1. Lecture 34: Orbital (Milankovitch) Theory of the Ice Ages
During the Quaternary, climate alternated between glacial and interglacial states, but we still don’t completely understand many of the details about how this occurred.

2. Interglacial Glacial warmer, less ice colder, more ice Holocene
Last glaciation
colder, more ice
Interglacial
Glacial

3. Orbital forcing of Earth’s climate
Changes in Earth’s orbital geometry
(eccentricity, tilt, precession)
Changes in the Earth's orbit can be precisely calculated using principles of celestial mechanics. Changes result from gravitational interactions between the Earth, the moon, and the larger planets in our solar system.
Changes in Earth’s orbital geometry give rise to changes in the seasonal distribution of insolation as a function of latitude. The total insolation averaged over the year doesn’t change much, but the seasonal distribution does.
These changes in solar radiaiton influence the growth and decay of glaciers that, together with other feedback processes (e.g., greenhouse gases) results in glacial-interglacial cycles.
Changes in the seasonal distribution of
Insolation (heat) as a function of latitude
Amplified by other processes
CO2, albedo
feedback
Glacial-interglacial climate change

4. James Croll Scottish (1821-1890)
Millwright, carpenter, tea shopkeeper, electrical sales, hotelkeeper, insurance salesman, janitor, Geologic Survey, Fellow of the
Royal Society
In the 19th century, James Croll developed a theory of the effects of variations of the earth's orbit on climate cycles. His idea was that decreases in winter sunlight would favour snow accumulation. He was the first to recognize the importance of a positive ice-albedo feedback to amplify solar variations.
decreases in winter radiation would favor snow accumulation, coupled this to the idea
of a positive ice-albedo feedback to amplify the solar variations.

5. Milutin Milankovitch, Serbian mathematician (1879-1958)
1941, “Canon of Insolation of the Earth and Its Application to the Problem of the Ice Ages,” 626 pages
improved upon Croll's work by making more precise calculations of solar insolation (all done by hand!)
Emphasized the importance of decreases in summer radiation which favors snow accumulation and glacial advance
Milutin Milankovitch improved upon Croll's work partly by the use of improved calculations of the earth's orbit then recently published by Ludwig Pilgrim in 1904.
In 1941, Milankovitch published his great work “Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem” (Canon of Insolation of the Earth and Its Application to the Problem of the Ice Ages) was completed, 626 pages
Milankovitch correctly hypothesized that summer radiation is the determining factor whether ice sheets grow or melt. It is always cold enough in winter for snow to be preserved, but summer temperature determines whether the snow from the previous season will be preserved or will melt.

6. The equilibrium line of a glacier is the location where
accumulation equals ablation
If accum>ablation, glacier advances
If ablation>accum glacier retreats
Changes in summer insolation controls the position of the equilibrium line and determines whether a glacier has a net positive or negative mass balance.
Decreased summer insolation
lowers the equilibrium line
and glacier advances.

7. in northern hemisphere
Cool summers
in northern hemisphere 60 65 70
Latitude of equivalent insolation 75
300
250
200
150
100 50
Milankovitch (1941) predicted that glaciations should correspond with summer insolation minima. Unfortunately, the known history of glaciations was too coarse in 1941 to provide an adequate test of Milankovitch’s hypothesis. The hypothesis was shelved for more than 30 years.
550
500
450
400
350
300
600

8. Earth’s orbital parameters that affect incoming solar radiation:
Precessions (seasonal distribution)
Obliquity (seasonal distribution)
Eccentricity (only parameter to affect total radiation but effects are small)

9. Today’s orbital parameters
Eccentricity grossly exaggerated
Today’s orbital parameters
152.5 x 106 km
147.5 x 106 km
July

10. Obliquity is responsible for seasons
June 21
Dec 21
Obliquity is the tilt of the Earth’s rotational axis relative to the plane of the ecliptic. Obliquity, which is presently at 23.5o, is responsible for seasonality.
Mar 21
Sept 21

