Astronomical Control of Solar Radiation

Earth's present-day orbit around the SunEarth's present-day orbit around the Sun Not permanentNot permanent Varies at cycles from 20,000-400,000 Varies at cycles from 20,000-400,000

years years Changes due toChanges due to

•Tilt of Earth's axisTilt of Earth's axis•Shape of Earth’s yearly path of Shape of Earth’s yearly path of revolution around the Sunrevolution around the Sun

What is the Reason For What is the Reason For Seasons?Seasons?

The Tilt or Obliquity of Axis of rotation relative The Tilt or Obliquity of Axis of rotation relative to the plane of the Earth’s Orbit about the Sunto the plane of the Earth’s Orbit about the Sun Primarily responsible for existence of seasonsPrimarily responsible for existence of seasons

What is the Reason For What is the Reason For Seasons?Seasons?

Eccentricity of Earth’s Orbit is a Eccentricity of Earth’s Orbit is a secondary factorsecondary factor

Earth’s orbitEarth’s orbitis not perfectlyis not perfectlycircular, butcircular, buthas an ellipticalhas an ellipticalshape shape

Orbit shaped byOrbit shaped bythe gravitationalthe gravitationalpull of nearbypull of nearbyplanetsplanets

Long-Term Changes in Orbit Known for centuries that Earth’s orbit not Known for centuries that Earth’s orbit not

fixed around Sunfixed around Sun Varies in regular cyclesVaries in regular cycles Gravitational attraction between Earth, Gravitational attraction between Earth,

its moon, the Sun and other planetsits moon, the Sun and other planetsVariations in Earth’s tiltVariations in Earth’s tiltEccentricity of orbitEccentricity of orbitRelative positions of solstices and Relative positions of solstices and equinoxes around the elliptical orbitequinoxes around the elliptical orbit

Simple Change in Axial Tilt No tilt, solar radiation always over equatorNo tilt, solar radiation always over equator

No seasonal change in solar radiationNo seasonal change in solar radiation Solstices and equinoxes do not existSolstices and equinoxes do not exist

90° tilt, solar radiation hits poles90° tilt, solar radiation hits poles Day-long darknessDay-long darkness Day-long lightDay-long light ExtremeExtreme seasonalityseasonality

Long-term Changes in Axial Tilt Change in tilt not extremeChange in tilt not extreme

Range from 22.5° to Range from 22.5° to 24.5°24.5°

Gravitational tug of Gravitational tug of large planetslarge planets

Changes in tilt have a Changes in tilt have a period of 41,000 yearsperiod of 41,000 years Cycles are regularCycles are regular

PeriodPeriodAmplitudeAmplitude

Affects both Affects both hemispheres equallyhemispheres equally

Effect of Changes in Axial Tilt Changes in tilt produce long-term Changes in tilt produce long-term

variations in seasonal solar radiationvariations in seasonal solar radiation Especially at high latitudesEspecially at high latitudes

Mainly effects seasonalityMainly effects seasonality Increased tilt amplifies seasonalityIncreased tilt amplifies seasonality Decreased tilt reduces seasonalityDecreased tilt reduces seasonality

Effect of Increased Tilt on Poles Larger tilt moves summer-hemisphere pole more Larger tilt moves summer-hemisphere pole more

towards the Sun and winter season away from Suntowards the Sun and winter season away from Sun Increased amplitude of seasonsIncreased amplitude of seasons

Decreased tilt does the opposite decreasing Decreased tilt does the opposite decreasing seasonalityseasonality

Changes in Eccentricity Shape of Earth’s orbit has changedShape of Earth’s orbit has changed

Nearly circularNearly circular More elliptical or eccentricMore elliptical or eccentric

Eccentricity Eccentricity increases as increases as the lengths of the lengths of axes become axes become unequal – unequal – when when aa = = bb, , = 0 and the = 0 and the orbit is orbit is circularcircular

Variations in Eccentricity changed from ~0.005 to changed from ~0.005 to

~0.0607~0.0607 Today Today is ~0.0167 is ~0.0167

Two main periods of Two main periods of eccentricityeccentricity 100,000 year cycle (blend 100,000 year cycle (blend

of four periods)of four periods) 413,000 years413,000 years

All other things equalAll other things equal Greater Greater leads to greater leads to greater

seasonalityseasonality Changes in Changes in affect both affect both

hemispheres equallyhemispheres equally

Precession of Solstices and Equinoxes

Positions of solstices and equinoxes Positions of solstices and equinoxes change through timechange through time Gradually shift position with respect toGradually shift position with respect to

