1. Astronomical Control of Solar Radiation Earth's present-day orbit around the Sun Earth's present-day orbit around the Sun  Not permanent  Varies at cycles from 20,000-400,000 years  Changes due to Tilt of Earth's axisTilt of Earth's axis Shape of Earth’s yearly path of revolution around the SunShape of Earth’s yearly path of revolution around the Sun

2. What is the Reason For Seasons? The Tilt or Obliquity of Axis of rotation relative to the plane of the Earth’s Orbit about the Sun The Tilt or Obliquity of Axis of rotation relative to the plane of the Earth’s Orbit about the Sun  Primarily responsible for existence of seasons

3. What is the Reason For Seasons? Eccentricity of Earth’s Orbit is a secondary factor Eccentricity of Earth’s Orbit is a secondary factor Earth’s orbit is not perfectly circular, but has an elliptical shape Orbit shaped by the gravitational pull of nearby planets

4. Long-Term Changes in Orbit Known for centuries that Earth’s orbit not fixed around Sun Known for centuries that Earth’s orbit not fixed around Sun  Varies in regular cycles  Gravitational attraction between Earth, its moon, the Sun and other planets  Variations in Earth’s tilt  Eccentricity of orbit  Relative positions of solstices and equinoxes around the elliptical orbit

5. Simple Change in Axial Tilt No tilt, solar radiation always over equator No tilt, solar radiation always over equator  No seasonal change in solar radiation  Solstices and equinoxes do not exist 90° tilt, solar radiation hits poles 90° tilt, solar radiation hits poles  Day-long darkness  Day-long light  Extreme seasonality seasonality

6. Long-term Changes in Axial Tilt Change in tilt not extreme Change in tilt not extreme  Range from 22.5° to 24.5°  Gravitational tug of large planets Changes in tilt have a period of 41,000 years Changes in tilt have a period of 41,000 years  Cycles are regular  Period  Amplitude  Affects both hemispheres equally

7. Effect of Changes in Axial Tilt Changes in tilt produce long-term variations in seasonal solar radiation Changes in tilt produce long-term variations in seasonal solar radiation  Especially at high latitudes Mainly effects seasonality Mainly effects seasonality  Increased tilt amplifies seasonality  Decreased tilt reduces seasonality

8. Effect of Increased Tilt on Poles Larger tilt moves summer-hemisphere pole more towards the Sun and winter season away from Sun Larger tilt moves summer-hemisphere pole more towards the Sun and winter season away from Sun  Increased amplitude of seasons Decreased tilt does the opposite decreasing seasonality Decreased tilt does the opposite decreasing seasonality

9. Changes in Eccentricity Shape of Earth’s orbit has changed Shape of Earth’s orbit has changed  Nearly circular  More elliptical or eccentric Eccentricity increases as the lengths of axes become unequal – when a = b,  = 0 and the orbit is circular

10. Variations in Eccentricity  changed from ~0.005 to ~0.0607  changed from ~0.005 to ~0.0607  Today  is ~0.0167 Two main periods of eccentricity Two main periods of eccentricity  100,000 year cycle (blend of four periods)  413,000 years All other things equal All other things equal  Greater  leads to greater seasonality  Changes in  affect both hemispheres equally

11. Precession of Solstices and Equinoxes Positions of solstices and equinoxes change through time Positions of solstices and equinoxes change through time  Gradually shift position with respect to  Earth’s eccentric orbit and its perihelion and aphelion

12. Precessing Top

17. Earth’s Axial Precession In addition to spinning about its axis In addition to spinning about its axis  Earth’s spin axis wobbles  Gradually leaning in different directions  Direction of leaning or tilting changes through time

18. Earth’s Axial Precession Caused by gravitational pull of Sun and Moon Caused by gravitational pull of Sun and Moon  On the bulge in Earth diameter at equator Slow turning of Earth’s axis of rotation Slow turning of Earth’s axis of rotation  Causes Earth’s rotational axis to point in different directions through time  One circular path takes 25,700 years

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

20. Precession of the Equinoxes Earth’s wobble and rotation of its elliptical orbit produce precession of the solstices and 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 Simplification of complex angular motions in three- dimensional space

