaps only small ones, such as we have today in Greenland and Antarctica.
As we end this brief introduction to the history of the ice ages, let’s again look to the future. As soon as the cycle of the ice ages was known, scientists realized that the ice age would eventually return. Some of them enjoyed scaring the public about the impending catastrophe. In Figure 1-7 we show the cover from a magazine of the 1940s showing the consequences of the return of the ice age to New York City. (One of the authors of the present book, RAM, saw this image as a child, and it made a lasting impression.) Unfortunately, the art genre of returning ice has been superceded, in the public forum, by paintings of asteroids about to hit the Earth, usually with a curious dinosaur momentarily distracted by the unusual scene. But, as we mentioned earlier, the more likely scenario for the early 21st century, is the continued gradual growth of global warming.
Figure 1 -7 The Ice Age returns to New York City
[The objective of geology is] "to confirm the evidences of natural religion; and to show that the facts developed by it are consistent with the accounts of the creation and deluge recorded in the Mosaic writings."
-- William Buckland,
Oxford Professor of Mineralogy and Geology
in The Connection of Geology with Religion Explained (1820)
To the modern reader, it may seem surprising that astronomical forces drive global climate change. In the 1950s, changes in the weather were attributed by many people to nuclear testing; in the 1990s, they were attributed to emission of carbon dioxide and other gases that enhance the Greenhouse effect. Yet in the 1840s, the obvious cause of climate change, to many people, was astronomy. It was understood at that time that the seasons were driven by astronomical causes, as is the 24 hour cycle of day and night. So when the existence of long-term changes of climate were discovered, it was natural to see if they could be attributed to astronomical forcing. This was long before the 100 kyr and 41 kyr cycles of the ice ages had been discovered.
By the 1840s, astronomers had already shown that the orbit of the earth undergoes slow changes. It is not the same ellipse this year that it was last year. The orbit would be an unchanging ellipse, if the Sun were the only source of attraction. The deviations come about because of the presence of the moon and other planets. Gravity from these objects means that the force on the earth is not a simple inverse square centered on the sun, and the natural result is that the orbit is not a simple repeating ellipse.
However the effects of the planets are relatively small. Jupiter has 10—3 of the mass of the Sun, and it is, on average, about 5 times further away. Venus, although having a mass 390 times smaller than Jupiter, comes much closer, within 0.28 AU (where the Astronomical Unit, or AU, is the average Earth-Sun distance) vs. 4.2 AU for Jupiter. Since gravity varies as 1/(distance squared), and tidal gradients vary as 1/(distance cubed), the effect of Venus is often more important than that of Jupiter. But all these effects are small enough that they can be treated as perturbations, small changes, on the classical elliptical orbit. The nice consequence of this is that the Earth’s orbit is always approximately an ellipse, and we can treat the perturbations of the planets as extra forces that gradually alter the parameters of that ellipse. For example, the major axis of the Earth slowly precesses or rotates relative to the "fixed" stars. This effect is big enough that it was discovered experimentally in 120 BC by the astronomer Hipparchus, who found differences between his own measurements and those of earlier astronomer Babylonian records.
By 1749, Alexis Claude Clairaut had shown, using Newton’s laws, that the north pole of the Earth precesses with a period of 25,800 years. So, for example, 13,000 years from now, the North Pole of the Earth will not be pointing towards the "North Star," but will be pointing away by an angle of about 47 degrees, close to the star Vega. This happens because the Sun and Moon exert a torque on the equatorial bulge of the Earth. This causes the axis of rotation of the Earth to wobble, an effect completely analogous to the wobble of a tilted top under the torque of gravity.