11. Obliquity Current value: 23.5o Range: 22o-24.5o Period: 41,000 yrs
Obliquity varies from a minimum of 22.1o to a maximum of 24.5 o with a period of 41,000 years.
Current value: 23.5o
Range: 22o-24.5o
Period: 41,000 yrs

12. Effect of Obliquity on Insolation
difference in obliquity from 22 to 24.5o with other parameters held at present values
Boreal summer
W m-2
This figure shows changes in the seasonal contrast of insolation in W m-2 caused by an increase in the obliquity from 22.0o to 24.5o with eccentricity and precession set at present values. This represents the maximum effect of obliquity.
Note that the high latitudes are affected more than the low latitudes.
Obliquity is in phase between the two hemisphere for the same season. For example, an increase in obliquity will result in more summer insolation for both the northern and southern hemipshere polar regions.
summer
austral
Effect on insolation is greatest at high latitudes
Same sign for respective summer season (hemispheric response is in phase).

13. varies at a period of 41 kyrs.
The top figure shows variations in obliquity for the last million years along with its affect on insolation at the poles and equator. Note the effect is greater at the poles than the equator.
Below is shown the periods of variation. By far the dominant period is 41,0000 years.
varies at a period of
41 kyrs.
Obliquity
frequency [1/ky] Period [ky] Amplitude

14. Eccentricity Current value: 0.017 Range: 0-0.06p
The eccentricity of the Earth’s orbit is currently
In the past, it has varied near 0 (circular) to 0.06.
a - p
Current value: 0.017
Range:
Period(s): ~100,000 yrs
~400,000 yrs
Eccentricity =
a + p
a = aphelion distance
p = perihelion distance

15. Eccentricity changes the total insolation received by the
Earth but the
difference is small!
0.5 W m-2/ 1370 W m-2
= 0.04%
Variations in eccentricity for the past million years. Eccentricity changes the global mean insolation but only by a small amount (~0.5 W m-2 between max and min eccentricity values)
The power spectrum of eccentricity is complex with dominant periods at ~406, 95 and 123 kyrs.
Dominant periods are
at ~400 and near 100 kyrs
Eccentricity
frequency [1/ky] Period [ky] Amplitude

16. Precession
(axial)
Precession is the “wobble” of the earth’s rotational axis with time.

17. Axial Precession Precession of the axis of the earth Year:
The projection of the earth’s rotational axis maps a circle in space that takes about 25,700 years to complete. This means the north star (Polaris presently) changes through time.
Thuban, a fourth-magnitude star in the constellation Draco, was the "Pole Star" at the time the Egyptians built the Pyramids.

18. Precession of the Ellipse
This animation shows precession of the ellipse at constant eccentricity.
Elliptical shape of Earth’s orbit rotates
Precession of ellipse is slower than axial precession
Both motions shift position of the solstices and equinoxes relative to
Earth-Sun distance

19. The effect of axial and elliptical precession is the change the
timing during the year of perihelion and aphelion
152.5 x 106 km
147.5 x 106 km
July

20. Precession of the Equinoxes
July 4 a
Earth’s wobble and rotation of its elliptical orbit produce precession of the solstices and equinoxes
One cycles takes 23,000 years
Simplification of complex angular motions in three-dimensional space p
Jan 4
The effect of axial and elliptical precession is to change the relation of the equinoxes and solstices relative to perhelion and aphelion. This is also known as precession of the equinoxes. a p a p a p

21. Extreme Solstice Positions
Today June 21 solstice is near aphelion (July 4)
Solar radiation a bit lower making summers a bit cooler
Configuration reversed ~11,500 years ago
Precession moves June solstice to perihelion
Solar radiation a bit higher, summers are warmer
Assumes no change in eccentricity
For example, perihelion (Jan 4) occurs close to winter solstice today (Dec. 21).
11,500 years ago, perihelion coincided with summer solstice and aphelion occurred during winter solstice.
Cool summers
Warm summers

