An Orbital Theory for Glacial Cycles Peter Bogenschutz March 2006 1. Introduction In the late 1800's, when ice ages were first discovered, variations in Earth's orbital mechanics were hypothesized to be the cause of advancing and receding ice sheets from the poles (Zachos 2001). James Croll, a janitor for Andersonian College in Scotland, was the first to theorize a connection between glacial cycles and the Earth's rotation around the sun. However, given his lack of formal scientific education his ideas were flawed and hence either ignored or rejected from the scientific community. It wasn't until several decades later, in the early 1900's, when Croll's theory was revived by Serbian engineer, Milutin Milankovitch. Milankovitch gave Croll's ideas intensive scientific treatment and and performed sophisticated mathematical calculations to come to the conclusion that glacial periods are driven and modified by three orbital cycles: Eccentricity, obliquity, and precession. An ice age is defined as an extended period of time, often on the order of several million years, which consists of periods of advancing and receding glaciers from the poles. While the causes of ices ages themselves are not clearly understood, they are thought to be driven by variations of carbon dioxide as well as land mass distribution (Hayes et al. 1976). Recent studies suggest that astronomical forcing (variations of the Sun's rotation around the universe) likely has an influence, yet not much is known about this process. Glacial/interglacial periods describe the advancing and receding ice sheets which occur within ice ages and often have periodicity of approximately 41-100 kyr. Observations show that Earth is currently in an ice age, albeit in an interglacial period, which is analogous to the dry season of a monsoon. The current ice age began approximately 2.5 million years ago, with the most previous glacial cycle ending around 10 kyr years ago. This study will describe the three Milankovitch cycles and how they pertain to the development and modification of glacial periods. The effect of each individual cycle will be examined as well as conditions required for a maximum possible glacial period. A brief analysis of theory comparison with observations of oxygen isotope ratio will be examined followed by a discussion of some problems uncovered pertaining to the Milankovitch cycles. An explanation of current work being done to alleviate these problems will also be addressed. 2. Milankovitch cycles The first Milankovitch cycle is eccentricity and describes the shape of the Earth's orbit around the Sun (Hayes et al. 1976). It is thought that this variation is due to gravitational pulls from other planets in our solar system, with the largest influence being from Venus.
Eccentricity has a cycle of about 100,000 years and varies between values of 0%, indicative of a circular path, to 5%, indicative of a slightly elliptical path (figure 1). However, it is important to note that the maximum value of 5% only occurs every 400 kyr, and a more typical maximum value of the 100 kyr cycle is around 2~3%. Current eccentricity is 1%. The oscillations from circular to slightly elliptical alters the distance from the Earth to Sun and therefore changes the amount of shortwave radiation that reaches the surface. This in turn will help to modify the seasonal contrasts of the two hemispheres. For instance, during a maximum eccentricity event if summer were to occur at the perihelion (passage of the earth closest to the sun) it would result in a warmer than normal summer at that hemisphere, whereas if summer occurred during the aphelion (passage furthest from the sun), it would act to lower the temperature during the summer. However, Milankovitch determined that since the variations in eccentricity are small, the differences of incoming solar radiation are not great enough to be the sole cause of glacial cycles. Eccentricity does play a small role on modifying the strength and duration of a glacial cycle, as will be discussed. The second Milankovitch cycle is precession, which describes the Earth's slow wobble while it spins on its axis (figure 2). This motion, analogous to a toy top running down, changes the direction of the Earth's axis of rotation relative to the Sun. Currently the axis of the northern hemisphere is pointed to our north star Polaris, however in approximately 10 kyr, when the axis of rotation has shift 180 degrees, the new north star will be Vega. This motion of Precession has a periodicity of approximately 23 kyr. Precession acts to work with eccentricity to determine which hemisphere will experience greater seasonal contrasts. For this example we will assume a maximum eccentricity value of 5% and use the current direction of axial rotation of Polaris. If the northern hemisphere winter occurs during the perihelion and summer season occurs during the aphelion, this will act to lessen the seasonal contrast due to more incoming solar radiation than normal occurring in the northern hemisphere winter and less in the summer. In this case, the southern hemisphere will be experiencing a greater seasonal contrast compared to normal since during the summer the hemisphere is closer to the sun and winter further away. However, precession does not directly modify the amount of solar radiation reaching the Earth, as that is a function of eccentricity. It is already determined that eccentricity plays little role on glacial cycles, therefore, this is also true for