Precession implies that the signs of the zodiac change, or "advance." When astrology was defined, about two thousand years ago, a person born in January was said to be under the sign of Capricorn, since the sun was in the constellation Capricorn at that time. Since then, the precession of the axis of the earth has changed by 2000/26000 = 1/13 of a cycle; this corresponds to a change by about one sign of the zodiac. This means that a person who is born in January any time in the last few hundred years, was born when the Sun was actually in Sagittarius — not Capricorn. Nevertheless, following tradition, such a person is still said to be "born under the sign of Capricorn." The more educated astrologers are aware of this change, and claim that they compensate for it .
Another consequence of the Earth’s precession is that the location of the sun at the spring equinox also changes. It is presently leaving the constellation Pisces and entering Aquarius. Astrologers say that this change could have a profound effect on our lives, and it is why they talk about the future (and sometimes the present; it depends on exactly where you draw the constellation boundaries) as "the Age of Aquarius."
Evidence for ancient glaciation, including polished bedrock and erratic boulders, is extensive. But in early 1800s, the prevailing paradigm to explain these was diluvianism — belief that they were artifacts of the great flood of the Bible. According to William Buckland, one of the most widely respected geologists of the time, the goal of geology was "to confirm the evidences of natural religion; and to show that the facts developed by it are consistent with the accounts of the creation and deluge recorded in the Mosaic writings." (quoted in , page 35). A detailed scientific case for ancient glaciation was first synthesized in detail by Jean de Charpentier in the early 1830s, and the great geologist Louis Agassiz became an early convert. By 1841 Charles Lyell, and even Buckland, had been won over, and over the next 20 years, the theory of ancient periods of extensive ice became generally accepted.
Soon after the existence of the ice ages was postulated, they were attributed to these orbital changes. The first person to create a detailed theory was Joseph Adhémar, who published a book on the subject in 1842 called Revolutions de la Mer, Deluges Periodics. He believed that the 26,000 year precession cycle was the cause, and he suggested that it was the direct gravitational attraction of the sun and moon on the ice caps, a result that many scientists at the time correctly rejected as absurd.
One person who was inspired, in part, by Adhémar’s book, was James Croll. In many ways, Croll is the true hero of the astronomical theory of the ice ages. For a moving account of his life and tribulations, we urge you to read the delightful and informative book, "Ice Ages, Solving the Mystery," by John Imbrie and his daughter Katherine Palmer Imbrie . Croll was a carpenter who became disabled from an accident, and was forced to take a menial job as a janitor. But his janitorial duties were at the Andersonian College and Museum in Scotland, and there he discovered a wonderful library. He found that he could finish his mopping and polishing work early, and spend the rest of the night reading books on physics in the library. Among these was the book by Adhémar, and new calculations of the Earth’s orbit by the astronomer Urbain Leverrier (one of the discovers of Neptune). Croll taught himself advanced physics, and set to work on the origins of the ice age. He decided that the most plausible driving force changing climate was variations in insolation, the sunlight hitting the Earth. He managed to get his papers published, and his theories received favorable attention. Eventually he accepted a job at the Geological Survey. In 1876, a year after his own book was published, Croll was given the high honor of being named a Fellow of the Royal Society of London.
Croll contributed many insights that are still recognized as important. He realized that the presence of large glaciers would reflect sunlight, and that this would enhance further the chill of the ice ages. He recognized the importance of ocean currents in climate, and incorporated them into his theories. He took into account not only precession, but the changes in the eccentricity of the Earth’s orbit — an effect that can contribute a 100 kyr cycle to the glaciation (which, of course, had not yet been discovered).
But Croll published several predictions that proved to be very wrong, and that eventually caused his theory to be abandoned. Since the insolation in the Northern Hemisphere is out of phase with the insolation on the Southern Hemisphere, he thought that the ice ages in the two hemispheres would alternate, and we now know they are synchronous. He also estimated that the time since the last ice age to be 80,000 years ago, much older than the true value; we now know it ended between 14,000 and 10,000 years ago.
