Astronomical Control of Solar Radiation
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Transcript Astronomical Control of Solar Radiation
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