PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY

Transcription

1 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY K. H. Nisancioglu, Bjerknes Centre for Climate Research, University of Bergen, Bergen, Norway & 29 Elsevier Ltd. All rights reserved. Introduction A tremendous amount of data on past climate has been collected from deep-sea sediment cores, ice cores, and terrestrial archives such as lake sediments. However, several of the most fundamental questions posed by this data remain unanswered. In particular, the Plio-Pleistocene glacial cycles which dominated climate during the past B2.8 My have puzzled scientists. More often than not during this period large parts of North America and northern Europe were covered by massive ice sheets up to 3 km thick, which at regular intervals rapidly retreated, giving a sea level rise of as much as 12 m. The prevalent theory is that these major fluctuations in global climate, associated with the glacial cycles, were caused by variations in insolation at critical latitudes and seasons. In particular, ice sheet growth and retreat is thought to be sensitive to high northern-latitude summer insolation as proposed by Milankovitch in his original astronomical theory. Brief History of the Astronomical Theory Long before the first astronomical theory of the ice ages, the people of northern Europe had been puzzled by the large erratic boulders scattered a long way from the Alpine mountains where they originated. Based on these observations the Swiss geologist and zoologist Louis Agassiz presented his ice age theory at a meeting of the Swiss Society of Natural Sciences in Neuchatel in 1837, where he claimed that the large boulders had been transported by Alpine glaciers covering most of Switzerland in a past ice age. A few years later, the French mathematician Joseph Alphonse Adhemar was the first to suggest that the observed ice ages were controlled by variations in the Earth s orbit around the Sun. At this point it was known that there had been multiple glaciations, and Adhemar proposed that there had been alternating ice ages between the North and the South Pole following the precession of the equinoxes. Indeed, the winter is warmer when the Earth is at the point on its orbit closest to the Sun, and colder when the Earth is furthest from the Sun. Adhemar correctly deduced that the precession of the equinoxes had a period of approximately 21 years, giving alternating cold and warm winters in the two hemispheres every 1 5 years. In 1864, James Croll expanded on the work by Adhemar and described the influence of changing eccentricity on the precession of the equinoxes. He assumed that winter insolation controlled glacial advances and retreats, and determined that the precession of the equinoxes played an important role in regulating the amount of insolation received during winter. Based on this, he estimated that the last ice age lasted from about 24 to 8 years ago. Croll was aware of the fact that the amplitude of the variations in insolation was relatively small, and introduced the concept of positive feedbacks due to changing surface snow and ice cover as well as changes in atmosphere and ocean circulation. In parallel to the work of Croll, geologists in Europe and America found evidence of multiple glacial phases separated by interglacial periods with milder climate similar to that of the present day, or even warmer. These periodic glaciations were consistent with Croll s astronomical theory. However, most geologists abandoned his theory after mounting evidence from varved lake sediments in Scandinavia and North America showed that the last glacial period ended as late as 15 years ago, and not 8 years ago as suggested by Croll. Milankovitch s Astronomical Theory of the Ice Ages Following Croll s astronomical theory there was a period where scientists such as Chamberlin and Arrhenius tried to explain the ice ages by natural variations in the atmospheric content of carbon dioxide. The focus of the scientific community on an astronomical cause of the ice ages was not renewed until the publication of Milankovitch s theory in a textbook on climate by the well-known geologists Wladimir Köppen and Alfred Wegener in This was the first comprehensive astronomical theory of the Pleistocene glacial cycles, including detailed calculations of the orbitally induced changes in insolation. Milutin Milankovitch was of Serbian origin, born in He obtained his PhD in Vienna in 194 and 54

