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Milankovitch cycles

Past and future Milankovitch cycles. VSOPallows prediction of past andfuture orbital parameters with great accuracy. is obliquity (axial tilt). e iseccentricity.islongitude of perihelion.esin() is the precession indexwhich together with obliquity, controls the seasonal cycle of insolation

is the calculated daily-averaged insolation at the top of theatmosphere, on the day of the summer solstice at 65 N latitude. Benthicforams and Vostok ice core show two distinct proxies for past globasealevel and temperature, from ocean sediment and Antarctic icerespectively. Vertical gray line is current conditions, at 2 ky A.D.Milankovitch Theory describes the collective effects of changes in theEarth's movements upon its climate, named after Serbian civil engineeandmathematicianMilutin Milankovi.Milankovi mathematically theorised

that variations ineccentricity,axial tilt,andprecessionof the Earth's orbit determined climatic patterns onEarth.The Earth's axis completes one full cycle of precession approximately every 26,000 years. At the same

time, the elliptical orbit rotates, more slowly, leading to a 23,000-year cycle between the seasons and theorbit. In addition, the angle between Earth's rotational axis and the normal to the plane of its orbit movesfrom 22.1 degrees to 24.5 degrees and back again on a 41,000-year cycle; currently, this angle is 23.44degrees and is decreasing.Other astronomical theories were advanced by Joseph Adhemar,James Crolland others, but verificationwas difficult due to the absence of reliably dated evidence and doubts as to exactly which periods wereimportant. Not until the advent of deep-ocean cores and a seminal paper byHays,ImbrieandShackleton"Variations in the Earth's Orbit: Pacemaker of the Ice Ages", in Science, 1976,[1] did the theory attain itspresent state.Earths movements

As the Earth spins around its axis and orbits around the Sun, several quasi-periodic variations occurAlthough the curves have a large number of sinusoidal components, a few components are dominant[1]

Milankovitch studied changes in the orbital eccentricity, obliquity, and precession of Earth's movementsSuch changes in movement and orientation change the amount and location of solar radiation reaching theEarth. This is known as solar forcing(an example ofradiative forcing). Changes near the north polar areaare considered important due to the large amount of land, which reacts to such changes more quickly thanthe oceans do.Orbital shape (eccentricity)Circular orbit, without eccentricity and with 0.5 eccentricity.

The Earth's orbit is an ellipse. The eccentricity is ameasure of the departure of this ellipse from circularityThe shape of the Earth's orbit varies from being nearlycircular (low eccentricity of 0.005) to being mildlyelliptical (high eccentricity of 0.058) and has a mean

eccentricity of 0.028. The major component of thesevariations occurs on a period of 413,000 years(eccentricity variation of 0.012). A number of otherterms vary between components 95,000 and 125,000

years (with a beat period 400 ka), and loosely combine into a 100,000-year cycle (variation of 0.03 to+0.02). The present eccentricity is 0.017.If the Earth were the only planet orbiting our Sun, the eccentricity of its orbit would not vary over time. TheEarth's eccentricity varies primarily due to interactions with the gravitational fields ofJupiterandSaturn.Asthe eccentricity of the orbit evolves, thesemi-major axisof the orbital ellipse remains unchanged. From theperspective of the perturbation theory used in celestial mechanics to compute the evolution of the orbit, the

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semi-major axis is anadiabatic invariant.According toKepler's third lawthe period of the orbit is determinedby the semi-major axis. It follows that the Earth's orbital period, the length of asidereal year,also remainsunchanged as the orbit evolves. As the semi-minor axis is decreased with the eccentricity increase, theseasonal changes increase[2].But the mean solar irradiation for the planet changes only slightly for smaleccentricity, due toKepler's second law.The same average irradiation does not correspond to the average of corresponding temperatures (due to

