The Greenhouse Effect Garver GEO 307. Take home points from Chapter 2 EMR carries energy through space If an object can absorb energy, it can also.

The Greenhouse EffectThe Greenhouse Effect

Garver Garver

GEO 307GEO 307

Take home points from Chapter 2Take home points from Chapter 2

EMR carries energy through spaceEMR carries energy through space If an object can absorb energy, it can also If an object can absorb energy, it can also

emit energy.emit energy. Objects emit at a rate equal to TObjects emit at a rate equal to T44

Chapter 3: Layer ModelChapter 3: Layer Model

Algebraic calculation of the effect of an IR Algebraic calculation of the effect of an IR absorber (a pane of glass) on the equil. T of the absorber (a pane of glass) on the equil. T of the Earth.Earth.

Not accurate or detailedNot accurate or detailed Not used for global forecastsNot used for global forecasts

Atmosphere

Boundary to Space

VIS IR

Bare Rock ModelBare Rock Model

T of Earth is controlled by the ways that energy T of Earth is controlled by the ways that energy comes from the Sun and is re-radiated to space as comes from the Sun and is re-radiated to space as IR.IR.

Sun’s T is high so its energy flux is highSun’s T is high so its energy flux is high– See SB lawSee SB law

Simple model of Earth TSimple model of Earth T

Layer model Layer model Toy system to learn fromToy system to learn from

Assumption: Assumption: energy in = energy outenergy in = energy out

– FFinin = F = Foutout

– Flux is in (W = J/S)Flux is in (W = J/S)

Incoming sunlight = Incoming sunlight = IIinin = = 1350 W/m1350 W/m22

solar constantsolar constant

Albedo = reflected light = Albedo = reflected light = Not absorbed and re-radiated as IRNot absorbed and re-radiated as IR Just Just ‘bounces’‘bounces’ back back

Earth = 0.30 - clouds, snow, iceEarth = 0.30 - clouds, snow, ice Venus = 0.70 - sulfuric acid cloudsVenus = 0.70 - sulfuric acid clouds

– But carbon dioxide creates gh effect, T But carbon dioxide creates gh effect, T 758 deg K758 deg K

Mars = 0.15 - no cloudsMars = 0.15 - no clouds– Some carbon dioxide, T Some carbon dioxide, T 253 K (afternoon)253 K (afternoon)

04/19/2304/19/23

Temperature ScalesTemperature Scales

KelvinKelvin CelsiusCelsius FahrenheitFahrenheit

Temperature Conversions:Temperature Conversions:ºC = 5/9(ºF-32) ºC = 5/9(ºF-32)

K = ºC + 273 K = ºC + 273   

Absolute zero at 0 K is −273.15 °C Absolute zero at 0 K is −273.15 °C

(−459.67(−459.67 °F) °F)

Incoming solar energy not reflectedIncoming solar energy not reflected

1350 W/m1350 W/m22 (1 - (1 - ) = ) = 1000 W/m1000 W/m22

Want flux for the whole planet (no mWant flux for the whole planet (no m22)) FFinin(W) = I(W) = Iinin(W/m(W/m22) x Area(m) x Area(m22))

What area do we use?What area do we use?

Sun shines on half the EarthSun shines on half the Earth Light is weaker/strongerLight is weaker/stronger

latitude, dawn/dusklatitude, dawn/dusk

NightDaySolar Constant

Sunlight hits Earth from same direction, makes a circular Sunlight hits Earth from same direction, makes a circular shadow,shadow, use the area of a circle, not a sphere.use the area of a circle, not a sphere.

Earth receives influx of energy equal to the intensity of Earth receives influx of energy equal to the intensity of sunlight multiplied by thesunlight multiplied by the area of a circle = area of a circle = rr22

earthearth

Area (m2) = r2earth

NightDaySolar Constant

Put them together, total incoming flux is:Put them together, total incoming flux is:

FFinin = = rr22earthearth (1 - (1 - ) I) Iin in

Remember: Remember: FFinin = F = Foutout

IIinin = 1350 W/m = 1350 W/m22

Reduce by albedo to 1000 W/mReduce by albedo to 1000 W/m22

Multiply by area of circle to get Flux (W)Multiply by area of circle to get Flux (W)

First layer model has no atmosphere, just a bare rock!First layer model has no atmosphere, just a bare rock!