2 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 55 was later appointed Professor of Applied Mathematics at the University of Belgrade. He was captured during World War I, but allowed to work at the Hungarian Academy of Sciences, where he completed his calculation of the variations of the orbital parameters of the Earth and their impact on insolation and climate. Milankovitch s basic idea was that at times of reduced summer insolation, snow and ice could persist at high latitudes through the summer melt season. At the same time, the cool summer seasons were accompanied by mild winter seasons leading to enhanced winter accumulation of snow. When combined, reduced summer melt and a slight increase in winter accumulation, enhanced by a positive snow albedo feedback, could eventually lead to full glacial conditions. During World War II, Milankovitch worked on a complete revision of his astronomical theory which was published as the Kanon der Erdbestrahlung in However, the scientific establishment was critical of Milankovitch, and his theory was largely rejected until the early 197s. By this time, great advances in sediment coring, deep-sea drilling, and dating techniques had made it possible to recover climate records covering the last 5 years. By studying the variations in oxygen isotopes of foraminifera in deepsea sediment cores as well as by reconstructing past sea level from terraces of fossil coral reefs, new support was emerging for an astronomical phasing of the glacial cycles. The oxygen isotope data from the long deep-sea cores presented in a paper in 1976 by Hays et al. wereconsideredasproofofthemilankovitch theory, as they showed cycles with lengths of roughly 2 and 4 years as well as 1 years in agreement with Milankovitch s original calculations. Orbital Parameters and Insolation The Earth s orbit around the Sun is an ellipse where the degree to which the orbit departs from a circle is measured by its eccentricity (e). The point on the orbit closest to the Sun is called the perihelion, and the point most distant from the Sun the aphelion (Figure 1). If the distance from the Earth to the Sun is r p at perihelion, and r a at aphelion, then the eccentricity is defined as e ¼ðr a r p Þ=ðr a þ r p Þ. (a) Today Spring equinox Spring Winter Summer solstice Aphelion ω Perihelion Winter solstice ε Summer Fall Fall equinox (b) 11 years ago Fall equinox Winter solstice Aphelion Sun ω Perihelion Summer solstice Earth Spring equinox Figure 1 Sketch of the Earth s orbit around the Sun today and at the end of the last glacial cycle (11 years ago), showing the positions of the solstices and equinoxes relative to perihelion. The longitude of perihelion (o) is measured as the angle between the line to the Earth from the Sun at spring equinox and the line to the Earth at perihelion.

3 56 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY Variations in the eccentricity of the Earth s orbit follow cycles of 1 and 4 years giving a change in annual mean insolation on the order of.2% or less. This change in insolation is believed to be too small to produce any notable effect on climate. A more significant change in insolation is caused by variations in the seasonal and latitudinal distribution of insolation due to obliquity. Obliquity (e) is the angle between Earth s axis of rotation and the normal to the Earth s plane around the Sun (Figure 1). This angle is today, but varies between values of and with a period of 41 years. A decrease in obliquity decreases the seasonal insolation contrast, with the largest impact at high latitudes. At the same time, annual mean insolation at high latitudes is decreased compared to low latitudes. An example of the effect of obliquity variations on seasonal insolation is shown in Figure 2(a). During times when obliquity is small, high-latitude summertime insolation decreases, whereas midlatitude wintertime insolation increases. The magnitude of the change in high-latitude summer insolation due to obliquity variations can be as large as 1%. The third and last variable affecting insolation is the longitude of perihelion (o). This parameter is defined as the angle between the line to the Earth from the Sun at spring equinox and the line to the Earth at perihelion (Figure 1). It determines the direction of the Earth s rotational axis relative to the orientation of the Earth s orbit around the Sun, thereby giving the position of the seasons on the orbit relative to perihelion. Changes in the longitude of perihelion result in the Earth being closest to the Sun at different times of the year. Today, the Earth is closest to the Sun in early January, or very near winter solstice in the Northern Hemisphere. All other things being equal, this will result in relatively warm winter and cool summer seasons in the Northern Hemisphere, whereas the opposite is the case in the Southern Hemisphere. At the time of the last deglaciation, 11 years ago the Earth was closest to the Sun at summer solstice, resulting in extra warm summers and cool winters in the Northern Hemisphere. An example of the effect of changes in precession on seasonal insolation is shown in Figure 2(b). If the Earth s orbit were a circle, the distance to the Sun would remain constant at all times of the year and it would not make any difference where on the orbit the seasons were positioned. Therefore, the impact of variations in the longitude of perihelion depends on the eccentricity of the Earth s orbit and is described by (a) Latitude (deg) (b) Latitude (deg) SE SS FE WS SE Time of year SE SS FE WS SE 6 6 Time of year W m (W m 2 ) Figure 2 Insolation difference in units of W m 2 as a function of latitude and season: (a) when decreasing obliquity from to 221 in the case of a perfectly circular orbit (e ¼ ); and (b) for a change in precession going from summer solstice at perihelion to summer solstice at aphelion while keeping obliquity at today s value (e ¼ 23.51) and using a mean value for eccentricity (e ¼.3). The annual mean insolation difference is shown to the right of each figure and the seasons are defined as follows: FE, fall equinox; SE, spring equinox; SS, summer solstice; WS, winter solstice.

