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 Earth’s yearly path of
revolution around the Sun
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
 Primarily responsible for existence of seasons
What is the Reason For Seasons?

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
Long-Term Changes in Orbit

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
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
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
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

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
Changes in Eccentricity

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, e = 0 and
the orbit is
circular
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
Precession of Solstices and Equinoxes

Positions of solstices and equinoxes change
through time
 Gradually shift position with respect to
 Earth’s eccentric orbit and its perihelion
and aphelion
Precessing Top
Precessing Top
Precessing Top
Precessing Top
Precessing Top
Earth’s Axial Precession

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
Earth’s Axial Precession


Caused by gravitational
pull of Sun and Moon
 On the bulge in Earth
diameter at equator
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
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 threedimensional space
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

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
Question?
 What
will be the effect of a change in
eccentricity on insolation?
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
Earth’s 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
Earth’s precession
Perihelion
March 20
Equinox
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

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
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
Summary

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
Changes in Insolation
Insolation is the solar radiation arriving at
the top of Earth’s atmosphere
 Changes in axial tilt and eccentricitymodulated 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

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

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

Opposing Seasonal Insolation
Seasonal insolation
trends move in opposite
directions
 Both vary by ~12%
 Long term mean
 340 W m-2

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
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
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

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
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 outof-phase between hemispheres
Precession causes
out-of-phase
changes between
hemispheres for
their summer and
winter seasons
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 Earth’s orbit, each
month has its only insolation
trend through time
separated by ~2000 y
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 deconvolve the
combined signals by
eye
Complications of Overlapping Cycles
Add
Complications of Overlapping Cycles
Add
Complications of Overlapping Cycles
Add
Earth’s climate records are even
more complex because of
modulation of the amplitude of
the cycles through time
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
Power Spectrum

Spectral analysis results in power spectrum
 Identify period and strength of cycle
 Power spectrum of sine waves
 Line spectra
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
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
Tectonic-Scale Changes in Earth’s Orbit

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