Milankovitch Cycles and Climate: Part III – Putting it All Together

In parts I and II, we looked at axial obliquity, axial precession, apsidal precession, orbital eccentricity and orbital inclination, and how their cycles can affect the climate. In this installment of the series, we’ll look briefly at how these cycles look when combined, and then discuss one of the most prominent unsolved problems raised by the theory: The 100,000 Year problem.

Putting it all together

Putting it all together

Notice that the peaks and valleys in temperature are roughly periodic, and that with the possible exception of apsidal precession, there are slight fluctuations in the periods and amplitudes of these orbital cycles. One reason for this has to do with fluctuations in solar output, but another likely reason has to do with the very causes of these orbital cycles themselves: namely, these cycles are driven by mutual gravitational perturbations between the Earth, Sun, Moon, and to a lesser extent, Jupiter and the other planets in the solar system (Borisenkov 1985, Spiegel 2010) .

These are what are referred to in physics as “n-body problems.” Isaac Newton recognized early on that some such orbital fluctuations would have to occur, but it turns out that n-body problems cannot be solved analytically for systems of n ≥ 3 (Heggie 2005). That means the resultant systems of differential equations has to be solved using what are called numerical methods, rather than being solved for a set of analytic functions describing the precise trajectories of each body in the system over time. As a result, the actual precise paths that celestial bodies take and the variations in their tilt and precession can be more complex than just a fixed elliptical path. To add insult to injury, these problems become even more complicated in General Relativity than in classical Newtonian Celestial Mechanics.

Milankovitch Cycle/Insolation animation c/o Cal Tech

Milankovitch Cycle/Insolation animation c/o Caltech

I want to also emphasize the fact that even though Milankovitch first proposed his ideas nearly a century ago, this is still an area of active research. There are still unsolved questions about how these cycles combine to help produce the glaciation data we see in the paleo-climatological records. For instance, there’s what is known as The 100,000 Year Problem. This refers to the fact that during the past million years, glacial-interglacial periods have occurred on roughly a 100,000 year cycle, which has been difficult to reconcile with the fact that the insolation changes due to the 100,000 year orbital eccentricity cycle are very small. The effect appears to exceed the magnitude of the cause.

There is no shortage of plausible hypotheses, each with their respective strengths and weaknesses, but as of yet there’s still no unified theory that explains how precisely the cycles all work together to produce the observed pattern of glacial and interglacial periods.

For instance, researchers such as Muller et al have hypothesized that orbital inclination may be more important in producing the observed 100kyr glaciation cycle than the other cycles (Muller 1997). The only physical mechanism thus far proposed for this is the possibility that different inclinations of the orbital plane may correspond to different densities of meteoroid and dust accretion. Such a change could alter stratospheric concentrations of dust and aerosols, which would change the amount of sunlight reflected back into space. So far there’s no evidence for sufficiently different amounts of accretion at different orbital inclinations for this to be the case, but it’s a testable hypothesis whose strengths and weaknesses are outlined by the lead author here (Muller 1995).

Other researchers have been able to reproduce the 100,000 year cycles in models involving the non-linear phase locking of interactions between the known orbital forcings and internal oscillations in the climate system (Tziperman et al 1997). The basic idea behind the non-linear phase locking models is that axial obliquity and/or precession may act as pacemakers for the glaciation cycle in a manner that is distinct from models based on mere amplifications of the effects of the eccentricity cycle.

The minutia of the actual physical mechanisms involved in the non-linear phase locking models is left quite vague. No definite conclusion is attempted regarding whether the dominant cycle is obliquity, precession or both; the models work just as well with CO2 changes driving glaciation in synchrony with the orbital cycles as they do with the orbital cycles driving them with CO2 changes merely amplifying the signal. But that’s because the goal with that paper was merely to figure out whether such models could reproduce the cycle. The same lead author (Tziperman) has also co-authored work that explored a sea ice triggering mechanism for glaciation (Gildor 2000).

Others have even argued that the last 800,000 or so of climate records extends insufficiently far back to establish that the apparent 100,000 year glaciation cycle and its relationship to the eccentricity cycle are even statistically significant (Wunsch 2004).