Precession. Milankovitch calculated that the final cycle, that of obliquity, has the strongest influence in both creating and modifying glacial cycles (Wunsch et al. 2004). Obliquity defines the variations in the Earth's axis in relation to the orbit plane around the Sun (figure 2). This angle of tilt varies from 21.5 to 24.5 degrees and has a periodicity of approximately 41 kyr. Currently the Earth's tilt is roughly 23.5 degrees. Obliquity, like eccentricity, acts to modify the severity of the seasonal contrasts, however as Milankovitch calculated, the effects of obliquity are much greater and is determined to be the most important of the three cycles. Unlike eccentricity and precession, obliquity effects both hemispheres in the same way. A minimal tilt will allow the Sun's solar radiation to be more evenly distributed between
winter and summer in both hemispheres, whereas a maximum tilt will result in greater seasonal contrasts. The role in which obliquity plays in creating and modifying glacial periods will be discussed in the next section. 3. Response to Milankovitch Theory Glacial cycles are created by a build up of snow at the poles which eventually progresses down towards the mid-latitudes. In order for this to happen it is essential that summers be more mild than average. For all three Milankovitch cycles it is shown that a mild summer is also indicative of a warmer than typical winter. This warmer winter is also a key ingredient to the formation of glacial cycles as it allows more room for moisture and hence a greater chance of significant snow to fall. The corresponding mild summer season will then reduce the amount of melting snow (Zachos et al 2006). Examining the opposite case of a greater seasonal contrast, a severely cold winter will not allow much snow to fall and the warmer than normal summer will cause the little accumulation to melt. As previously addressed, Milankovitch determined that obliquity has the most dramatic effect on the variations of radiation reaching the Earth's surface. Therefore, it is deduced that a minimal tilt, corresponding to less seasonal contrast, is the key ingredient in creating a glacial cycle on Earth. Although their effects are significantly lower than that of obliquity, both precession and eccentricity can play a role on modifying the glacial cycle. To consider a case in which the maximum possible glacial period in the northern hemisphere is to occur, the axis of rotation of the earth needs to be pointed towards Polaris and there must also be maximum eccentricity (5%), in addition to the essential ingredient of obliquity. Here the precession and maximum eccentricity are working with the minimal tilt to further decrease the seasonal contrast. Now consider the southern hemisphere for this case, where the precession and eccentricity are working to increase the seasonal contrasts since these two cycles have opposing effects on the two hemispheres. Would the southern hemisphere experience a glacial cycle at the same time as the northern hemisphere? This question of simultaneous glacial cycles in both hemispheres was one of the major flaws in Croll's hypothesis (Raymo 1998). His orbital theory only contained effects of eccentricity and precession, therefore Croll hypothesized that glacial periods happen in each hemisphere out of phase. Observations of oxygen isotope ratio show the contrary and is supported by Milankovitch theory. Referencing the example above, even though the southern hemisphere is experiencing a greater seasonal contrast in response to eccentricity and precession, it is the minimal tilt of obliquity which dominates the variations in solar radiation. Therefore, the southern hemisphere will experience a glacial cycle at the same time as the northern hemisphere, albeit most likely will not be quite as strong. The above example raises some very important conclusions. First, glacial cycles happen simultaneously in both hemispheres. Secondly, it is entirely possible to have a glacial cycle in a particular hemisphere even if eccentricity and precession are working
to raise seasonal contrast, since they merely act to modify the strength to a small degree. It is important to note that this example assumes equal land mass distribution for both hemispheres. In a realistic example, even if orbital forcing from the three Milankovitch cycles were equal in both hemispheres, it is likely that the glacial cycle would be stronger in the northern hemisphere due to more dense concentration of land near the polar regions, compared to the southern hemisphere. To determine how the glaciers advance from the poles to the mid-latitudes, examine the series of events of positive feedbacks (Hays et al. 1976). The first process is the minimal tilt required to raise the temperatures at the poles in the winter and create more snowfall, while the next summer will be cooler than average, restricting much of the snow from melting. Therefore, the preceding winter at the pole, additional snow will fall, allowing for a continual build up of the snow pack from each additional winter. This gain in snow pack will raise the surface albedo, hence reflecting an increasing amount of solar radiation back to space and in turn reducing the global surface temperature of the Earth. This reduction of temperature will then allow snow to fall at a lower latitude than it did the previous winter. Then the cycle will repeat, until incrementally the snow pack builds at each latitude and advances to a low enough latitude where the summer temperature is too warm to support the snow pack from accumulating season to season. The key elements in this cycle are the increase of surface albedo due to the snowfall and the cooler summers. The strength of the glacial cycle is measured by the average global temperature, which is believed to be correlated with the latitudinal advance of the glaciers. Glaciers begin to recede once the incoming solar radiation at the mid-latitudes becomes great enough during the summer season to melt the snow pack at the lowest latitudes (Ji et al. 2006). This is often in response to the tilt of the Earth increasing. Once this process begins it is the decrease of the surface albedo and warmer temperatures of the summer which allows the glaciers to incrementally melt at higher latitudes. 