4 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 57 the precession parameter (e sin o). The combined effect of eccentricity and longitude of perihelion can give changes in high-latitude summer insolation on the order of 15% and varies with periods of 19 and 23 years, but is modulated by the longerperiod variations in eccentricity. Figure 3 shows the variations in obliquity (e), eccentricity (e), and the precession parameter (e sin o). Plio-Pleistocene Glacial Cycles Some of the longest continuous records of past climate come from deep-sea sediment cores. Ocean sediments are laid down over time, and by drilling into the seafloor, layered sediment cores can be extracted containing valuable information about the conditions at the time when the layers were formed. By studying the relative abundance of oxygen isotopes in shells of tiny marine organisms (foraminifera) found in the sediments, it is possible to estimate the amount of water tied up in the continental ice sheets and glaciers. This is because water molecules containing the lighter isotope of oxygen ( 16 O) are more readily evaporated and transported from the oceans to be deposited as ice on land. Thus, leaving the ocean water enriched with the heavy oxygen isotope ( 18 O) during glacial periods. However, the fractionation of the oxygen isotopes when forming the shells of the foraminifera also depends on the surrounding water temperature: low water temperature gives higher d 18 O values (the ratio of 18 O and 16 O relative to a standard). Therefore records of d 18 O are a combination of ice volume and temperature. By analyzing benthic foraminifera living on the seafloor where the ocean is very cold, and could not have been much colder during glacial times, the contribution of temperature variations to the d 18 O value is reduced. The benthic d 18 O ice volume record of Hays et al. from 1976 was one of the very first continuous records of the late Pleistocene extending back to the Brunhes Matuyama magnetic reversal event (78 years ago), making it possible to construct a timescale by assuming linear accumulation rates. Analysis of the data showed cycles in ice volume with periods of about 2 years and 4 years, with a particularly strong cycle with a period of roughly 1 years. Later studies extended the record past the Brunhes Matuyama reversal, showing that the late Pliocene ( Ma) and early Pleistocene records (1.8.8 Ma) were dominated by smalleramplitude cycles with a period of 41 years, rather than the large 1 years cycles of the late Pleistocene (.8 Ma). Many records generated since this time have confirmed these early observations, namely: (a) (b) Summer (c) Summer Winter Winter Figure 3 The three most important cycles regulating insolation on Earth are obliquity, eccentricity, and precession: (a) obliquity, or tilt of the Earth s axis varies with a period of 41 years; (b) eccentricity of the Earth s orbit varies with periods of 1 years and 4 years; and (c) precession of the equinoxes has a dominant period of 21 years and is modulated by eccentricity. 1. from about 3 to.8 Ma, the main period of ice volume change was 41 years, which is the dominant period of orbital obliquity; 2. after about.8 Ma, ice sheets varied with a period of roughly 1 years and the amplitude of