This is not the only unresolved problem related to Milankovitch cycles. In addition to the 100k year problem, there’s also a similar 400k year problem, which exists because a strong variation in the eccentricity cycle doesn’t appear to correspond to an extra strong 400k period climatological cycle.

Then there’s also what’s called the “Stage 5” Problem: aka the Causality Problem (Oppo et al 2001). This refers to the fact that the penultimate interglacial period (corresponding to Marine Oxygen-Isotopic Stage 5) appears to have occurred about 10k years prior to the forcing hypothesized to have caused it. Another issue is what’s called the Split Peak Problem, which refers to the fact that eccentricity cycles have cleanly resolved variations at both 95k and 125k years which don’t appear to translate into two cleanly resolved peaks in insolation (Zachos et al 2001).  Instead, what’s observed is a single peak on a roughly 100k frequency.

So, as you can see, determining the precise manner in which the combinations of these cycles affect global climate is no easy task, and we still don’t know everything.

That said, what we DO know is that these cycles are not sufficient to explain the rate of the current warming. For one, they occur over much longer periods of time than the current trend (on the order of tens or hundreds of thousands of years versus a couple hundred years).

Moreover, Earth’s Orbital Eccentricity is nearly circular, and both Axial Obliquity and Axial Precession are currently changing in opposition to the warming trend; Axial Obliquity is getting smaller: not larger, which means if anything that we in the Northern Hemisphere should be cooling (or at least not warming). Similarly, precession is changing such that it should be moderating the warming, but it’s not. If anything, other variables (i.e. human activities) may be delaying the next glacial period (Berger 2002). So, even though we don’t know everything about how Milankovitch cycles affect the climate, we do know that they can’t explain the current warming trend.

References:

Berger, A., & Loutre, M. F. (2002). An exceptionally long interglacial ahead?.Science297(5585), 1287-1288.

Borisenkov, Y. P., Tsvetkov, A. V., & Eddy, J. A. (1985). Combined effects of earth orbit perturbations and solar activity on terrestrial insolation. Part I: Sample days and annual mean values. Journal of the atmospheric sciences,42(9), 933-940.

Ellis, R., & Palmer, M. (2016). Modulation of ice ages via precession and dust-albedo feedbacks. Geoscience Frontiers.

Gildor, H., & Tziperman, E. (2000). Sea ice as the glacial cycles’ climate switch: Role of seasonal and orbital forcing. Paleoceanography15(6), 605-615.

Heggie, D. C. (2005). The classical gravitational N-body problem. arXiv preprint astro-ph/0503600.

Muller, R. A., & MacDonald, G. J. (1995). Glacial cycles and orbital inclination. Nature377(6545), 107-108.

Muller, R. A., & MacDonald, G. J. (1997). Spectrum of 100-kyr glacial cycle: Orbital inclination, not eccentricity. Proceedings of the National Academy of Sciences94(16), 8329-8334.

Oppo, D. W., Keigwin, L. D., McManus, J. F., & Cullen, J. L. (2001). Persistent suborbital climate variability in marine isotope stage 5 and Termination II. Paleoceanography, 16(3), 280-292.

Rial, J. A. (2004). Earth’s orbital eccentricity and the rhythm of the Pleistocene ice ages: the concealed pacemaker. Global and Planetary Change41(2), 81-93.

Rial, J. A. (1999). Pacemaking the ice ages by frequency modulation of Earth’s orbital eccentricity. Science285(5427), 564-568.

Spiegel, D. S., Raymond, S. N., Dressing, C. D., Scharf, C. A., & Mitchell, J. L. (2010). Generalized Milankovitch cycles and long-term climatic habitability.The Astrophysical Journal, 721(2), 1308.

Tziperman, E., Raymo, M. E., Huybers, P., & Wunsch, C. (2006). Consequences of pacing the Pleistocene 100 kyr ice ages by nonlinear phase locking to Milankovitch forcing. Paleoceanography21(4).

Wunsch, C. (2004). Quantitative estimate of the Milankovitch-forced contribution to observed Quaternary climate change. Quaternary Science Reviews23(9), 1001-1012.

Zachos, J. C., Shackleton, N. J., Revenaugh, J. S., Pälike, H., & Flower, B. P. (2001). Climate response to orbital forcing across the Oligocene-Miocene boundary. Science, 292(5515), 274-278.

