Astronomical Control of Solar Radiation

1
Astronomical Control of Solar Radiation

• 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 axis
• Shape of Earths 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 Earths Orbit about
  the Sun
• Primarily responsible for existence of seasons

3
What is the Reason For Seasons?

• Eccentricity of Earths Orbit is a secondary
  factor
• Earths 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 Earths orbit not fixed
  around Sun
• Varies in regular cycles
• Gravitational attraction between Earth, its moon,
  the Sun and other planets
• Variations in Earths 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 seasonal change in solar radiation
• Solstices and equinoxes do not exist
• 90 tilt, solar radiation hits poles
• Day-long darkness
• Day-long light
• Extreme
• seasonality

6
Long-term Changes in Axial Tilt

• 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
• 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
• Especially at high latitudes
• 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
• Increased amplitude of seasons
• Decreased tilt does the opposite decreasing
  seasonality

9
Changes in Eccentricity

• Shape of Earths orbit has changed
• Nearly circular
• More elliptical or eccentric

Eccentricity increases as the lengths of axes
become unequal when a b, e 0 and the orbit
is circular
10
Variations in Eccentricity

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

11
Precession of Solstices and Equinoxes

• Positions of solstices and equinoxes change
  through time
• Gradually shift position with respect to
• Earths eccentric orbit and its perihelion and
  aphelion

12
Precessing Top
13
Precessing Top
14
Precessing Top
15
Precessing Top
16
Precessing Top
17
Earths Axial Precession

• In addition to spinning about its axis
• Earths spin axis wobbles
• Gradually leaning in different directions
• Direction of leaning or tilting changes through
  time

18
Earths Axial Precession

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

19
Precession of the Ellipse

• Elliptical shape of Earths orbit rotates
• Precession of ellipse is slower than axial
  precession
• Both motions shift position of the solstices and
  equinoxes

20
Precession of the Equinoxes

• Earths 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

21
Change in Insolation by Precession

• No change in insolation
• Precession of solstices and equinoxes
• Around perfectly circular orbit
• Large change in insolation
• Precession of solstices and equinoxes
• Around an eccentric orbit
• Depending on the relative positions of
• Solstices and equinoxes
• Aphelion and perihelion
• Precessional change in axial tilt

22
Extreme Solstice Positions

• Today June 21 solstice at aphelion
• Solar radiation a bit lower
• 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?

24
Changes in Eccentricity

• Changes in eccentricity affect the magnitude of
  perihelion and aphelion
• Precessional index esinw
• Includes precession of axial tilt and of the
  ellipse
• Converts angular motion into a wave function

25
Earths Precession as Sine Wave

• 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
  Earths precession

Perihelion
March 20 Equinox
26
Precessional Index

• esinw
• Sinw sine wave representation of the slow 360
  rotation of the solstices and equinoxes
• e eccentricity term
• Introduces amplitude variations into sinw
• Provides long-term modulation of the precessional
  index

27
Eccentricity-modulated Precession

• Precession has regular 23,000 year cycle
• Eccentricity has 100,000 and 413,000 year cycles
• 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
• Amplitude of this cycle is modulated at the
  eccentricity periods
• 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 Earths 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 Earths atmosphere
• Changes in axial tilt and eccentricity-modulated
  precession
• Contain all information necessary to calculate
  changes in distribution of insolation
• At any latitude or season
• Insolation usually illustrated during June and
  December solstices

31
Boreal Summer Insolation

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

32
Boreal Winter Insolation

• Similar pattern as boreal summer
• Strong 23,000 precession signal at low to middle
  latitudes
• High latitudes
• Summer
• 41,000 cycle
• High latitudes
• Winter
• Small
• amplitude

33
Opposing Seasonal Insolation

• Seasonal insolation trends move in opposite
  directions
• Both vary by 12
• Long term mean
• 340 W m-2

34
Obliquity (41,000 year cycle)

• Not evident in low 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 anomalies
• Winter small because no insolation at high
  latitudes

35
Summary

• 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
• 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
• Change in total energy
• No change in seasonal energy
• Change in insolation due to e
• Vary by 0.2 about a mean value
• 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
• On opposite sides of 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
• 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

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
• 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 Earths 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?
• 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 Cycles
Add
42
Complications of Overlapping Cycles
Add
43
Complications of Overlapping Cycles
Add
Earths 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
• 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 functions
• With different wavelengths

45
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
• 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
• Record must be sufficiently long
• At least 2 samples per cycle are required
• Define the cycle
• Cycle must not be undersampled

48
Tectonic-Scale Changes in Earths Orbit

• Earths 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