Earth’s eccentric orbit and its Earth’s eccentric orbit and its perihelion and aphelionperihelion and aphelion

Precessing Top

Precessing Top

Precessing Top

Precessing Top

Precessing Top

Earth’s Axial Precession In addition to spinning about its axisIn addition to spinning about its axis

Earth’s spin axis wobblesEarth’s spin axis wobbles Gradually leaning in different directionsGradually leaning in different directions Direction of leaning or tilting changes through Direction of leaning or tilting changes through

timetime

Earth’s Axial Precession Caused by gravitational Caused by gravitational

pull of Sun and Moonpull of Sun and Moon On the bulge in Earth On the bulge in Earth

diameter at equatordiameter at equator Slow turning of Earth’s Slow turning of Earth’s

axis of rotationaxis of rotation Causes Earth’s Causes Earth’s

rotational axis to rotational axis to point in different point in different directions through directions through timetime

One circular path One circular path takes 25,700 yearstakes 25,700 years

Precession of the Ellipse Elliptical shape of Elliptical shape of

Earth’s orbit Earth’s orbit rotatesrotates Precession of Precession of

ellipse is slower ellipse is slower than axial than axial precessionprecession

Both motions Both motions shift position of shift position of the solstices the solstices and equinoxes and equinoxes

Precession of the Equinoxes Earth’s wobble and Earth’s wobble and

rotation of its rotation of its elliptical orbit elliptical orbit produce precession produce precession of the solstices and of the solstices and equinoxesequinoxes One cycles takes One cycles takes

23,000 years23,000 years Simplification of Simplification of

complex angular complex angular motions in three-motions in three-dimensional spacedimensional space

Change in Insolation by Precession

No change in insolationNo change in insolation Precession of solstices and equinoxesPrecession of solstices and equinoxes

Around perfectly circular orbitAround perfectly circular orbit Large change in insolationLarge change in insolation

Precession of solstices and equinoxesPrecession of solstices and equinoxesAround an eccentric orbitAround an eccentric orbitDepending on the relative positions ofDepending on the relative positions of

•Solstices and equinoxesSolstices and equinoxes•Aphelion and perihelionAphelion and perihelion•Precessional change in axial tiltPrecessional change in axial tilt

Extreme Solstice Positions Today June 21 solstice at aphelionToday June 21 solstice at aphelion

Solar radiation a bit lowerSolar radiation a bit lower Configuration reversed ~11,500 years agoConfiguration reversed ~11,500 years ago

Precession moves June solstice to perihelionPrecession moves June solstice to perihelion Solar radiation a bit higherSolar radiation a bit higher Assumes no change in eccentricityAssumes no change in eccentricity

Question? What will be the effect of a change in What will be the effect of a change in

eccentricity on insolation?eccentricity on insolation?

Changes in Eccentricity Changes in eccentricity Changes in eccentricity

affect the magnitude of affect the magnitude of perihelion and aphelionperihelion and aphelion

Precessional index = Precessional index = sinsin Includes precession of Includes precession of

axial tilt and of the ellipseaxial tilt and of the ellipse Converts angular motion Converts angular motion

into a wave functioninto a wave function

Earth’s Precession as Sine Wave

Sine wave function allow representation ofSine wave function allow representation of Sweeping motion of a radius vector around a circleSweeping motion of a radius vector around a circle Onto a coordinate systemOnto a coordinate system

Circular motion represented as sine waveCircular motion represented as sine wave Allows representation of the angular movements in Allows representation of the angular movements in

Earth’s precessionEarth’s precession

Perihelion

March 20Equinox

Precessional Index sinsin

SinSin = sine wave representation of the = sine wave representation of the slow 360° rotation of the solstices and slow 360° rotation of the solstices and equinoxesequinoxes

= eccentricity term= eccentricity term Introduces amplitude variations into Introduces amplitude variations into

sinsin Provides long-term modulation of the Provides long-term modulation of the

precessional indexprecessional index

Eccentricity-modulated Precession Precession has regular 23,000 year cyclePrecession has regular 23,000 year cycle

Eccentricity has 100,000 and 413,000 year cyclesEccentricity has 100,000 and 413,000 year cycles Eccentricity modulates precession by changing the Eccentricity modulates precession by changing the

amplitude of the angular motion of precessionamplitude of the angular motion of precession

Long-Term Changes in Precession

Precessional index cycle Precessional index cycle mainly at 23,000 yearsmainly at 23,000 years