Photo Credits:

Incredio – https://commons.wikimedia.org/wiki/File:MilankovitchCyclesOrbitandCores.png, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=45036243

 

Milankovitch Cycles and Climate: Part II – Orbital Eccentricity, Apsidal Precession and Orbital Inclination

In part I, we looked at some of the ways in which changes in axial obliquity and precession can affect the climate. In this article, we’ll look at orbital eccentricity, apsidal precession and orbital inclination, and some of their climatological consequences.

Orbital Eccentricity: This refers how elliptical earth’s orbital path is. The greater the eccentricity of a planet’s orbital path, the less circle-like and more elliptical (oval-like) it is. An ellipse has an eccentricity greater than or equal to zero, but less than one. An eccentricity value of e = 0 corresponds to a perfect circle, whereas e = 1 corresponds to a parabola, and e > 1 corresponds to a hyperbola. At higher eccentricity values (albeit less than one), there is a greater discrepancy between a planet’s perihelion and aphelion: a planet’s nearest and furthest points from the Sun during its orbit.

Earth’s orbital eccentricity changes over cycles of about 100,000 and 413,000 years or so due to the gravitational influence of massive planets such as Jupiter and Saturn. During these cycles, earth’s orbital eccentricity varies between about e = 0 (perfectly circular) to about e = 0.06.

Orbital Eccentricity

Orbital Eccentricity

Orbital eccentricity is the only Milankovitch cycle that affects total annual insolation on the earth: the total amount of solar energy per unit area reaching the earth, and it does so by a factor of 1/(1- e2 )1/2 for a given solar irradiance (Spiegel 2010). That means that while eccentricity (e) varies between 0 and 0.06, insolation should vary between a factor of 1/(1-(0)2)1/2 = 1 and a factor of 1/(1- (0.06)2 )1/2 = 1.0018 for a given solar output. Currently, Earth’s eccentricity is approximately e = 0.017, which works out to 1/(1-(0.017)2)1/2 = 1.00014. So the variation in insolation isn’t very significant. However, that doesn’t mean that these cycles don’t have a significant effect on climate. At greater eccentricity values, the seasons occurring while Earth is closer to the aphelion are of longer duration than the ones occurring while the Earth is closer to the perihelion.

Additionally, the regional and seasonal climatological effects of changes in axial obliquity and precession are more pronounced during periods of greater orbital eccentricity than when Earth’s orbit is circular (or nearly circular). This is because greater eccentricity values correspond to greater differences between the closest point to the sun (perihelion) and furthest point (aphelion) in Earth’s orbital path. In turn, those greater differences between the perihelion and aphelion can either amplify or moderate the discrepancies in seasonal insolation caused by axial tilt and precession. A hemisphere tilted towards the sun at the perihelion and away from the sun at the aphelion would have its summers and winters slightly reinforced, while a hemisphere tilted away from the sun at the perihelion and towards the sun at the aphelion would experience a slight moderating effect on its summers and winters.

Apsidal precession: The theory of Milankovitch cycles also predicts that the orientation of earth’s entire elliptical orbital path rotates in cycles of 21,000 years. That is to say that the location of the perihelion in Earth’s orbit changes over thousands of years (Greenberg 1981). The following graphic should clarify what is meant by this:

Apsidal Precession and the Seasons.

Apsidal Precession and the Seasons.

There is some evidence to suggest that these changes in the orientation of the perihelion work together in combination with the axial precession cycle to affect temporal and geographical insolation and precipitation patterns (Merlis 2013). In other words, it affects where and when higher and lower local levels of sunshine and rain occur.

Orbital Inclination: Although the planets and asteroids follow elliptical orbits in accordance with Kepler’s first law, they don’t all orbit in precisely the same plane. Their orbital planes are often inclined with respect to one another, and their angles of inclination can change slightly over time. The Earth’s orbital plane is also called the Plane of the Ecliptic (or simply the ecliptic).

By Lasunncty (talk). (Lasunncty (talk)) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

Orbital Inclination.