non-linearity of theStefanBoltzmann law). For an irradiation with corresponding temperature 20C and itssymmetric variation 50% (e.g. from the seasons change[3]) we obtain asymmetric variation ocorresponding temperatures with their average 16C (i.e. deviation -4C). And for the irradiation variationduring a day (with its average corresponding also to 20C) we obtain the average temperature (for zerothermal capacity)-113C.Currently the difference between closest approach to the Sun (perihelion)and furthest distance (aphelion)isonly 3.4% (5.1 millionkm). This difference is equivalent to about a 6.8% change in incoming solar radiation.Perihelion presently occurs around January 3, while aphelion is around July 4. When the orbit is at its mostelliptical, the amount of solar radiation at perihelion is about 23% greater than at aphelion. This difference isroughly 4 times the value of the eccentricity. [clarification needed]

Season (Northern Hemisphere) Durations

data fromUnited States Naval Observatory

Year Date: GMT Season Duration

2005 Winter Solstice 12/21/2005 18:35 88.99 days

2006 Spring Equinox 3/20/2006 18:26 92.75 days

2006 Summer Solstice 6/21/2006 12:26 93.65 days

2006 Autumn Equinox 9/23/2006 4:03 89.85 days

2006 Winter Solstice 12/22/2006 0:22 88.99 days

2007 Spring Equinox 3/21/2007 0:07 92.75 days

2007 Summer Solstice 6/21/2007 18:06 93.66 days

2007 Autumn Equinox 9/23/2007 9:51 89.85 days

2007 Winter Solstice 12/22/2007 06:08Orbital mechanics requires that the length of the seasons be proportional to the areas of the seasonaquadrants, so when the eccentricity is extreme, the seasons on the far side of the orbit can be substantiallylonger in duration. When autumn and winter occur at closest approach, as is the case currently in thenorthern hemisphere, the earth is moving at its maximum velocity and therefore autumn and winter areslightly shorter than spring and summer. Thus, summer in the northern hemisphere is 4.66 days longer thanwinter and spring is 2.9 days longer than autumn.

Axial tilt (obliquity)22.1-24.5 range of Earth's obliquity.The angle of the Earth's axial tilt (obliquity) varies with respect to theplane of the Earth's orbit. These slow 2.4 obliquity variations are

roughly periodic, taking approximately 41,000 years to shift between atilt of 22.1 and 24.5 and back again. When the obliquity increases, theamplitude of the seasonal cycle in insolation (INcident SOLaradiATION) increases, with summers in both hemispheres receivingmore radiative flux from the Sun, and the winters less radiative flux. Asa result, it is assumed that the winters become colder and summerswarmer.But these changes of opposite sign in the summer and winter are not of

the same magnitude. The annual mean insolation increases in high latitudes with increasing obliquity, while

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lower latitudes experience a reduction in insolation. Cooler summers are suspected of encouraging the startof an ice age by melting less of the previous winter's ice and snow. So it can be argued that lower obliquityfavors ice ages both because of the mean insolation reduction in high latitudes as well as the additionareduction in summer insolation. However no significant climate changes are associated with extreme axiatilts.Scientists using computer models to study more extreme tilts than those that actually occur have concluded

that climate extremes at high obliquity would be particularly threatening to advanced forms of life thatpresently exist on Earth. They noted that high obliquity would not likely sterilize a planet completely, buwould make it harder for fragile, warm-blooded land-based life to thrive as it does today. [4].Currently the Earth is tilted at 23.44 degrees from its orbital plane, roughly half way between its extremevalues. The tilt is in the decreasing phase of its cycle, and will reach its minimum value around the year10,000C.E.

Axial precessionPrecessional movement.Precession is the change in the direction of the Earth's axis of rotation relative tothe fixed stars, with a period of roughly 26,000 years. This gyroscopic motion isdue to the tidal forces exerted by the sun and the moon on the solid Earth,associated with the fact that the Earth is an oblate spheroidshape and not a

perfect sphere. The sun and moon contribute roughly equally to this effect.When the axis is aligned so it points toward the Sun during perihelion, one polarhemisphere will have a greater difference between the seasons while the otherhemisphere will have milder seasons. The hemisphere which is in summer atperihelion will receive much of the corresponding increase in solar radiation, butthat same hemisphere will be in winter at aphelion and have a colder winter.