5 58 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY ka ~1 ka 3. δ 18 O (per mil) Figure 4 Benthic foraminiferal d 18 O ice volume record from the North Atlantic plotted to a paleomagnetic timescale covering the last 3 My. The transition from a dominant 41 to a 1 -year periodicity in ice volume occurs close to the Brunhes Matuyama magnetic reversal event (B78 years ago). oscillations in d 18 O increases, implying growth of larger ice sheets. The long benthic d 18 O record from a deep-sea sediment core extracted from the North Atlantic shown in Figure 4 illustrates both of these points. This isotope record is plotted with a paleomagnetic timescale determined by the depth of magnetic field reversals recorded by ferromagnetic grains in the sediment core. Using this simple timescale, which is not biased by orbital tuning, one can clearly observe the 41 -year periodicity of the late Pliocene and early Pleistocene (3..8 My), as well as the dominance of the stronger B1 -year periodicity of the late Pleistocene (last 8 years). Note that the main periods of orbital precession (19 and 23 years) are of less importance in the benthic ice volume record, whereas it is known that they increase in strength after about 8 years (the mid-pleistocene transition). The lack of an imprint from orbital precession in the early part of the record and the reason for the dominance of roughly 1 years periodicity in the recent part of the record are some of the major unanswered questions in the field. Only eccentricity varies with periods matching the roughly 1 years periods observed in the late Pleistocene. Although eccentricity is the only orbital parameter which changes the annual mean global insolation received on Earth, it has a very small impact. This was known to Croll and Milankovitch, who saw little direct importance in variations in eccentricity and assumed that changes in precession and obliquity would dominate climate by varying the amount of seasonal, rather than annual mean insolation received at high latitudes. Milankovitch postulated that the total amount of energy received from the Sun during the summer at high northern latitudes is most important for controlling the growth and melt of ice. To calculate this insolation energy, he divided the year into two time periods of equal duration, where each day of the summer season received more insolation than any day of the winter season. The seasons following these requirements were defined as the caloric summer and caloric winter half-years. These caloric half-years are of equal duration through time and the amount of insolation energy received in each can be compared from year to year. For Milankovitch s caloric summer half-year insolation (Figure 5),obliquity (e) dominates at high latitudes (4651 N), whereas climatic precession (e sin o) dominates at low latitudes (o551 N). In the mid-latitudes (B N), the contribution by obliquity and climatic precession are of similar magnitude. In the Southern Hemisphere, variations in caloric halfyear insolation due to obliquity are in phase with the Northern Hemisphere and could potentially amplify the global signal, whereas variations due to climatic precession are out of phase. By taking into account the positive snow albedo feedback, Milankovitch used his caloric insolation curves to reconstruct the maximum extent of the glacial ice sheets back in time (Figure 6). Milankovitch s predicted cold periods occurred roughly every 4 8 years, which fit reasonably well with the glacial advances known to geologists at that time. However, as the marine sediment core data improved, it became clear that the last several glacial periods were longer and had a preferred period of roughly 1 years (Figure 4), which was not consistent with Milankovitch s original predictions. Based on these observations, and without knowledge of the 41 years cycles of the

6 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY N 6 N 4 N (J m 2 ) Figure 5 Caloric summer half-year insolation following Milankovitch s definition plotted for the latitudes of 41 N, 61 N, and 81 N. Caloric half-years are periods of equal duration where each day of the summer half-year receives more insolation than any day of the winter half-year. early Pliocene and late Pleistocene, scientists reasoned that climatic precession and its modulation by eccentricity must play the leading role in past climates. Following Andre Berger and others, who recalculated and improved the records of orbital insolation, most researchers replaced the caloric halfyear insolation as a driver of glacial climate by midmonth, or monthly mean insolation, for example, June or July at 651 N(Figure 7). As can be seen from Figure 7, monthly mean insolation is dominated by precession. As insolation time series at a given time of the year (e.g., June or July) are in phase across all latitudes of the same hemisphere, the proxy records could be compared equally well with insolation from other latitudes than the typical choice of 651 N shown here. This means that any direct response of climate at high latitudes to monthly or daily insolation requires a strong presence of precession in the geologic record. Although both the frequencies of precession and obliquity are clearly found in the proxy records, a simple linear relationship between summer insolation and glacial cycles is not possible. This is particularly true for the main terminations spaced at roughly 1 years, which must involve strongly nonlinear mechanisms. The strong positive feedback on global climate caused by greenhouse gases, such as CO 2, was pointed out as early as 1896 by the Swedish physical chemist Svante Arrhenius. Shortly thereafter, the American geologist Thomas Chamberlin suggested a possible link between changing levels of CO 2 and glacial cycles. From the long ice cores extracted from Antarctica, covering the last 74 years, it is now known that atmospheric levels of CO 2 closely follow the glacial temperature record (Figure 8). Although greenhouse gases, such as CO 2, cannot explain the timing and rapidity of glacial terminations, the changing levels of atmospheric greenhouse gases clearly contributed by amplifying the temperature changes observed during the glacial cycles. Modeling the Glacial Cycles Following the discovery of the orbital periods in the proxy records, a considerable effort has gone into modeling and understanding the physical mechanisms involved in the climate system s response to variations in insolation and changes in the orbital parameters. In this work, which requires modeling climate on orbital timescales (41 years), the typical general circulation models (GCMs) used for studying modern climate and the impact of future changes in greenhouse gases require too much computing power. These GCMs can be used for simulations covering a few thousand years at most, but provide valuable equilibrium simulations of the past climates, such as the Last Glacial Maximum (LGM). Instead of the GCMs, it has been common to use Energy Balance Models (EBMs) to study changes in climate on orbital timescales. These types of models can be grouped into four categories: (1) annual mean atmospheric models; (2) seasonal atmospheric models with a mixed layer ocean; (3) Northern Hemisphere ice sheet models; and (4) coupled climate ice sheet models, which in some cases include a representation of the deep ocean. Studies with the first type of simple climate models were pioneered by the early work of Budyko in the 196s, who investigated the sensitivity of climate to changes in global annual mean insolation. However, changes in the Earth s orbital parameters result in a