The orbital inclination angles of planets, asteroids and other celestial objects are usually computed with respect to Earth’s ecliptic, and thus the Earth’s inclination with respect to its own ecliptic would therefore be zero by definition, but this is primarily for purposes of convenience. The inclination of the ecliptic changes over time on a cycle of approximately 70,000 years. This is known as Precession of the Ecliptic. Milankovitch did not study this cycle, but I’ve included it anyway for the sake of completeness. Additionally, its climatological effects are still a matter of scientific debate. Earlier calculations suggested that its effect on insolation would be negligible (Berger 1976), but other researchers have postulated that it may play a role in the explanation of one of the hitherto unsolved problems raised by the theory of Milankovitch cycles (Muller 1995). In fact, Muller et al even went as far as to argue that when the inclination is computed with respect to the Invariable Plane of the solar system: the plane through the solar system’s barycenter (center of mass) and perpendicular to its angular momentum vector (approximately the orbital plane of Jupiter), rather than with respect to Earth’s 1850 orbital plane, the cycle works out to closer to 100,000 years rather than the traditionally accepted 70,000 years (Muller 1995).

The relevance of this claim will become clearer in part III when we discuss how these cycles combine together to affect climate, and when we take a look at one of the most prominent unsolved questions raised by the theory.

References:

Berger, A. L. (1976). Obliquity and precession for the last 5 000 000 years.Astronomy and Astrophysics51, 127-135.

Greenberg, R. (1981). Apsidal precession of orbits about an oblate planet.The Astronomical Journal86, 912-914.

Merlis, T. M., Schneider, T., Bordoni, S., & Eisenman, I. (2013). The tropical precipitation response to orbital precession. Journal of Climate26(6), 2010-2021.

Muller, R. A., & MacDonald, G. J. (1995). Glacial cycles and orbital inclination. Nature377(6545), 107-108.

Spiegel, D. S., Raymond, S. N., Dressing, C. D., Scharf, C. A., & Mitchell, J. L. (2010). Generalized Milankovitch cycles and long-term climatic habitability.The Astrophysical Journal, 721(2), 1308.

Photo Credits:

Orbital Eccentricity: By NASA, Mysid – Vectorized by Mysid in Inkscape from NASA image at http://earthobservatory.nasa.gov/Library/Giants/Milankovitch/Images/ecc_zero.gif., Public Domain, https://commons.wikimedia.org/w/index.php?curid=3993043

Apsidal Precession and the Seasons:  By Krishnavedala (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons.

Orbital Inclination: By Lasunncty (talk). (Lasunncty (talk)) [CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons

Milankovitch Cycles and Climate: Part I – Axial Tilt and Precession

The theory of Milankovitch cycles is named after Serbian astronomer and geophysicist, Milutin Milanković, who in the 1920s postulated three cyclical movement patterns related to Earth’s orbit and rotation and their resultant effects on the Earth’s climate. These cycles include axial tilt (obliquity), elliptical eccentricity, and axial precession. In aggregate, these cycles contribute to profound long term changes in earth’s climate via orbital forcing.

Axial Obliquity: The Earth’s rotational axis is always tilted slightly; currently, its axis is about 23.4 degrees from the vertical. Alternatively, you could say that its equatorial plane is tilted about 23.4 degrees relative to its orbital plane. This tilt is responsible for Earth’s seasons. During the Northern Hemisphere (NH) summer, Earth is further away from the Sun than it is during the NH winter due to its slightly elliptical orbit, yet it receives more sunlight because it’s tilted towards the Sun. During this same time period, the Southern Hemisphere (SH) is tilted away from the Sun, which is why NH summer coincides with SH Winter and vice versa. Contrastingly, during the NH winter, the Earth is closer to the Sun, yet receives less sunlight because it’s tilted away from it. During that same period, the SH is tilted towards the Sun, and is thus experiencing summer.