21. Change in Insolation by Precession No change in insolation No change in insolation  Precession of solstices and equinoxes  Around perfectly circular orbit Large change in insolation Large change in insolation  Precession of solstices and equinoxes  Around an eccentric orbit  Depending on the relative positions of Solstices and equinoxesSolstices and equinoxes Aphelion and perihelionAphelion and perihelion Precessional change in axial tiltPrecessional change in axial tilt

22. Extreme Solstice Positions Today June 21 solstice at aphelion Today June 21 solstice at aphelion  Solar radiation a bit lower Configuration reversed ~11,500 years ago Configuration reversed ~11,500 years ago  Precession moves June solstice to perihelion  Solar radiation a bit higher  Assumes no change in eccentricity

23. Question? What will be the effect of a change in eccentricity on insolation? What will be the effect of a change in eccentricity on insolation?

24. Changes in Eccentricity Changes in eccentricity affect the magnitude of perihelion and aphelion Changes in eccentricity affect the magnitude of perihelion and aphelion Precessional index =  sin  Precessional index =  sin   Includes precession of axial tilt and of the ellipse  Converts angular motion into a wave function

25. Earth’s Precession as Sine Wave Sine wave function allow representation of Sine wave function allow representation of  Sweeping motion of a radius vector around a circle  Onto a coordinate system  Circular motion represented as sine wave Allows representation of the angular movements in Earth’s precession Allows representation of the angular movements in Earth’s precession Perihelion March 20 Equinox

26. Precessional Index  sin   sin   Sin  = sine wave representation of the slow 360° rotation of the solstices and equinoxes  = eccentricity term  = eccentricity term  Introduces amplitude variations into sin   Provides long-term modulation of the precessional index

27. Eccentricity-modulated Precession Precession has regular 23,000 year cycle Precession has regular 23,000 year cycle Eccentricity has 100,000 and 413,000 year cycles Eccentricity has 100,000 and 413,000 year cycles Eccentricity modulates precession by changing the amplitude of the angular motion of precession Eccentricity modulates precession by changing the amplitude of the angular motion of precession

28. Long-Term Changes in Precession Precessional index cycle mainly at 23,000 years Precessional index cycle mainly at 23,000 years Amplitude of this cycle is modulated at the eccentricity periods Amplitude of this cycle is modulated at the eccentricity periods Modulation effect not real cycle Modulation effect not real cycle  Envelopes of modulation are not real cycles  Offsetting effects of maximum and minimum values cancel each other  i.e., net amplitude change at 100,000 and 413,000 is zero

29. Summary Gradual changes in Earth’s orbit around the Sun result in changes in solar radiation Gradual changes in Earth’s orbit around the Sun result in changes in solar radiation  Received by season  Received by hemisphere  The axial tilt cycle is 41,000 years  The precession cycle is 23,000 years  Eccentricity variations at 100,000 years and 413,000 years  Modulate the amplitude of the precession cycle

30. Changes in Insolation Insolation is the solar radiation arriving at the top of Earth’s atmosphere Insolation is the solar radiation arriving at the top of Earth’s atmosphere  Changes in axial tilt and eccentricity- modulated precession  Contain all information necessary to calculate changes in distribution of insolation At any latitude or seasonAt any latitude or season Insolation usually illustrated during June and December solstices Insolation usually illustrated during June and December solstices

31. Boreal Summer Insolation Insolation changes as a function of latitude Insolation changes as a function of latitude Strong 23,000 precession signal at low to middle latitudes Strong 23,000 precession signal at low to middle latitudes  High latitudes  Summer 41,000 cycle 41,000 cycle  High latitudes  Winter  Small amplitude amplitude

32. Boreal Winter Insolation Similar pattern as boreal summer Similar pattern as boreal summer Strong 23,000 precession signal at low to middle latitudes Strong 23,000 precession signal at low to middle latitudes  High latitudes  Summer 41,000 cycle 41,000 cycle  High latitudes  Winter  Small amplitude amplitude

33. Opposing Seasonal Insolation Seasonal insolation trends move in opposite directions Seasonal insolation trends move in opposite directions Both vary by ~12% Both vary by ~12%  Long term mean  340 W m -2