7 51 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY Latitude equivalent Latitude equivalent Günz I Günz II Mindel I Millenia Mindel II Riss I Riss II Millenia Würm I Würm II Würm III Figure 6 Milankovitch s reconstructed maximum glacial ice extent for the past 6 years. From Milankovitch M (1998) Canon of Insolation and the Ice-Age Problem (orig. publ. 1941). Belgrade: Zavod za Udzbenike I Nastavna Sredstva.

8 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 511 (a) 55 W m (b) 4 55 W m Figure 7 Summer solstice insolation at (a) 651 N and (b) 251 N for the past 5 years CO 2 (ppmv) δd ice (% % ) CH 4 (ppbv) Time (years before 195) 2 1 Figure 8 Variations in deuterium (dd; black), a proxy for local temperature, and atmospheric concentrations of the greenhouse gases carbon dioxide (CO 2 ; red), and methane (CH 4 ; green), from measurements of air trapped within Antarctic ice cores. Data from Spahni R, Chappellaz J, Stocker TF, et al. (25) Atmospheric methane and nitrous oxide of the late Pleistocene from Antarctica ice cores. Science 31: and Siegenthaler U, Stocker TF, Monnin E, et al. (25) Stable carbon cycle-climate relationship during the late Pleistocene. Science 31:

9 512 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY redistribution of insolation with latitude and time of the year, with a negligible impact on global annual mean insolation. Therefore, annual mean models are not adequate when investigating the impact of orbital insolation on climate, as they cannot capture the parts of the insolation variations which are seasonal and translate them into long-term climate change. The second type of models includes a representation of the seasonal cycle, and has been used to investigate the orbital theory of Milankovitch. In this case, the seasonal variations in orbital insolation are resolved. However, as for the first type of models, past changes in ice cover are assumed to follow the simulated variations in the extent of perennial snow. This approach assumes that ice cover and the powerful ice albedo feedback are governed only by temperature, as the extent of snow in these models is fixed to the latitude with a temperature of 1C. In reality, the growth and decay of land-based ice sheets are governed by the balance of accumulation and ablation. Therefore, when investigating changes in ice cover, it is necessary to include an appropriate representation of the dynamics and mass balance of ice sheets in the model. The third type of models improves upon this by focusing on modeling past changes in mass balance and size of typical Northern Hemisphere ice sheets, such as the Laurentide. This type of studies was initiated by Weertman in the 196s who used simple ice sheet models, forced by a prescribed distribution of accumulation minus ablation, to predict ice thickness versus latitude. These models do not calculate the atmospheric energy balance in order to estimate snowfall and surface melt; instead, changes to the prescribed distribution of net accumulation follow variations in mean summer insolation. The fourth type of models include zonal mean seasonal climate models coupled to the simple Weertman-type ice sheet model, as well as earth models of intermediate complexity (EMICs) coupled to a dynamic ice sheet. These models give a more realistic representation of the climate as compared with the simpler models. Partly due to the lack of good data on variations in global ice volume older than about half a million years, most model studies have focused on understanding the more recent records dominated by the B1 years glacial cycles. All of these models respond with periods close to the precession and obliquity periods of the insolation forcing. However, the amplitude of the response is in most cases significantly smaller than what is observed in the proxy records. At the same time, the dominant B1 year cycles of the ice volume record, characterized by rapid deglaciations, are only found when including a time lag in the response of the model. Such an internal time lag can be produced by taking into account bedrock depression under the load of the ice, or by adding a parametrization of ice calving into proglacial lakes, or marine incursions at the margin of the ice sheet. Alternatively, the B1 -year cycles have been explained as free, self-sustained oscillations, which might be phase-locked to oscillations in orbital insolation. One of the very few model studies that have investigated variations in ice volume before the late Pleistocene transition (B8 years ago) used a two-dimensional climate model developed at Louvain-la-Neuve in Belgium. It falls within the definition of an EMIC and includes a simple atmosphere coupled to a mixed layer ocean, sea ice and ice sheets. By forcing this model with insolation and steadily decreasing atmospheric CO 2 concentrations, the model reproduces some of the characteristics of the ice volume record. The 41 -year periodicity is present in the simulated ice volume for most of the past 3 My and the strength of the 1 -year signal increases after about 1 My. However, a longer 4 -year year period is also present and often dominates the simulated Northern Hemisphere ice volume record. This nicely illustrates the remaining questions in the field. It is expected that models responding to the 1 -year period will also respond to the longer 4 -year period of eccentricity. However, this later period is not present in the ice volume record. At the same time, the late Pleistocene transition from a dominance of 41 to B1 -year period oscillations in ice volume is not well understood. Explanations for the transition which have been tested in models are: a steady decrease in CO 2 forcing and its associated slow global cooling; or a shift from a soft to a hard sediment bed underlying the North American ice sheet through glacial erosion and exposure of unweathered bedrock. Neither of these changes are in themselves abrupt, but could cause a transition in the response of the ice sheets to insolation as the ice sheets grew to a sufficiently large size. In addition to the challenge of modeling the mid- Pleistocene transition, no model has successfully reproduced the relatively clean 41 -year cycles preceding the transition. Following the transition, the models only exhibit a good match with the observed glacial cycles when forced with reconstructed CO 2 from Antarctic ice cores together with orbital insolation. Summary The Plio-Pleistocene glacial cycles represent some of the largest and most significant changes in past