The other hemisphere will have a relatively warmer winter and cooler summer.When the Earth's axis is aligned such that aphelion and perihelion occur near the equinoxes, the Northernand Southern Hemispheres will have similar contrasts in the seasons.

At present, perihelion occurs during the Southern Hemisphere's summer, and aphelion is reached duringthe southern winter. Thus the Southern Hemisphere seasons are somewhat more extreme than theNorthern Hemisphere seasons, when other factors are equal.

Apsidal precession

Planets orbitingthe Sun followelliptical (oval)orbits that rotategradually overtime (apsidalprecession). Theeccentricity of

this ellipse is exaggerated for visualization.Most orbits in the Solar System have a much

smaller eccentricity, making them nearlycircular.Effects of apsidal precession on the seasonsIn addition, the orbital ellipse itself precessesin space, primarily as a result of interactionswith Jupiter and Saturn. This orbitalprecession is in the same sense to thegyroscopic motion of the axis of rotation, shortening the period of the precession of the equinoxes withrespect to the perihelion from 25,771.5 to ~21,636 years.

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Orbital inclinationThe inclination of Earth's orbit drifts up and down relative to itspresent orbit with a cycle having a period of about 70,000 yearsMilankovitch did not study this three-dimensional movement. Thismovement is known as "precession of the ecliptic" or "planetaryprecession".

More recent researchers noted this drift and that the orbit alsomoves relative to the orbits of the other planets. The invariableplane,the plane that represents theangular momentumof the solasystem, is approximately the orbital plane ofJupiter.The inclinationof the Earth's orbit has a 100,000 year cycle relative to the

invariable plane; by chance, this is very similar to the 100,000 year eccentricity period. This 100,000-yeacycle closely matches the 100,000-year pattern of ice ages.It has been proposed that a disk of dust and other debris exists in the invariable plane, and this affects theEarth's climate through several possible means. The Earth presently moves through this plane aroundJanuary 9 and July 9, when there is an increase in radar-detectedmeteorsand meteor-relatednoctilucentclouds.[2][3]

A study of the chronology of Antarctic ice cores using oxygen to nitrogen ratios in air bubbles trapped in the

ice, which appear to respond directly to the local insolation, concluded that the climatic responsedocumented in the ice cores was driven by Northern Hemisphere insolation as proposed by the Milankovitchhypothesis (Kawamura et al., Nature, 23 August 2007, vol 448, p912-917). This is an additional validation ofthe Milankovitch hypothesis by a relatively novel method, and is inconsistent with the "inclination" theory ofthe 100,000-year cycle.ProblemsBecause the observed periodicities of climate fit so well with the orbital periods, the orbital theory hasoverwhelming support. Nonetheless, there are several difficulties in reconciling theory with observations.The nature of sediments can vary in a cyclic fashion, and these cycles can be displayed in the sedimentaryrecord. Here, cycles can be observed in the colouration and resistance of different strata100,000-year problemThe 100,000-year problem is that the eccentricity variations have a significantly smaller impact on sola

forcing than precession or obliquity and hence might be expected to produce the weakest effects. However,observations show that during the last 1 million years, the strongest climate signal is the 100,000-year cycleIn addition, despite the relatively large 100,000-year cycle, some have argued that the length of the climaterecord is insufficient to establish a statistically significant relationship between climate and eccentricityvariations.[4] Some models can however reproduce the 100,000 year cycles as a result of non-lineainteractions between small changes in the Earth's orbit and internal oscillations of the climate system.[5][6]400,000-year problemThe 400,000-year problemis that the eccentricity variations have a strong 400,000-year cycle. That cycle isonly clearly present in climate records older than the last million years. If the 100 kavariations are havingsuch a strong effect, the 400 ka variations might also be expected to be apparent. This is also known as thestage 11 problem, after the interglacial in marine isotopic stage 11 which would be unexpected if the400,000-year cycle has an impact on climate. The relative absence of this periodicity in the marine isotopic

record may be due, at least in part, to the response times of the climate system components involved inparticular, thecarbon cycle.

