lecture 8: orbital variation and insolation change (chapter 7)

Lecture 8: Orbital Variation and Insolation Change

(Chapter 7)

Earth’s revolution around the sun on the ecliptic

Orbit Today

Tilt of the earth’s axis of rotation

Tilt Effect

Tilting and season

Tilt and Season

Extreme tilt

Extreme Tilts

Earth’s revolution around the sun on the ecliptic

Perihelion/Aphelion Today

Change of tilt

Eccentricity of the earth’s orbit

Change of Eccentricity

Precession of equinoxes (wobble and shift of perihelion)

Perihelion

Aphelion

Precession of angle (between perihelion and equinox axes)

Extreme Solstice (large eccentricity * large tilt)

0ka

11ka

Modulation of Precession Index by Eccentricity

Precession Index Modulated by Eccentricity

Seasonal insolation

Where precession signal is large, why?

Where tilt signal is large, why?

What signal is dominant in the annual mean, why?

What is the phase of each signal, in different hemisphere?

~10%

Seasonal insolation

Insolation time series of different months

Apr, 1

Kepler’s laws: equal area!

May 1|Calender=Apr 1 +30 days

May 1|Celestial=Apr 1 +30o

Jul 1|Celestial=Apr 1 +90o

Jul 1|Calender=Apr 1 +91 days

Calendar months (fixed-day) vs. Celestial months (fixed-degree, or fixed-angular)

Calendar vs. Celestial months

Starting Vernal Equinox

Chen et al., 2010, Clm Dyn

0 ka 126 -0 ka, Calendar month

Celestial month Calendar-Celestial

126 ka (PH June) -- 0 ka (PH Jan)

Caloric months (relative warmth)

Caloric summer is the 182 days of insolation more than the other 182 days (Caloric winter)

Searching for orbital signal in climate records

simple

complicated

Milutin Milankovitch was a Serbian engineer and meteorologist - born in 1879 he attended the Vienna institute of  technology graduating in 1904 with a doctorate in technical sciences. He then went on to work in the University of Belgrade where he spent time working on a mathematical theory of climate based on the seasonal and latitudinal variations of solar radiation received by the Earth.        Milankovitch proposed that the changes in the intensity of solar radiation received from the Earth were effected by three fundamental factors.  The first is called eccentricity, a period of about 100,000 years in which the nearly circular orbit of the Earth changes into a more elliptical orbit. The next factor is called obliquity, a period of about 41,000 years where the Earth's axis tilt varies between 21.5 and 24.5 degrees.  The final factor is called precession, a period of approximately 23,000 years where the Earth's axis wobbles like a spinning top.

Milankovitch TheoryOrbital theory of glaciations and climate model

(2) a simple climate model

Milankovitch(1920):(1) accurate calculations of insolation change due to orbital changes

Koeppen and Wegner (1924): give strong support to linking cool summers to initiation of glacials

Sensitivity experiments: Response of temperature to changes in orbital parameters

116 ka 11 ka

Rejection of Orbital Theory

JEK - 2014

Simpson reported LARGE summer temperature chargesAnd LARGE winter temperature changes, but he concluded that these extremes cancelled in the annual average. Therefore Milankovitch’s idea was unimportant.

Simpson (1940):

New observations from marine sediments resurrect Orbital Theory

JEK - 2014

Hays, Imbrie and Shackleton, 1976

Marine observations Spectra with orbital period peaks

but, relative magnitude ?

Power spectral analysis

Proof of orbital forcing!

Spectral analysis

...)2sin(

)sin(

...)2cos()2sin(

)cos()sin(

)]cos()sin([)(

22

110

22

110

0

tc

tcb

tbta

tbtab

ntbntatf nn

22nnn bac

where

Fourier analysis

is the power (amplitude) at frequency nnT /2or period

but, relative magnitude ?

Power spectral analysis

Proof of orbital forcing!

Undersampling!

Homework set 3

• Insolation forcing

• Power spectrum

End of Lecture 8