34. Obliquity (41,000 year cycle) Not evident in low latitudes Not evident in low latitudes Evident in high latitudes Evident in high latitudes  Small amplitude  More obvious in winter season high latitude  Summer season changes exceed winter  Changes in annual mean insolation at high latitudes Have the same sign as summer insolation anomaliesHave the same sign as summer insolation anomalies  Winter small because no insolation at high latitudes

35. Summary Monthly seasonal insolation changes Monthly seasonal insolation changes  Dominated by 23,000 year cycle  At low and middle latitudes  Effects of 41,000 year cycle  More evident at higher and middle latitudes No cycle of insolation change at 100,000 and 413,000 years No cycle of insolation change at 100,000 and 413,000 years  Eccentricity is not significant as a direct cycle of seasonal change  Contributes only to the modulation of the amplitude of the 23,000 year cycle

36. Eccentricity change in Insolation Eccentricity produces small insolation changes Eccentricity produces small insolation changes  Change in total energy  No change in seasonal energy Change in insolation due to  Change in insolation due to   Vary by ~0.2% about a mean value Change in seasonal insolation due to tilt and precession Change in seasonal insolation due to tilt and precession  Vary by ~10% about a mean value

37. Tilt Changes In-Phase Summer insolation maximum in the N. hemisphere occur at the same time in the 41,000 year cycle as summer insolation maximum in the S. hemisphere Summer insolation maximum in the N. hemisphere occur at the same time in the 41,000 year cycle as summer insolation maximum in the S. hemisphere  On opposite sides of orbit N and S poles are exactly out of phase at a fixed position in the orbit N and S poles are exactly out of phase at a fixed position in the orbit Tilt causes in-phase changes for polar regions of both hemispheres in their respective summer and winter seasons

38. Precession Changes Out-of-Phase Earth-Sun distance controls change in insolation Earth-Sun distance controls change in insolation  Insolation maximum on June 21 is a summer maximum in the N hemisphere  But a winter insolation maximum in the S hemisphere Therefore insolation signals in terms of seasons are out- of-phase between hemispheres Therefore insolation signals in terms of seasons are out- of-phase between hemispheres Precession causes out-of-phase changes between hemispheres for their summer and winter seasons

39. Monthly Precession Curves Seasonal insolation changes associated with precession are lagged Seasonal insolation changes associated with precession are lagged  Each season (month) experiences the same cycle of increasing or decreasing insolation  But the insolation anomalies are offset by 23,000/12 = 1916 years Because all seasons precess around Earth’s orbit, each month has its only insolation trend through time separated by ~2000 y

40. Orbital-Scale Changes in Climate Records How can one disentangle records containing more than one orbital-scale cycle? How can one disentangle records containing more than one orbital-scale cycle? The effects of different cycles add in varying combinations The effects of different cycles add in varying combinations  May be nearly impossible to de- convolve the combined signals by eye

41. Complications of Overlapping CyclesAdd

42. Add

43. Add Earth’s climate records are even more complex because of modulation of the amplitude of the cycles through time

44. Time Series Analysis Time series analysis used to de-convolve orbital scale changes in insolation Time series analysis used to de-convolve orbital scale changes in insolation  Climate proxy data are collected  Plotted as a function of time  Requires precise dating of record  Spectral analysis performed  Detect cycles in records of climate change Explores the data set for correlations with sine wave functionsExplores the data set for correlations with sine wave functions –With different wavelengths

45. Power Spectrum Spectral analysis results in power spectrum Spectral analysis results in power spectrum  Identify period and strength of cycle  Power spectrum of sine waves  Line spectra

46. Power Spectrum of Real Data Actual climate data never true sine waves Actual climate data never true sine waves  Does not result in line spectra  Reveals timescales of oscillation “SPECTRUM” OF GLOBAL TEMPERATURE VARIABILITY

47. Aliasing of Climate Records Period of cycle must be repeated at least 4 times to be identified by spectral analysis Period of cycle must be repeated at least 4 times to be identified by spectral analysis  Record must be sufficiently long At least 2 samples per cycle are required At least 2 samples per cycle are required  Define the cycle  Cycle must not be undersampled

48. Tectonic-Scale Changes in Earth’s Orbit Earth’s orbital characteristics have changed on tectonic time scales Earth’s orbital characteristics have changed on tectonic time scales  Evidence from 440 my coral suggests spin rate changed  Axial tilt and precession changed  Time scales very long