Stage 5 problem

The stage 5 problemrefers to the timing of the penultimate interglacial (inmarine isotopic stage5) whichappears to have begun 10 thousand years in advance of the solar forcing hypothesized to have beencausing it. This is also referred to as the causality problem.

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Effect exceeds cause

420,000 years of ice core data from Vostok, Antarctica researchstation.

The effects of these variations are primarily believed to be due tovariations in the intensity of solar radiation upon various parts ofthe globe. Observations show climate behaviour is much moreintense than the calculated variations. Various internacharacteristics of climate systems are believed to be sensitive tothe insolation changes, causing amplification (positive feedback

and damping responses (negative feedback).

The unsplit peak problem

The unsplit peak problemrefers to the fact that eccentricity has cleanly resolved variations at both the 95and 125kaperiods. A sufficiently long, well-dated record of climate change should be able to resolve bothfrequencies[5],but some researchers interpret climate records of the last million years as showing only asingle spectral peak at 100 ka periodicity. It is debatable whether the quality of existing data ought to besufficient to resolve both frequencies over the last million years.

The transition problem

Variations of Cyle Times, curvesdetermined from ocean sediments

The transition problem refers to the

change in the frequency of climatevariations 1 million years ago. From 1-3million years, climate had a dominant mode matching the 41kacycle in obliquity. After 1 million years agothis changed to a 100 ka variation matching eccentricity. No reason for this change has been established.

Identifying dominant factor

Milankovic himself believed that reductions in summer insolation in northern high latitudes was the dominanfactor leading to glaciation, which lead to him (incorrectly) deducing an approximately 41 kyr period for iceages [7].Subsequent research has shown that the 100 kyr eccentricity cycle is more important, resulting in100,000-yearice agecycles of theQuaternary glaciationover the last few million years.

Theory incomplete

The Milankovitch theory of climate change is not perfectly worked out; in particular, the largest observedresponse is at the 100,000-year timescale, but the forcing is apparently small at this scale, in regard to theice ages.[8]The frequency modulation[9]or various feedbacks (fromcarbon dioxide,cosmic raysor fromicesheet dynamics)explain this discrepancy.

Present and future conditions

http://en.wikipedia.org/wiki/Ice_corehttp://en.wikipedia.org/wiki/Ice_corehttp://en.wikipedia.org/wiki/Vostok,_Antarcticahttp://en.wikipedia.org/wiki/Vostok,_Antarcticahttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Negative_feedbackhttp://en.wikipedia.org/wiki/Negative_feedbackhttp://en.wikipedia.org/wiki/Negative_feedbackhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Kiloannumhttp://www.marine.usf.edu/PPBlaboratory/paleolab_pdfs/Zachos_etal_2001_Science.pdfhttp://www.marine.usf.edu/PPBlaboratory/paleolab_pdfs/Zachos_etal_2001_Science.pdfhttp://www.marine.usf.edu/PPBlaboratory/paleolab_pdfs/Zachos_etal_2001_Science.pdfhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-6http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-6http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-6http://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Quaternary_glaciationhttp://en.wikipedia.org/wiki/Quaternary_glaciationhttp://en.wikipedia.org/wiki/Quaternary_glaciationhttp://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Milankovitch-7http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Milankovitch-7http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Milankovitch-7http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-8http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-8http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-8http://en.wikipedia.org/wiki/Carbon_dioxidehttp://en.wikipedia.org/wiki/Carbon_dioxidehttp://en.wikipedia.org/wiki/Carbon_dioxidehttp://en.wikipedia.org/wiki/Cosmic_rayshttp://en.wikipedia.org/wiki/Cosmic_rayshttp://en.wikipedia.org/wiki/Cosmic_rayshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Ice_sheet_dynamicshttp://en.wikipedia.org/wiki/Cosmic_rayshttp://en.wikipedia.org/wiki/Carbon_dioxidehttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-8http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Milankovitch-7http://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Quaternary_glaciationhttp://en.wikipedia.org/wiki/Ice_agehttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-6http://en.wikipedia.org/wiki/Kiloannumhttp://www.marine.usf.edu/PPBlaboratory/paleolab_pdfs/Zachos_etal_2001_Science.pdfhttp://en.wikipedia.org/wiki/Kiloannumhttp://en.wikipedia.org/wiki/Negative_feedbackhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Vostok,_Antarcticahttp://en.wikipedia.org/wiki/Ice_core