The insolation theory of Croll was revived in the early 1900s by Milutin Milankovitch, a Serbian originally employed as an engineer, but who had become a professor at the University of Belgrade where he taught physics, mathematics, and astronomy. He took on the riddle of the ice ages as a challenge. Ludwig Pilgrim had recently completed new and more detailed orbital calculations, and Milankovitch made use of these. He had the critical insight that insolation on the Northern Hemisphere might completely dominate, since that is the location of two thirds of the Earth’s land area. The ice ages in both the Northern and Southern Hemispheres are in synchrony because they are both driven by the same force: insolation on the Northern Hemisphere land. With this Gordian slice, Milankovitch solved the problem of alternating hemispheric ice ages.
Milankovitch then set out on the heroic task (at that time) of doing detailed insolation calculations based on Pilgrim’s orbital work. Today these calculations are an interesting task for an undergraduate to do over the course of a summer, using a desktop computer. But Milankovitch had to do all the calculations by hand, and it took him many years (interrupted by war and imprisonment — again we urge you read the book by Imbrie and Imbrie!). Milankovitch’s calculations showed (correctly) that the insolation was dominated by a 23,000 year cycle; we have modern data for this plotted on page *. Milankovitch concluded that the ice ages would be most intense when the insolation dropped below a certain threshold. Since the envelope of the insolation curve has an approximately 100 kyr cyclicity, his theory has implicit in it a prediction that such a cycle might be seen in the ice ages.
Milankovitch concluded, somewhat prematurely, that the problem was completely solved, and he devoted much of his time in later years to writing popular accounts of the ice ices, including a series of letters to a (presumably fictional) young girl. This effort did a lot to increase the public interest in the ice ages, and undoubtedly led to the artwork shown in Figure 1-7.
But Milankovitch’s theory was abandoned when precise age estimates, made possible by Willard Libby’s invention of radiocarbon dating, appeared to show that the timing of the ice ages were in conflict with Milankovitch’s detailed calculations. In retrospect, this was unfair. The Milankovitch theory actually explains many of the phenomena that we now see in the data. Do we throw out the astronomical theory of the seasons, simply because the first day of Spring is not always Spring-like? The warm weather of spring can be delayed by a month, or it can come early by a month; the important fact is that it always comes. We demand too much of a theory if we require it to predict all the details in addition to the major behavior.
In fact, it was the observations of the regularity of the ice age cycles that led to the revival of the insolation theory. Science and technology advanced, thanks to the work of many people. Harold Urey, Cesare Emiliani, and others developed and promoted the use of isotopes as proxies for changes in the Earth. The technology for obtaining sea floor cores rapidly improved. In 1970, Wally Broecker and Jan van Donk published a seminal paper that showed for the first time that the dominant variation in the ice ages was a repeating cycle of 100,000 years. This was a frequency that appeared in the insolation theory. The use of geomagnetic reversals in sea floor cores allowed an vastly improved time scale. In 1976, James D. Hays, John Imbrie, and Nicholas Shackleton published their paper showing the presence of both a 41 and 23 kyr cycle in data derived from sea floor sediments. The same frequencies were dominant in spectral analysis of the insolation. Even if the details of the theory were wrong, the presence of the same frequencies as those present in the orbits of the planets was a strong reason to revive the astronomical theory.
Although it had been resuscitated, the insolation theory continued to have problems. In the glacial data, the 100 kyr cycle dominated, with the 41 kyr cycle weaker, and the 23 kyr precession signal weakest of all. Yet in insolation theory, it is the 23 kyr cycle that dominates, with a weaker 41, and an extremely weak 100. Why were these strengths reversed? A possible answer came from the old threshold idea of Milankovitch, which had been revived by Kenneth Mesolella and George Kukla, and put into an elegant mathematical form by Imbrie and Imbrie. They showed that a nonlinear response of the climate to insolation could greatly strengthen the 100 kyr cycle, through a mechanism that we discuss on page *. This was both physically plausible, and seemed to solve the amplitude problem.
