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### Orbital forcing of Earth’s climate

Milankovitch Theory of the Ice Ages

Milutin Milankovitch (1941)

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)

Forcing: Boreal

Summer insolation

Changes in Earth’s orbital geometry

(eccentricity, tilt, precession)

Changes in the seasonal distribution of

Insolation (heat) as a function of latitude

Amplified by other processes

Glacial-interglacial climate change

James Croll

- Scottish (1821-1890)

- Millwright, carpenter, tea shopkeeper, electrical sales, hotelkeeper, insurance salesman, janitor, Geologic Survey, Royal Fellow

decreases in winter radiation would favor snow accumulation, coupled this to the idea

of a positive ice-albedo feedback to amplify the solar variations.

- 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 partly by using more precise calculations
- Emphasized decreases in summer radiation favored snow accumulation and glacial advance

Obliquity creates inter-hemispheric heat imbalance (caloric equator shifts seasonally)

- Current value: 23.5o
- Range: 22o-24.5o
- Period: 41,000 yrs

Effect of Obliquity on Insolation

difference in obliquity from 22 to 24.5o with other parameters held at present values

Effect on insolation is greatest at high latitudes

Same sign for respective summer season (hemispheric response is in phase).

41 kyrs.

Obliquity

frequency [1/ky] Period [ky] Amplitude

0.02439 40.996 0.011168

0.02522 39.657 0.004401

0.02483 40.270 0.003010

0.01862 53.714 0.002912

0.03462 28.889 0.001452

r

r’

Perihelion

Aphelion

a

b

Earth travel around the sun in an elliptical orbit with the Sun at one focus

What makes eccentricity vary?The gravitational pull of the other planets

- The pull of another
- planet is strongest
- when the planets
- are close together

- The net result of
- all the mutual inter-
- actions between
- planets is to vary the
- eccentricities of their
- orbits

the total insolation

received by the

Earth but the

difference is small!

0.5/342.7 = 0.15%

Dominant periods are

at ~400 and 100 kyrs

Eccentricity

frequency [1/ky]Period [ky]Amplitude

0.00246406.1820.010851

0.0105594.8300.009208

0.00807123.8820.007078

0.0101498.6070.005925

0.00769130.0190.005295

(axial)

Precession of the Ellipse

- Elliptical shape of Earth’s orbit rotates
- Precession of ellipse is slower than axial precession
- Both motions shift position of the solstices and equinoxes

Precession of the Equinoxes

- 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

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

Effect of precession from its minimum value (boreal winter at perihelion) to its

maximum value (boreal summer)

Precession affects insolation at both high and low latitudes.

Opposite sign in northern and southern hemispheres for respective season

(out of phase)

at ~19, 22 and 24 kyrs

Precession

frequency [1/ky]Period [ky]Amplitude

0.0422123.6900.018839

0.0446722.3850.016981

0.0527518.9560.014792

0.0523619.0970.010121

0.0432623.1140.004252

- (cool summers)
- Low obliquity (low seasonal contrast)
- High eccentricity and NH summers during aphelion (cold summers in the north)

The equilibrium line of a glacier is the location where winter

accumulation of snow is equal to the summer loss.

Decreased summer insolation lowers the equilibrium line

and glacier advances.

- High obliquity (high seasonal contrast)
- High eccentricity and NH summers during perihelion (hot summers in the north)

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. 1121-1132

(eccentricity)

(obliquity)

(precession)

Marine oxygen isotope record shows

the same periodicities predicted by

orbital forcing.

Classic Milankovitch forcing

(might consider alternatives)

Forcing

small

?

big

Response

Why does the climate system have so much 100-kyr power

Traditionally explained by non-linear response involving internal feedbacks.

Non-linear ice volume models invoking threshold response

Ice Sheet Growth Lags Summer Insolation

Model 1: Calder (1974)

18O

Ice

volume

V = ice volumei = summer insolation at 65°N

i0 = insolation threshold

k = kA (accumulation) if i < i0

k = kM (melting) if i > i0

18O (observed)

Ice

volume

Produces some

100-kyr power

Model 2: Imbrie and Imbrie (1980)

- Written in dimensionless form (i.e., variables are divided by a scaling value)

18O

Ice

volume

Not observed

In climate record

(time series might

be too short)

V = ice volume

i = summer insolation at 65°N

t = tM if V > i (melting)

t = tA otherwise

Ice

volume

18O

due to low eccentricity

Response (Imbrie and Imbrie, 1980)

forcing

Ice volume lags insolation forcing by a constant or varying

amount of time.

Model 3: Paillard (1998)

Switching between

three states:

Interglacial (I)

Weak glacial (g)

Full glacial (G)

Model 3: Paillard (1998)

- Very good agreement with record, both in time and frequency domain.
- Weakness?: Highly nonlinear, with a large number of adjustable parameters.
- (too easily tweaked?)

Ice

volume

18O

"Ignoring anthropogenic and other possible sources of variation acting at frequencies

higher than one cycle per 19,000 years, this model predicts that the long-term cooling

trend which began some 6,000 years ago will continue for the next 23,000 years."

(Imbrie and Imbrie, 1980)

The Present Interglacial, How and When Will it End? January 1972, Providence, RI.

Organizers

George Kukla, Czechoslovakian Academy of Sciences, Prague

Robley Matthews, Brown University, Providence

A conference summary appeared in Science in October 1972.

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