22. maximum value (boreal summer)
Effect of precession from its minimum value (boreal winter at perihelion) to its
maximum value (boreal summer)
Boreal summer
Effect of precession from its minimum value (boreal winter at perihelion) to its maximum value (boreal summer at
perihelion) with present-day values for eccentricity and obliquity. Contour interval is 10 W m-2. The brown areas correspond to zone with a zero insolation. Note that precession affects all latitudes and the sign is opposite for northern and southern hemipsheres for the same season. E.g., when northern hemisphere summer is warm, southern hemisphere summer is cool. The hemispheres are out of phase for precession.
summer
austral
Precession affects insolation at both high and low latitudes.
Opposite sign in northern and southern hemispheres for respective season
(out of phase)

23. Dominant periods at ~19, 22 and 24 kyrs Precession
Precession for the past million years. Note that precession affects incoming solar radiation at all latitudes. The dominant frequencies are at ~19, 22 and 24 kyrs. Often these are not distinguishable in paleoclimate records and precession is expressed as a broad peak centered on ~21 kyrs.
Dominant periods
at ~19, 22 and 24 kyrs
Precession
frequency [1/ky] Period [ky] Amplitude

24. Eccentricity modulates the amplitude of precession
100, 400 kyrs a
a=p1 p2
The amplitude of the precessional cycle is modulated by eccentricity. If eccentricity is 0, there is no difference between perihelion and aphelion so the affect of precession is minimized. The greater the eccentricity, the larger the effect of precession on seasonal insolation.
19, 23 kyrs

25. The three orbital parameters combine to change boreal summer insolation
today
The three orbital parameters (eccentricity, obliquity, precession) for the last million years and 100 kyrs into the future.

26. Last
Ice
Age
Difference in Northern Hemisphere insolation at summer solstice relative to today
How do orbital parameters combine to produce changes in insolation? Visualization of Northern Hemisphere insolation anomaly (relative to today) at summer solstice from 25,000 years (LGM) to 10,000 (early Holocene). Note large negative anomaly 25,000 year ago and large positive anomaly at 11,000 yrs bp in the early Holocene.
Holocene
interglacial

27. Ice Growth (glacial) Configuration
(cool summers)
Low obliquity (low seasonal contrast)
NH summers during aphelion (cold summers in the north)
High eccentricity
Glaciation can only develop if the summer high northern latitudes are cold enough to prevent the winter snow from melting, thereby allowing a positive annual balance of snow and ice.
Ice growth occurs during cool summers. What orbital configuration corresponds to cool summers?
Minimum tilt, June 21 aphelion, and highly eccentric orbit

28. Ice Decay (Deglaciation) Configuration
High obliquity (high seasonal contrast)
NH summers during perihelion (hot summers in the north)
High eccentricity
Ice decay configuration would correspond to minimum northern hemisphere summer temperatures.
High obliquity, perihelion during summer, and high eccentricity.

29. Classic Milankovitch Forcing: Insolation at 65°N, June 21
Ice
decay
Insolation forcing at 65oN on summer solstice for the past 400 kyrs. Milankovitch theory predicts ice growth when summer insolation is low, and ice decay when it is high.
Ice
growth

30. Milankovitch Theory Revived
The measurement of long, continuous oxygen isotope variations in deep-sea were instrumental in providing evidence for the Milankovitch theory of the ice ages.
The Milankovitch Theory was not well received until the early 1970s when investigations of the deep-sea sediments brought widespread acceptance of Milanković's view, because the periodicities observed in the marine record matched the predictions by Milankovitch.
Pacific deep core V28-238
Shackleton & Opdyke, 1972

31. Variations in the Earth's Orbit: Pacemaker of the Ice Ages
J. D. Hays, John Imbrie, N. J. Shackleton
Science, 194, No. 4270, (Dec. 10, 1976), pp
(eccentricity)
(obliquity)
(precession)
The “smoking gun” came in a publication to Science in 1976 by Jim Hays, John Imbrie and Nick Shackleton (pictured from right to left).
Marine oxygen isotope record shows
the same periodicities predicted by
orbital forcing.