But there was another issue: the nonlinear ice model strengthened even more an additional cycle with a 400 kyr period that was not observed. In fact, the 400 kyr cycle should have been the strongest cycle of all, according to that theory. One way to get rid of this was to make the ad hoc assumption that the 400 kyr cycle was so long that it was suppressed by the more rapid time constants that are natural in ice production and destruction processes. At least one such assumption should certainly be allowed in any complicated theory.
Other problems continued to nag the insolation theory. In 1992, measurements of climate with precise dates became available from a water-filled cave in Nevada called Devils Hole. The sudden rise in temperature at this location appeared to precede the increase in insolation that was supposed to trigger it. This was a "causality problem," since the presumed effect appeared to precede the cause. This problem persists, and has recently become critical with the vindication of the Devils Hole chronology by radiometric dates from coral records. We will discuss the causality problem at length in Section 8.3.
Another problem with the insolation theory is called the "Stage-11 problem." Stage-11, in the jargon of paleoclimate, refers to a period about 400,000 years ago when variations in insolation were very weak, and yet the cyclical behavior of the ice ages was very strong. A similar problem exists at present: insolation variations are weak, and yet there was a great termination just 10-14 thousand years ago; this might be called the "Stage-1 problem." Various solutions have been proposed to address these problems, but they all involve ad hoc assumptions and the introduction of arbitrary parameters.
The set of problems continues to grow. It has led some to abandon the astronomical theory altogether, and postulate that the cycles of the ice ages are driven by natural oscillations of the ocean/continent/atmosphere system. Yet it is hard to dispute that the astronomical theory can account for the values of the observed frequencies. This agreement, more than anything else, gives life to the astronomical theory. It is also the reason for the central role played by spectral analysis in this book. Moreover, it is possible to make a general argument, independent of the frequency agreement, that the ice ages are astronomically driven. This was first done by the authors of this book in a paper in Science Magazine . The argument is based on the narrow structure seen in the spectrum of the data, and is explained on in Section 2.1 on page *.
The attention given to line shape has created another serious problem for the insolation theory. A high-resolution analysis of the 100 kyr cycle shows that the insolation theory, and its variants, all predict that the peak will have a split structure: it will be resolved into a 95 kyr line and a 125 kyr line. (An exception to this general rule is a model recently published by W. Berger, and explained in Section 6.4.8.) The bulk of the data shows that this prediction is contradicted. The 100 kyr cycle is a single narrow line. Ad hoc mechanisms that were plausible for eliminating the 400 kyr line are not plausible for turning the predicted doublet into a singlet. It is remarkable that this problem was not noticed until 1994. The seriousness of the problem was emphasized in an article in Science Magazine in 1997. Although there had been many theories published to account for the ice ages, none of them predicted the narrowness of this peak. A review of the theories published in 1993 included a "short list" of nine different "groups" of models, reproduced on page *, and yet every one of these theories was contradicted by the simple observation that the 100 kyr peak was narrow.
It is dangerous to dismiss a theory based on any one contradiction, since minor modifications of the theory can often solve apparently intractable difficulties. But the growing number of problems with the insolation theory is cause for serious concern. It may be the fact that the insolation theory predicted the correct values of the frequencies that leads to its tenacity in holding the minds of paleoclimatologists. But there are alternatives now appearing. In 1993, it was discovered that there is another astronomical oscillation (orbital inclination) that could contribute to climate that has a spectrum that is an excellent match to the narrow 100 kyr peak. The theory based on this does not have a Stage-11 problem (or a Stage-1 problem), nor a causality problem. It does not predict a nonexistent 400 kyr peak, and it accounts in a natural way (no adjustable parameters) for the shift of frequencies that took place about one million years ago, when the dominant frequency of ice age oscillation changed from 41 kyr to the present value of 100 kyr. This is, however, a new theory, and although we like it (it is our theory), it is not yet widely accepted, so we relegate detailed discussion of it to near the end of this book, Chapter 7.
… Spectra