4. Theory Comparison with Observations It wasn't until 1970 when the seminal paper was published which verified the variations of glacial cycles at 41 kyr. Similar to other paleoclimate studies, data from ocean sediments are used to verify the frequency of the glacial cycles. In particular, the oxygen isotope ratio is thought to reflect the amount of Earth's water frozen in ice and is useful for glacial studies since it is a measure of the global ice volume. In order for the oxygen isotope ratio versus depth to be useful it must be transformed into record versus time, which involves estimating the sedimentation rate and also through a process of tuning the data (McDermott et al. 2001). Most oxygen isotope ratio records used for glacial studies comes from Vostok, Antarctica. Results of the oxygen isotope records show a distinct 41 kyr cycle of glacial periods within ice ages for several millions of years. Figure three shows such a time series for the past five and a half million years. Here it is shown that the Earth entered an ice age roughly 2.75 million years ago and thereafter a phase of glacial periods on the 41 kyr cycle. This is to be expected since obliquity is the dominate Milankovitch cycle. However, around one million years ago a distinct 100 kyr cycle began, which proved to
be very puzzling as it appears that glacial cycles are being driven by eccentricity. As the theory suggests, eccentricity alone cannot be responsible for starting glacial cycles. This has become known as the 100 kyr problem, or transition problem, and was the first of many challenges discovered associated with the Milankovitch theory. 5. Challenges The 100 kyr problem has become the most studied and debated discrepancies associated with the Milankovitch theory (Roe et al. 1999). However, focus has also been placed on several other problems in the theory. One in which is related to the 100 kyr problem, known as the 400 kyr or stage 11 problem, relates to the relatively strong eccentricity values every 400 kyr, which has never been detected in climate data. If the 100 kyr cycles are having such a profound effect suddenly, then it should also be true that the 400 kyr cycle should be detected. Therefore, the 400 kyr problem may suggest that the recent change to a 100 kyr cycle is not being driven by eccentricity, rather some unknown forcing that is possibly not related to Earth orbital mechanics (Broecker 2002). The stage five problem, often referred to as the causality problem, is the discrepancy between the timing of the start of the interglacial periods compared to what is suggested in theory. It is shown in climate records that that the glaciers begin to melt in the midlatitudes approximately 10 thousand years before the Milankovitch theory suggests that solar forcing could cause it to happen. Some scientists believe this could just be due to errors in the process of tuning the observational data. The effect exceeds cause problem suggests that observations of glacial periods are not as strong as the magnitudes calculated by Milankovitch, often by several orders of magnitude (Karner et al. 2000). All of these problems suggest that glacial cycles, while largely driven by variations in Earth orbital mechanics, are also being influenced by outside forcing. A few of these suspected forcings include the amount of dust in the atmosphere, reflectivity of the ice sheets, concentration of other gases such as methane, the changing characteristics and distribution of clouds, and land mass distribution. However, the effects these forcings have on glacial periods has not been studied intensively enough to be conclusive. Work is currently being done in an attempt to address some of the problems associated with the Milankovitch cycles, with a particular intent on trying to solve the 100 kyr problem. Among these is the study of a possible fourth orbital cycle, orbital inclination (figure four). This process suggests that the Earth does not rotate around the Sun in a two dimensional plane, but three dimensionally. At this point specifics, such as periodicity or what effects this may play on climate, is not well known. The current leading theory of the 100 kyr problem is linked with a meteor collision near the sun which is thought to have occurred nearly one million years ago (Muller et al. 1997). This collision is thought to be possible for the accretion of extraterrestrial dust in space which could be working with the timing of orbital inclination or eccentricity in causing 100 kyr cycles, which results in a reduction of solar radiation from reaching the surface of the Earth. While this theory is being intensively studied it is also highly controversial.