32. Marine isotope record provides support for the Milankovitch Theory but there are still some unanswered questions
So many
problems
1. 100,000-year problem
2. The Mid Pleistocene transition problem
3. Stage 11 (Termination V) problem
Although orbital forcing of Earth’s climate is well accepted, the details of how orbitally-induced insolation changes affect climate are debated. Several challenges have been raised to the “Classical” Milankovitch Theory that summer insolation at 65oN is the main driver.
Three problems with classical astronomical theory:
Cyclicity is close to 100 kyrs but there is insignificant changes in radiative forcing at this period (100-kyr problem)
Mid Pleistocene transition change from 41 to 100 kyr periodicity occurred without major changes in orbital forcing
Stage 11 problem, the most prominent glacial-interglacial transition of the Pleistocene (Term V) occurs at a time of minimal forcing
Causality problem -- supposed effect occurs before the casue
4. Causality Problem:
Timing of Term II
Milutin Milankovitch

33. I II III IV V VI Ice decay Ice growth 5 1 9 11 7 13 8 14 4 10 2 6 12
The oxygen isotope record (ice volume) doesn’t look exactly like the insolation forcing so clearly other factors must come into play. Comparison between (a) the SPECMAP stacked δ18O composite and (b) insolation curve for 65°N, June 21. The vertical red lines denote the Terminations (glacial-to-interglacial transitions).
Ice
growth

34. Insolation Benthic 18O 65oN 100 ky 41 ky 23 ky
The power spectrum for oxygen isotopes looks very different from that of insolation for the past 450 kyrs. It is dominated by 100-kyr (eccentricty) power, 41-kyr obliquity and little precessional power.

35. ? 1. The 100-kyr Problem Forcing small big Response
Classic Milankovitch forcing
(might consider alternatives)
Forcing
small
Why does the climate system have so much 100-kyr power when the supposed forcing does not?
Traditionally explained by non-linear response involving internal feedbacks. ?
big
Response
Why does the climate system have so much 100-kyr power when the forcing is so weak?
but recall that eccentricity also modulates amplitude of the precession cycle

36. 2. The Middle Pleistocene Transition32 16
The MPT is very apparent in power spectra of the benthic d18O record of the last 2 million years. Note that there is no 100-kyr power in the early Pleistocene and the spectra is dominated by obliquity. This has been referred to as the so-called “41-kyr” world. The power spectrum of the late Pleistocene is dominated by 100-kyr cycle. Note however that the power of the 41-kyr cycle remains about the same as during the early Pleistocene.
Schulz and Zeebe (2006)

37. Insolation (June 65oN ) Milankovitch Forcing
According to Classic Milankovitch theory, glacial-interglacial cycles are controlled by summer insolaiton at 65oN that controls
The power spectra for the forcing (June 65oN insolation) according to classic Milankovitch theory has a very different character than the benthic d18O record. It is dominated by precession with some 41-kyr power, bu contains no 100-kyr power. There is also no apparent change in orbital forcing (I.e., summer insolation 65oN) across the MPT.
This suggests that the MPT must be driven by processes internal to the climate system
Schulz and Zeebe (2006)
100 kyr
100 kyr

38. ? 100-kyr world 18O 41-kyr world Insolation (forcing)
Comparison of power spectra of benthic d18O and insolation (June 65oN) before and after the MPT. ?