8/11/2019 4Milankovitch cycles.pdf

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Past and future of dailyaverage insolation at top othe atmosphere on the dayof the summer solstice, at 65N latitude. The green curve

is with eccentricity ehypothetically set to 0. The

red curve uses the actual (predicted) value of e. Blue dot is current conditions, at 2 ky A.D.

As mentioned above, at present, perihelion occurs during the Southern Hemisphere's summer and aphelionduring the southern winter. Thus the Southern Hemisphere seasons should tend to be somewhat moreextreme than the Northern Hemisphere seasons. The relatively low eccentricity of the present orbit results ina 6.8% difference in the amount of solar radiation during summer in the two hemispheres.

Since orbital variations are predictable[10], if one has a model that relates orbital variations to climate, it ispossible to run such a model forward to "predict" future climate. Two caveats are necessary: thatanthropogenic effects may modify or even overwhelm orbital effects and that the mechanism by which

orbital forcinginfluences climate is not well understood.

The amount of solar radiation (insolation) in the Northern Hemisphere at 65 N seems to be related tooccurrence of an ice age. Astronomical calculations show that 65 N summer insolation should increasegradually over the next 25,000 years. A regime of eccentricity lower than the current value will last for aboutthe next 100,000 years. Changes in Northern Hemisphere summer insolation will be dominated by changesin obliquity . No declines in 65 N summer insolation, sufficient to cause an ice age, are expected in thenext 50,000 years.

An often-cited 1980 study byImbrieand Imbrie determined that, "Ignoring anthropogenic and other possiblesources of variation acting at frequencies higher than one cycle per 19,000 years, this model predicts thathe long-term cooling trend which began some 6,000 years ago will continue for the next 23,000 years."[11]

More recent work by Berger and Loutre suggests that the current warm climate may last another 50,000years.[12]

The best chances for a decline in Northern hemisphere summer insolation that would be sufficient fotriggering an ice age is at 130,000 years or possibly as far out at 620,000 years .[13

http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Varadi2003-9http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Varadi2003-9http://en.wikipedia.org/wiki/Anthropogenichttp://en.wikipedia.org/wiki/Anthropogenichttp://en.wikipedia.org/wiki/Orbital_forcinghttp://en.wikipedia.org/wiki/Orbital_forcinghttp://en.wikipedia.org/wiki/Insolationhttp://en.wikipedia.org/wiki/Insolationhttp://en.wikipedia.org/wiki/Insolationhttp://en.wikipedia.org/wiki/John_Imbriehttp://en.wikipedia.org/wiki/John_Imbriehttp://en.wikipedia.org/wiki/John_Imbriehttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Imbriel1980-10http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Imbriel1980-10http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Imbriel1980-10http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Berger2002-11http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Berger2002-11http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Berger2002-11http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-12http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-12http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-12http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-12http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Berger2002-11http://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Imbriel1980-10http://en.wikipedia.org/wiki/John_Imbriehttp://en.wikipedia.org/wiki/Insolationhttp://en.wikipedia.org/wiki/Orbital_forcinghttp://en.wikipedia.org/wiki/Anthropogenichttp://en.wikipedia.org/wiki/Milankovitch_cycles#cite_note-Varadi2003-9