However, that axial tilt slowly varies between about 22.1 degrees and 24.5 degrees over long quasi-periodic cycles of roughly 41,000 years. The last maximum is estimated to have occurred around 8,700 BCE, and the next minimum should occur roughly around the year 11,800 CE. A more exaggerated tilt corresponds to more severe seasons: warmer summers and colder winters. As you may have guessed, less exaggerated tilt corresponds to milder seasons: cooler summers and warmer winters. The latter phases can lead to increased glaciation. This is because cooler summers mean less ice loss per year, and warmer winters mean more precipitation (rain or snow) to build up ice sheets. Now, you might be wondering why exaggerated tilt wouldn’t build ice sheets with its extra cold winters, but remember that the freezing point of water at 1 ATM of pressure is still going to be 0 degrees Celsius. Reaching negative 50 degrees C in the winter isn’t likely to facilitate much greater glaciation than reaching negative 10 degrees C, and those extra cold winters would involve less precipitation. To add insult to injury, the extra hot summers would melt greater portions of the existing ice each year. That’s why smaller axial tilt values are thought to correspond to increased glaciation and larger tilt values to deglaciation. Moreover, greater surface areas of ice cover can function to resist warming via the ice-albedo feedback (or snow-albedo feedback), which I mentioned briefly in my article on how continental drift affects climate (here and here).

Axial Tilt (photo credit).

Axial Tilt (photo credit).

Axial Precession: At any given obliquity, the direction of the earth’s rotational axis can “wobble” around the vertical in its own cycles (called precession) even while maintaining a more or less constant angle between the rotational axis and the vertical. This is caused by gravitational influences on the earth from the sun and moon. It takes roughly just under 26,000 years for the earth to complete an entire cycle of precession. Estimates differ from different sources, in part due to the fact that the rate of precession is not constant. This is also the reason earth’s axis points either towards Polaris or Vega as the “North Star” roughly every 13,000 years.

Axial Precession.

Axial Precession.

In the contrasting case (i.e. precession in the opposite phase of its current configuration), NH Winters would occur when Earth was furthest away from the sun and summers would occur when it was closest. That would mean extra hot summers, and thus more glacial melting. It would also mean extra cold winters, but those colder winters also correspond to less precipitation. That’s why our current precession should be more conducive to building the NH ice sheets, but the opposite is occurring due to reasons we’ll delve into soon enough. Again, loss of ice also means less help from the ice-albedo feedback effect, which could otherwise help resist further warming. Although axial precession does not affect total annual insolation, it can have a profound effect on where and when that solar energy is distributed, and consequently on the formation or disintegration of ice sheets. Right now, the northern hemisphere is closer to the sun in the NH Winter and further away in the NH Summer. This makes NH Summers less hot and NH Winters less cold than would be the case if Earth were in the opposite phase in its precession cycle. Presumably, the warmer NH Winters should be conducive to more precipitation (snow fall), which would contribute to glaciation, whereas the moderate summers would be conducive to less glacial melting than if the precession were in the opposite configuration from its current phase.

Keep in mind that the magnitude of these seasonal effects also depends on how eccentric our orbit is around the sun, and neither obliquity nor precession affects the total amount of energy coming in from the sun. Their immediate warming or cooling effects are only regional, but regional warming can lead to global warming by altering ocean circulation patterns, redistributing heat throughout the oceans, and consequently causing the oceans to release stored CO2, by decreasing its solubility, which can drive additional warming via the greenhouse effect.

In part II, we’ll look at three other orbital cycles: orbital eccentricity, apsidal precession and orbital inclination. After that, we’ll look at their combined effects on climate in part III, and then discuss the limitations of our current knowledge by examining some unsolved problems regarding the relationship between these cycles and Earth’s glaciation cycles.

References:

Capitaine, N., Wallace, P. T., & Chapront, J. (2003). Expressions for IAU 2000 precession quantities. Astronomy & Astrophysics412(2), 567-586.

Hays, J. D., Imbrie, J., & Shackleton, N. J. (1976, December). Variations in the Earth’s orbit: pacemaker of the ice ages. American Association for the Advancement of Science.

Martin, P., Archer, D., & Lea, D. W. (2005). Role of deep sea temperature in the carbon cycle during the last glacial. Paleoceanography20(2).

Schmittner, A., & Galbraith, E. D. (2008). Glacial greenhouse-gas fluctuations controlled by ocean circulation changes. Nature456(7220), 373-376.

Skinner, L. C., Fallon, S., Waelbroeck, C., Michel, E., & Barker, S. (2010). Ventilation of the deep Southern Ocean and deglacial CO2 rise. Science,328(5982), 1147-1151.

Toggweiler, J. R., Russell, J. L., & Carson, S. R. (2006). Midlatitude westerlies, atmospheric CO2, and climate change during the ice ages.Paleoceanography21(2).