Amplitude of this cycle is Amplitude of this cycle is modulated at the eccentricity modulated at the eccentricity periodsperiods

Modulation effect not real Modulation effect not real cyclecycle Envelopes of modulation are Envelopes of modulation are

not real cyclesnot real cycles Offsetting effects of Offsetting effects of

maximum and minimum maximum and minimum values cancel each othervalues cancel each other

i.e., net amplitude change i.e., net amplitude change at 100,000 and 413,000 is at 100,000 and 413,000 is zerozero

Summary Gradual changes in Earth’s orbit around Gradual changes in Earth’s orbit around

the Sun result in changes in solar the Sun result in changes in solar radiationradiation Received by seasonReceived by season Received by hemisphereReceived by hemisphere

The axial tilt cycle is 41,000 yearsThe axial tilt cycle is 41,000 yearsThe precession cycle is 23,000 yearsThe precession cycle is 23,000 years

Eccentricity variations at 100,000 years Eccentricity variations at 100,000 years and 413,000 yearsand 413,000 yearsModulate the amplitude of the Modulate the amplitude of the precession cycleprecession cycle

Changes in Insolation Insolation is the solar radiation arriving at Insolation is the solar radiation arriving at

the top of Earth’s atmospherethe top of Earth’s atmosphere Changes in axial tilt and eccentricity-Changes in axial tilt and eccentricity-

modulated precessionmodulated precessionContain all information necessary to Contain all information necessary to calculate changes in distribution of calculate changes in distribution of insolationinsolation•At any latitude or seasonAt any latitude or season

Insolation usually illustrated during June Insolation usually illustrated during June and December solsticesand December solstices

Boreal Summer Insolation Insolation changes as a function of latitudeInsolation changes as a function of latitude Strong 23,000 precession signal at low to Strong 23,000 precession signal at low to

middle latitudesmiddle latitudes High latitudesHigh latitudes

SummerSummer 41,000 cycle41,000 cycle

High latitudesHigh latitudesWinterWinterSmallSmall

amplitudeamplitude

Boreal Winter Insolation Similar pattern as boreal summerSimilar pattern as boreal summer Strong 23,000 precession signal at low to Strong 23,000 precession signal at low to

middle latitudesmiddle latitudes High latitudesHigh latitudes

SummerSummer 41,000 cycle41,000 cycle

High latitudesHigh latitudesWinterWinterSmallSmall

amplitudeamplitude

Opposing Seasonal Insolation Seasonal insolation Seasonal insolation

trends move in trends move in opposite directionsopposite directions

Both vary by ~12%Both vary by ~12% Long term meanLong term mean 340 W m340 W m-2-2

Obliquity (41,000 year cycle) Not evident in low latitudesNot evident in low latitudes Evident in high latitudesEvident in high latitudes

Small amplitudeSmall amplitudeMore obvious in winter season high latitudeMore obvious in winter season high latitude

Summer season changes exceed winterSummer season changes exceed winterChanges in annual mean insolation at high Changes in annual mean insolation at high

latitudeslatitudes•Have the same sign as summer Have the same sign as summer

insolation anomaliesinsolation anomalies Winter small because no insolation at high Winter small because no insolation at high

latitudeslatitudes

Summary Monthly seasonal insolation changesMonthly seasonal insolation changes

Dominated by 23,000 year cycleDominated by 23,000 year cycleAt low and middle latitudesAt low and middle latitudes

Effects of 41,000 year cycleEffects of 41,000 year cycleMore evident at higher and middle More evident at higher and middle

latitudeslatitudes No cycle of insolation change at 100,000 and No cycle of insolation change at 100,000 and

413,000 years413,000 years Eccentricity is not significant as a direct cycle Eccentricity is not significant as a direct cycle

of seasonal changeof seasonal changeContributes only to the modulation of the Contributes only to the modulation of the

amplitude of the 23,000 year cycleamplitude of the 23,000 year cycle

Eccentricity change in Insolation

Eccentricity produces small insolation Eccentricity produces small insolation changeschanges Change in total energyChange in total energy No change in seasonal energyNo change in seasonal energy

Change in insolation due to Change in insolation due to Vary by ~0.2% about a mean valueVary by ~0.2% about a mean value

Change in seasonal insolation due to tilt Change in seasonal insolation due to tilt and precessionand precession Vary by ~10% about a mean valueVary by ~10% about a mean value