Among other work is the study of how human activity will effect glacial cycles. This raises another highly debated question of whether the current melting of the ice sheets at the poles is due to human induced global warming or simply from the fact that orbital mechanics is currently on a trend to increase seasonal contrasts. The cause of the ice ages themselves is another important problem which warrants much research, however is on a much larger time scale than glacial periods and thus will likely be decades or longer before the scientific community is able to make significant progress with this issue. 4. Summary Variations of Earth's orbital mechanics likely play a large role in the development of glacial periods. While the Milankovitch theory consists of three cycles, it is obliquity which has the most dramatic effect on glacial cycles with eccentricity and precession working together to have a minimal effect. Glacial cycles occur when the seasonal contrast is small and is most likely to happen when the tilt of the Earth is as it's minimum, helping to induce cooler summers. While the Milankovitch theory has been verified for several millions of years in the past, corresponding to glacial cycles as a result of obliquity, the most troubling problem arises in the past million years where glacial cycles appear to be driven by eccentricity. The introduction of such a problem, among others, suggests that a possible significant outside forcing is current driving glacial cycles and that the traditional Milankovitch theory may not have a strong effect anymore. Currently the leading theory for this transition is the accretion of space dust causing a reduction in solar radiation on the 100 kyr cycle. References Broecker, W.S., 1992. Climate cycles-upset for Milankovitch theory. Nature, 359, 779-780. Hays, J., J. Imbrie, and N. Shackleton, 1976: Variations in the Earth's orbit: pacemaker for the ice ages. Science, 194, 1121-1132. Ji, J., W. Balsam, X. Chen, J. Chen, Y. Chen, and H. Wang, 2006: Rate of solar insolation change and the glacial/interglacial transition. Geophysical Research Letters, 33. Karner, B.D. and R. Muller, 2000: A causality problem for Milankovitch. Science, 288, 2143-2144. McDermott, F., Mattey, D.P., Hawkesworth, C. 2001. Centennial-scale Holocene climate variability revealed by a high-resolution speleothem oxygen 18 record from SW Ireland. Science. 294, 1328-1331.
Muller, R.A. and G. MacDonald, 1997: Glacial cycles and astronomical forcing. Science, 277, 215-218. Raymo, M.E., 1998. Glacial puzzles. Science, 281, 1467-1468. Roe, G.H., Allen, M.R.., 1999. A comparison of competing explanations for the 100,000- yr ice age cycle. Geophysical Research Letters, 26, 2259-2262. Wunsh, C., 2004: Quantitative estimate of the Milankovitch-forced contribution to observed quaternary climate change. Quaternary Science Review, 23, 1001-1012. Zachos, J., M. Pagani, L. Sloan, E. Thomas, K. Billups, 2001: Trends, rhythms, and aberrations in global climate 65 Ma to present. Science, 292, 686-693.
Fig 1. Examples of orbit with no eccentricity (left) and eccentricity of 0.5 (right) From http://en.wikipedia.org/wiki/milankovitch_cycles. Fig 2. Example of variations in Earth's Precession (left) and Obliquity (right). From http://en.wikipedia.org/wiki/milankovitch_cycles
Fig 3. Time series from past 5.5 million years ago of tuned oxygen 18 data retrieved from Vostok, Antarctica. From http://en.wikipedia.org/wiki/milankovitch_cycles Fig 4. Example of the type of motion associated with orbital inclination. From http://en.wikipedia.org/wiki/milankovitch_cycles