10 PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 513 climate, with a clear imprint in terrestrial and marine proxy records. Many of the physical mechanisms driving these large cycles in ice volume are not well understood. However, the pursuit to explain these climate changes has greatly advanced our understanding of the climate system and its future response to man-made forcing. New and better resolved proxy records will improve our spatial and temporal picture of the glacial cycles. Together with the advent of comprehensive climate models able to simulate longer periods of the glacial record, scientists will be able to better resolve the interaction of the atmosphere, ocean, biosphere, and ice sheets and the mechanisms linking them to the astronomical forcing. Nomenclature e r a r p d 18 O e o See also eccentricity aphelion perihelion oxygen isotope ratio (ratio of 18 O and 16 O relative to a standard) obliquity longitude of perihelion Deep-Sea Drilling Methodology. Deep-Sea Drilling Results. Monsoons, History of. Oxygen Isotopes in the Ocean. Satellite Remote Sensing of Sea Surface Temperatures. Stable Carbon Isotope Variations in the Ocean. Further Reading Bard E (24) Greenhouse effect and ice ages: Historical perspective. Comptes Rendus Geoscience 336: Berger A, Li XS, and Loutre MF (1999) Modelling Northern Hemisphere ice volume over the last 3 Ma. Quaternary Science Reviews 18: Budyko MI (1969) The effect of solar radiation variations on the climate of the Earth. Tellus 5: Crowley TJ and North GR (1991) Paleoclimatology. New York: Oxford University Press. Hays JD, Imbrie J, and Shackleton NJ (1976) Variations in the Earth s orbit: Pacemakers of the ice ages. Science 194: Imbrie J and Imbrie KP (1979) Ice Ages, Solving the Mystery. Cambridge, MA: Harvard University Press. Köppen W and Wegener A (1924) Die Klimate Der Geologischen Vorzeit. Berlin: Gebrüder Borntraeger. Milankovitch M (1998) Canon of Insolation and the Ice- Age Problem (orig. publ. 1941). Belgrade: Zavod za Udzbenike I Nastavna Sredstva. Paillard D (21) Glacial cycles: Toward a new paradigm. Reviews of Geophysics 39: Saltzman B (22) Dynamical Paleoclimatology. San Diego, CA: Academic Press. Siegenthaler U, Stocker TF, Monnin E, et al. (25) Stable carbon cycle climate relationship during the late Pleistocene. Science 31: Spahni R, Chappellaz J, Stocker TF, et al. (25) Atmospheric methane and nitrous oxide of the late Pleistocene from Antarctica ice cores. Science 31: Weertman J (1976) Milankovitch solar radiation variations and ice age ice sheet sizes. Nature 261: