Climate vs Weather - Cornell University · 2010-04-07 · Climate change and its manifestation in terms of weather (climate extremes) Characterizing ... Today: Intro to most basic

J. J. Hack/A. Gettelman: June 2005

ClimatevsWeather

J. J. Hack/A. Gettelman: June 2005

WhatisClimate?

J. J. Hack/A. Gettelman: June 2005

Climate change and its manifestation in terms of weather (climate extremes)

CharacterizingClimate

J. J. Hack/A. Gettelman: June 2005

Question3:Whycan’twepredictweather? Weatherisaninherentlychaoticsystem Classicexample:theLorenzsystem

ClimatevsWeather

!"#$%"&'($)($*"#$+#&*"#,

-.#/$)/$012)3#/()'/&4$(5(*#3(6$/#&,75$

)/)*)&4$%'/2)*)'/($)/$&$25/&3)%&4$(5(*#3$%&/$

"&.#$8-9:$2);;#,#/*$2#(*)/)#(<$

!"#$&**,&%*',$)*(#4;$#/='5($(*,>%*>,#$&/2$)*$)($

*"#$?&,&3#*#,($';$*"#$&**,&%*',$+#$&,#$&;*#,$

)/$?,#2)%*)/@$*"#$%4)3&*#

!"#$&**,&%*',$)($*"#$%4)3&*#A',#/B$C**,&%*',

CharacterizingClimate

Jones

!"#$!%&!'()'*'&+*%,#%,'&-#.*/!

EvidenceofaChangingClimateIntergovernmentalPanelonClimateChange(IPCC):

Warmingis“unequivocal”

!"#$% &'(%)#%

*+),*-#* &.*,)#$)/-

/01234567891: $;283<:

=53089>79>56?81@;232 A3229;8B12>2CC2=6

37179A>62?@2356B321 ?56;2?567=5D>?8E2D1

Jones

Pandora’sBox

!"#$%&$'($)*#$)&$+*(%,-).

!/*0,12$,3$456$71,8&*0

Jones

Whydowetrytopredict?

!"#$%#&'#()*+#,''$#+%#),$'"*+-,$#+.'#/-"+.#*0*+'1#2'++'"3

!"#$%#&'($)*+&',&-%./%*0(%12,3+*(%./%*0(%4+$*0%,)%

-45,#+%#+.-+#&'#.-$#%6#+.'#6),7+5%,5,8#%6#+.'#.)1-,#

5.'6%,&%*0(%&,&(*((&*0%1(&*#$67%89.:(2.1;<

9.0#$%'*#1-+.'1-+57*#:;-0#-#4'0#"%;'3

<

1-,0

Whyusecomputationalmodels?

Jones

Friday:NatalieMahowaldwilltalkaboutfullclimatemodels

Today:Introtomostbasicconceptsofenergybalancemodels

SimplestEnergyBalanceModels

Energygainsequal

Energylosses

Energylosses

Energygains

SimplestEnergyBalanceModels

Sun:~6000K,emitsmainlyinvisiblespectrum(shortwave)Earth:~300K,emitsmainlyinIR(longwave)

IntegrateoverwavelengthfortempTtogettotalemissionfluxσT4‐‐Stefan‐Boltzmann

SpectralIntensityvs

Wavelength

Forblackbodiesatdifferenttemperatures(0°C=273K)

Energygainsequal

Energylosses

Energylosses

EnergygainsBlackBodyRadiation‐Planck

EnergyBalance,NoAtmosphereHypothesis:Earth’stemperatureisaconsequenceof

1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

Energygainsequal

Energylosses

Energylosses

Energygains

FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

Energygainsequal

Energylosses

Energylosses

Energygains

FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

EnergylossbyAlbedoReflectedsolarradiation=αSπa2

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

EnergylossbyAlbedoReflectedsolarradiation=αSπa2

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°C

FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

EnergylossbyAlbedoReflectedsolarradiation=αSπa2

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°C

TooCold–SnowballEarth!FollowingMarshallandPlumb

EnergyBalance,NoAtmosphere

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

EnergylossbyAlbedoReflectedsolarradiation=αSπa2

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°CObservedglobalaveragesurfacetempTs=288K=15°C FollowingMarshallandPlumb

EnergyBalance,NoAtmosphereHypothesis:Earth’stemperatureisaconsequenceof

1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

Energygainsequal

Energylosses

Energylosses

Energygains

Conclusions:

Withthesehypotheses,surfacetempis33°CtoolowWeneedtoincludeatmospheretocorrectthis

255Kisagoodestimateforthetopoftheatmosphere.Whichdoessatisfythehypothesesmoreclosely.

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°CObservedglobalaveragesurfacetempTs=288K=15°C FollowingMarshallandPlumb

Aside:DEViewpoint

EnergyGainSolarflux*cross‐sectarea=Sπa2W

Hypothesis:Earth’stemperatureisaconsequenceof1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

EnergylossbyAlbedoReflectedsolarradiation=αSπa2

EnergylossbyTerrestrialRadiationTerrestrialflux*surfacearea=σTe44πa2

Energygainsequal

Energylosses

Energylosses

Energygains

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°CObservedglobalaveragesurfacetempTs=288K=15°C

Aside:asadifferentialequationfortempTeSign(dTe/dt)=energygain–energyloss=((1‐α)S–σTe4)πa2

• whenTe=255K,dTe/dt=0• whenTe>255K,dTe/dt<0• whenTe<255K,dTe/dt>0

Energybalancecorrespondstoattractingequilibrium.

EnergyBalance,NoAtmosphereHypothesis:Earth’stemperatureisaconsequenceof

1.  Blackbodyradiation2.  DistancefromSun3.  Size4.  Albedo(reflectivity)

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

Energygainsequal

Energylosses

Energylosses

Energygains

Conclusions:

Withthesehypotheses,surfacetempis33°CtoolowWeneedtoincludeatmospheretocorrectthis

255Kisagoodestimateforthetopoftheatmosphere.Whichdoessatisfythehypothesesmoreclosely.

BalanceSπa2=αSπa2+σTe44πa2

 (1‐α)S=4σTe4 Te=255K=‐18°CObservedglobalaveragesurfacetempTs=288K=15°C FollowingMarshallandPlumb

AtmosphericAbsorptionSpectrum

CIMSS/UWisc

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

FollowingMarshallandPlumb

SolarFlux

Recalltotalsolarradiation(W)Solarflux*cross‐sectarea=Sπa2

wElf!O=1IEl2

+-

-tsolar flux-t

------t

/

terrestrial ff r* {

1,2.SolarfluxSWm‐2

2.Raysapprox.parallel

3.Area=πa2

4.Albedoα

1.TerrestrialfluxσTe4

3.SurfaceArea4πa2

Energygainsequal

Energylosses

Energylosses

Energygains

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4 =2σTa4

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4 =2σTa4

So,Ts=2¼Ta≈1.19Ta=303K=30°C

FollowingMarshallandPlumb

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4 =2σTa4

So,Ts=2¼Ta≈1.19Ta=303K=30°C

Surfaceis15°Cwarmerthanobserved.

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4 =2σTa4

So,Ts=2¼Ta≈1.19Ta=303K=30°C

Note:downwellingfromatmosphereisatmagnitudeofsolarflux.

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Solarflux(W/m2):Totalsolarin/surfacearea=Sπa2/4πa2=S/4

Energybalanceoftotalsystem: S/4=αS/4+σTa4

(1‐α)S/4=σTa4 So,asbefore,Ta=255K

Energybalanceatsurface: S/4+σTa4=αS/4+σTs4

σTs4=(1‐α)S/4+σTa4 =2σTa4

So,Ts=2¼Ta≈1.19Ta=303K=30°C

Note:Atmosphereiscoolerthanthesurface.

EnergyBalance,1‐LayerAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Conclusions:Withthesehypotheses• Topofatmosphereis255K(observed250K)• Surfacetempis15°Ctoohigh• Atmosphereiscoolerthansurface

FollowingMarshallandPlumb

EnergyBalance,WithAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Conclusions:Withthesehypotheses• Topofatmosphereis255K(observed250K)• Surfacetempis15°Ctoohigh• Atmosphereiscoolerthansurface

NewHypotheses:• AtmospherepartiallyopaquetoterrestrialIR

Conclusion:Withrealisticε,surfacetempisstilltoohigh

FollowingMarshallandPlumb

EnergyBalance,WithAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation Energygains

equalEnergylosses

Energylosses

Energygains

TerrestrialSolar

Atmosphere

Space

Surface

Conclusions:Withthesehypotheses• Topofatmosphereis255K(observed250K)• Surfacetempis15°Ctoohigh• Atmosphereiscoolerthansurface

NewHypotheses:• AtmospherepartiallyopaquetoterrestrialIR• Manylayersofatmosphere• Accurateεforeachlayer• Accurateεforeachwavelength

Conclusion:Withrealisticatmosphere,surfacetempisstilltoohigh

FollowingMarshallandPlumb

EnergyBalance,WithAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation

NewHypotheses:• AtmospherepartiallyopaquetoIR• Manylayersofatmosphere• Accurateεforeachlayer• Accurateεforeachwavelength

Conclusion:Withrealisticatmosphere,surfacetempisstilltoohigh

AtmospherictemperaturewithheightDogetqualitativereproductionoftemperaturedistributioninatmosphere.

EnergyBalance,WithAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation

NewHypotheses:• AtmospherepartiallyopaquetoIR• Manylayersofatmosphere• Accurateεforeachlayer• Accurateεforeachwavelength

Conclusion:Withrealisticatmosphere,surfacetempisstilltoohigh

AtmospherictemperaturewithheightRadiativeenergybalanceisNOTenoughtoexplainsurfacetemperature.

EnergyBalance,WithAtmosphereHypotheses:Earth’stemperatureisaconsequenceof

1.  Radiation,distancefromsun,size,albedo2.  Singlelayer,uniformatmosphere3.  Atmospheretransparenttosolarradiation4.  Atmosphereopaquetoterrestrialradiation

NewHypotheses:• AtmospherepartiallyopaquetoIR• Manylayersofatmosphere• Accurateεforeachlayer• Accurateεforeachwavelength

Conclusion:Withrealisticatmosphere,surfacetempisstilltoohigh

AtmospherictemperaturewithheightWhy?Coldfluidabovehotfluidisanunstableequilibrium,soconvectionsetsin…fluiddynamicsandweatherintroposphere

! !"#$%&'()*"#+",+-($$

!.()%&+'(/"&+0()-"$/1%&%2

! $(3*#*)4+0"!%(#2++

! !"#$%&'()*"#+",+%#%&54

!"#$%&'#$'())'*+,-"'."*/-&&-&

! "2Du u p gkDt

# # #$ % &' %( ) )*

6*$!&%)*7% 0/8)+"#+5&*92+

! !"##%!)+/*%!%$+",+-"9%3+0:"8#9(&4+!"#9*)*"#$2+

! *#*)*(3*7%+

! $"3'%+!"-/8)()*"#(334

)

NumericalClimateModel

27

3°x2°

1°x1°

ClimateModelGridSize

Jacobson

J. J. Hack/A. Gettelman: June 2005

Observations: 20th Century Warming Model Solutions with Human Forcing

HypothesisTesting

!!"#$%&'()#*+,+%-&#./0&,12#3456,&#7,/8+,#9,45+:&#./0&,1#

1‐DimensionalEnergyBalanceBudyko‐Sellers‐North.Hypotheses:

1.  Rotationalsymmetryofearth2.  Energybalancecalculatedforeachlatitudexi,withtempTi3.  Atmosphericdynamicsprovideheattransportbetweenlayers4.  AlbedodependsonTi(iceornot)–capturesice‐albedofeedback

SolveequationsforTiprofile,andforlocationoficeline

!"#$%&%'(%#)*$+),"#+)-./$&0$)%$#%#*12$3)')%.#$+&4#'5$

6&')*$7)4()-&%$

8'3#4&9$*#:#.,#4$'(1",$(%.*#)/#/$

(0$!;<=$4*&>/$3#'&?$0*##@(%1A$

B(%#)*(@)-&%$&0$CD,1&(%1$

!#**#/,*()'$7)4()-&%$

8//D+#$,"),$),+&/>"#*(.$)%4$&.#)%(.$

+&E#+#%,/$/+&&,"$,"#$,#+>#*),D*#$>*&F'#$$

8,+&/>"#*(.$)%4$&.#)%(.$"#),$,*)%/>&*,5$

Abbot

1‐DEnergyBalanceEquationsLatitudex,temperatureT

Budyko‐SellersModelPredictions

CO2 draw down

Runaway ice-albedo

feedback

Very low weathering allows CO2 to build up to

~10% of atmosphere over 1-10 million years

Tropical ice melts and

reverse ice-albedo

feedback occurs

!"#$%&'()*)"+#',-.#*/'0$-.1+#/')'2341$+)5-"'.3)%$)6'78)7'

63%87'#90*)3"'78#'%#-*-%3+)*'-2/#$:)5-"/;''

Abbot

SnowballEarth:700Myrsago

10 deg variation

in temperature

100 ppm variation

in carbon dioxide

< Gas bubbles in ice

<< EPICA Dome C

Ice Core, Antarctica

The last 600K yrs

2Martin

Morerecent:last600Kyrs

Climate archives: !what information do we have?"

Ruddiman, W. F., 2008. Earth's Climate: past and future"

Martin

Glacial-interglacial cycles!

TemperatureRecord‐2Myrs

Sun

Asorbitchangesslightly,amountofsolarradiationreceivedchanges.• Canexplaintimingofendoficeages• Cannotexplainspeedoramplitudeofrise

Thousandyearsbeforepresent400 300 200 100 0

Milankovichcycles:Variationinorbit&axis,20K,40Kand100Kyears

CombineBudykomodelwithMilankovichcycles

Sun

Temp

CO2

Green‐houseGases

Geol.CarbonCycle

SUN

Thousandyearsbeforepresent400 300 200 100 0

Milankovichcycles:Variationinorbit&axis,20K,40Kand100Kyears

IncludeTemp‐CO2feedbackfromgeologicalcarboncycletohelpunderstandspeedandamplitudeofrise.

Glacial-interglacial cycles!

TemperatureRecord‐2Myrs

PaleoClimateRecord–70MyearsTemperature Carbon

Millionyearsago

Zachos

Whatmodelscapturethisbehavior?

Especiallyabruptchanges.

Instructivetodevelopahierarchyofmodelsofincreasingcomplexity.

Whendorobustbehaviorsofsimplemodelspersistasweincreasecomplexity?

Usedifferentlevelsofmodelhierarchytogiveinsightintofeedbackinteractionsbetweenclimateprocesses.