1. Lecture 8: Orbital Variation and Insolation Change (Chapter 7)

2. Earth’s revolution around the sun on the ecliptic Orbit Today

3. Tilt of the earth’s axis of rotation Tilt Effect

4. Tilting and season Tilt and Season

5. Extreme tilt Extreme Tilts

6. Earth’s revolution around the sun on the ecliptic Perihelion/Aphelion Today

7. Change of tilt

8. Eccentricity of the earth’s orbit

9. Change of Eccentricity

10. Precession of equinoxes (wobble and shift of perihelion) PerihelionAphelion

11. Precession of angle (between perihelion and equinox axes)

12. Extreme Solstice (large eccentricity * large tilt) 0ka 11ka

13. Modulation of Precession Index by Eccentricity

14. Precession Index Modulated by Eccentricity

15. 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%

16. Seasonal insolation

17. Insolation time series of different months

18. Apr, 1 Kepler’s laws: equal area! May 1| Calender =Apr 1 +30 days May 1| Celestial =Apr 1 +30 o Jul 1| Celestial =Apr 1 +90 o Jul 1| Calender =Apr 1 +91 days Calendar months (fixed-day) vs. Celestial months (fixed-degree, or fixed-angular)

19. Calendar vs. Celestial months Starting Vernal Equinox Chen et al., 2010, Clm Dyn 0 ka 126 -0 ka, Calendar month Celestial monthCalendar-Celestial 126 ka (PH June) -- 0 ka (PH Jan)

20. Caloric months (relative warmth) Caloric summer is the 182 days of insolation more than the other 182 days (Caloric winter)

21. Searching for orbital signal in climate records simple complicated

22. 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.

23. Milankovitch Theory Orbital 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

24. Rejection of Orbital Theory JEK - 2014 Simpson reported LARGE summer temperature charges And LARGE winter temperature changes, but he concluded that these extremes cancelled in the annual average. Therefore Milankovitch’s idea was unimportant. Simpson (1940):

25. New observations from marine sediments resurrect Orbital Theory JEK - 2014 Hays, Imbrie and Shackleton, 1976 Marine observationsSpectra with orbital period peaks

26. but, relative magnitude ? Power spectral analysis Proof of orbital forcing!

27. Spectral analysis where Fourier analysis is the power (amplitude) at frequency or period

28. but, relative magnitude ? Power spectral analysis Proof of orbital forcing!

29. Undersampling!

30. Homework set 3 Insolation forcing Power spectrum

31. End of Lecture 8