Tilt Changes In-Phase Summer insolation maximum in the N. hemisphere Summer insolation maximum in the N. hemisphere

occur at the same time in the 41,000 year cycle as occur at the same time in the 41,000 year cycle as summer insolation maximum in the S. hemispheresummer insolation maximum in the S. hemisphere On opposite sides of orbitOn opposite sides of orbit

N and S poles are exactly out of phase at a fixed N and S poles are exactly out of phase at a fixed position in the orbit position in the orbit

Tilt causes in-phaseTilt causes in-phasechanges for polarchanges for polarregions of bothregions of bothhemispheres inhemispheres intheir respectivetheir respectivesummer and wintersummer and winterseasonsseasons

Precession Changes Out-of-Phase

Earth-Sun distance controls change in insolationEarth-Sun distance controls change in insolation Insolation maximum on June 21 is a Insolation maximum on June 21 is a summersummer

maximum in the N hemispheremaximum in the N hemisphere But a But a winterwinter insolation maximum in the S hemisphere insolation maximum in the S hemisphere

Therefore insolation signals in terms of seasons are out-Therefore insolation signals in terms of seasons are out-of-phase between hemispheresof-phase between hemispheres

Precession causesPrecession causesout-of-phaseout-of-phasechanges betweenchanges betweenhemispheres forhemispheres fortheir summer andtheir summer andwinter seasonswinter seasons

Monthly Precession Curves Seasonal insolation changes associated with Seasonal insolation changes associated with

precession are laggedprecession are lagged Each season (month) experiences the same Each season (month) experiences the same

cycle of increasing or decreasing insolationcycle of increasing or decreasing insolation But the insolation anomalies are offset by But the insolation anomalies are offset by

23,000/12 = 1916 years23,000/12 = 1916 years

Because all seasons precessBecause all seasons precessaround Earth’s orbit, eacharound Earth’s orbit, eachmonth has its only insolationmonth has its only insolationtrend through timetrend through timeseparated by ~2000 yseparated by ~2000 y

Orbital-Scale Changes in Climate Records

How can one How can one disentangle records disentangle records containing more than containing more than one orbital-scale one orbital-scale cycle?cycle?

The effects of The effects of different cycles add in different cycles add in varying combinationsvarying combinations May be nearly May be nearly

impossible to de-impossible to de-convolve the convolve the combined signals combined signals by eyeby eye

Complications of Overlapping Cycles

AddAdd

Complications of Overlapping Cycles

AddAdd

Complications of Overlapping Cycles

AddAdd

Earth’s climate records are Earth’s climate records are evenevenmore complex because ofmore complex because ofmodulation of the amplitude modulation of the amplitude ofofthe cycles through timethe cycles through time

Time Series Analysis Time series analysis used to de-convolve Time series analysis used to de-convolve

orbital scale changes in insolationorbital scale changes in insolation Climate proxy data are collectedClimate proxy data are collected Plotted as a function of timePlotted as a function of time

Requires precise dating of recordRequires precise dating of record Spectral analysis performedSpectral analysis performed

Detect cycles in records of climate Detect cycles in records of climate changechange•Explores the data set for Explores the data set for correlations with sine wave correlations with sine wave functionsfunctions–With different wavelengthsWith different wavelengths

Power Spectrum Spectral analysis results in power spectrumSpectral analysis results in power spectrum

Identify period and strength of cycleIdentify period and strength of cycle Power spectrum of sine wavesPower spectrum of sine waves

Line spectra Line spectra

Power Spectrum of Real Data Actual climate data never true sine wavesActual climate data never true sine waves

Does not result in line spectraDoes not result in line spectra Reveals timescales of oscillationReveals timescales of oscillation

“SPECTRUM” OF GLOBAL TEMPERATURE VARIABILITY

Aliasing of Climate Records Period of cycle must be repeated at least 4 Period of cycle must be repeated at least 4

times to be identified by spectral analysistimes to be identified by spectral analysis Record must be sufficiently longRecord must be sufficiently long

At least 2 samples per cycle are requiredAt least 2 samples per cycle are required Define the cycleDefine the cycle Cycle must not be undersampledCycle must not be undersampled

Tectonic-Scale Changes in Earth’s Orbit

Earth’s orbital Earth’s orbital characteristics have characteristics have changed on changed on tectonic time scalestectonic time scales Evidence from Evidence from

440 my coral 440 my coral suggests spin suggests spin rate changedrate changedAxial tilt and Axial tilt and precession precession changedchanged

Time scales very Time scales very longlong