39. 3. Stage 11/Termination V ProblemII
III IV V VI
Ice
decay 11
Strong
Response 12
The Stage 11 problem refers to the fact that insolation forcing is very weak about 400,000 years ago, yet termination V (transition from MIS 12 to 11) represents one of the largest deglaciations of the late Pleistocene. How can the response be so strong with such a weak forcing?
Weak
Forcing
Ice
growth

40. sea level begins to rise before boreal summer insolation
4. Causality Problem
sea level begins to rise before
boreal summer insolation
Termination II/Stage 5 Problem
The “causality problem” refers to the timing of the start of deglaciaiton relative to boreal summer insolation forcing. U/Th of corals from Tahiti drilling clearly shows the rise in sea level at Termination II began at about 142,000 yrs BP, significantly earlier than the rise in boreal summer insolation.
A. L. Thomas, G. M. Henderson, et al., Penultimate Deglacial Sea-Level Timing from U/Th Dating of
Tahitian Corals. Science doi: /science (23 April) 2009

41. Milutin Milankovitch (1879-1958)
NATURE|Vol 451|17 January 2008|
Mystery is far from being solved.
My sense is the missing piece of the puzzle is understaking the Iinteractin of the millennial and orbital bands.
Obtaining long, millennially-resolved records of climate variability over long periods of time is something that IODP is uniquely suited to do.
A few well-placed expeditions may very well finish the job.
Milutin Milankovitch ( )

42. Ice Sheet Growth Lags Summer Insolation
Non-linear ice volume models invoking threshold response
How to
explain the
100-kyr
power?
Ice Sheet Growth Lags Summer Insolation
Various non-linear ice volume models have used a combination of threshold response and time constants (lag) to produce 100-kyr power. The models initiate ice growth after insolation has exceeded a threshold insolation value.
An ice sheet 3 km thick may take 10,000 years to grow under most favorable conditions, so ice volume lags summer insolation cooling. The time constant for ice decay is usually faster.

43. Model 1: Calder (1974) V = ice volume i = summer insolation at 65°N
Calder (1974) represents one of the first attempts to similuate ice volume from insolation forcing. It produced some low-frequency variability near 100-kyr but falls short of the observed signal.
V = ice volume i = summer insolation at 65°N
i0 = insolation threshold
k = kA (accumulation) if i < i0
k = kM (melting) if i > i0
18O (observed)
Ice
Volume model
Model produces some
100-kyr power

44. Model 2: Imbrie and Imbrie (1980)
Written in dimensionless form (i.e., variables are divided by a scaling value)
18O
Ice
volume
dV/dt = (i-V)/
The most commonly used ice volume model is that of Imbrie and Imbrie (1980). It produces power at all the Milankovitch frequencies: 400, 100, 41, 23, 19 kyrs. The precessional frequencies are much greater than observed in the d18O record and the 400-kyr eccentricity cycle is not observed at all in the d18O record.
Not observed
In climate record
(time series might
be too short)
V = ice volume
i = summer insolation at 65°N
t = t M if V > i (melting)
t = t A otherwise
Ice
Volume model
18O

45. Smaller, thinner ice sheet Ice sheets responded linearly to
Hypothesis:
Roy et al. (2004)
41 kyr world
Less ice volume
Smaller, thinner ice sheet
Ice sheets responded linearly to
obliquity forcing
100-kyr world
New source of low-frequency variability:
Ice volume and thickness increases
Ice sheet mass is capable of surviving
weak summer insolation maxima
Deglaciations begin to skip precession
and/or obliquity cycles
Lenthens duration of glacial cycle
New source of high-frequency variability:
Large, thick ice-sheet begins behaving
dynamically (non-linearly)
100-kyr cycle driven by internal ice
sheet dynamics (paced by insolation)
Clark and Pollard (1998) proposed the Regolith Hypothesis to explain the MPT. The hypothesis suggests that a change in the basal boundary condition of the Laurentide ice sheet was responsible for the MPT.
Prior to the MPT, the LIS was underlatin by soft, deformable sediment (regolith), which limited the thickness of the ice sheet. Glacial erosion slowly removed the regolith layer and the bed became progressively underlain by hard substrate (Canadian shield) which permitted the growth of a much thicker ice sheet.