We’re trying to find a single value for We’re trying to find a single value for TTee of Earth of Earth to go along with a single value of the to go along with a single value of the heat fluxes heat fluxes FFinin and F and Foutout

Rate at which Earth radiates energy is given by Rate at which Earth radiates energy is given by SB law:SB law:

FFout out = Area x = Area x TT44earthearth

= emissivity, 0 to 1, unitless= emissivity, 0 to 1, unitless = 1 would be a blackbody= 1 would be a blackbody

EmissivityEmissivity

From WikipediaFrom Wikipedia

The The emissivityemissivity of a material (written of a material (written εε or or ee) is the relative ) is the relative

ability of its surface to emit energy by radiation. It is the ratio of ability of its surface to emit energy by radiation. It is the ratio of

energy energy radiated by a particular material to energy radiated by by a particular material to energy radiated by

a a black body at the same temperature. A true at the same temperature. A true black body

would have an ε = 1 while any real object would have ε < 1. would have an ε = 1 while any real object would have ε < 1.

Emissivity is a Emissivity is a dimensionless quantity..

The effective The effective emissivity of earth, about 0.612of earth, about 0.612

As we did for solar energy, need to convert As we did for solar energy, need to convert intensity, I, to flux, F, by multiplying by area.intensity, I, to flux, F, by multiplying by area.

What area do we use?What area do we use? Energy leaves in all directionsEnergy leaves in all directions So, we need the area of a sphere;So, we need the area of a sphere;

AAspheresphere = 4 = 4 rr22earthearth

Total Energy Flux from EarthTotal Energy Flux from Earth

FFoutout = 4= 4 rr22earthearthTT44

earthearth

SB law x AreaSB law x Area

FFinin = F = Foutout

rr22earthearth (1 - (1 - )I)Iin =in = 4 4 rr22

earthearthTT44earthearth

Flux Flux

inin

Flux Flux

outout

TT44earthearth

(1 - (1 - )I)Iinin

Can cancel out some factorsCan cancel out some factors

44rr22earthearth TT44

earthearth = = rr22earthearth (1 - (1 - )I)Iinin

TT44earthearth = = (1 - (1 - )I)Iinin

44

No atmosphereNo atmosphere

We know everything here except T of earthWe know everything here except T of earth

Now, rearrange and put Now, rearrange and put TTearthearth alone: alone:

TT44earthearth = = (1 - (1 - ) I) Iiinn

TTearthearth = 4 = 4 (1 - (1 - ) I) Iinin

44

44

TTearthearth = 4 = 4 (1 - (1 - ) I) Iinin44

Now we have a model that shows the relationship Now we have a model that shows the relationship between crucial climate quantities:between crucial climate quantities:

1.1. Solar intensity Solar intensity 2.2. Albedo Albedo

But, if we calculate TBut, if we calculate Tearth earth we get 255 K (-15we get 255 K (-15˚̊C).C).

This is too cold, why?This is too cold, why?

Need a model with a single pane of glass as its atmosphereNeed a model with a single pane of glass as its atmosphere

Simple model lacks gh effectSimple model lacks gh effect

Layer Model with GH EffectLayer Model with GH Effect

Energy diagram for a Energy diagram for a planet with a single pane planet with a single pane of glass for an of glass for an atmosphere. atmosphere.

Glass is transparent to Glass is transparent to incoming incoming VISVIS but a but a blackbody to outgoing blackbody to outgoing IRIR

VISVIS

IRIR

IRIR

IRIR

Incoming Incoming VISVIS passes thru atm, absorbed by surface passes thru atm, absorbed by surface Surface radiates Surface radiates IRIR as as TT44

groundground

IIup,groundup,ground, which is entirely absorbed by atm, which is entirely absorbed by atm Atm has a top and bottom, so Atm has a top and bottom, so

it radiates energy it radiates energy upup and and downdown:: IIup,atmup,atm

IIdown ,atmdown ,atm

TT44groundground

The model assumes that the energy budget is in a steady The model assumes that the energy budget is in a steady state: state: energy in = energy outenergy in = energy out

This applies to individual pieces of the model as well.This applies to individual pieces of the model as well. So energy budget for atm:So energy budget for atm:

IIup,up,atmatm + I+ Idown,down,atmatm = = IIup,up,ggroundround

(units are Watts/Area)(units are Watts/Area)

Or,Or,

TT44atmatm TT44

groundground

TT44groundground

22TT44atmatm

Budget for the ground is differentBudget for the ground is different now because we have now because we have heat flowing down from atm.heat flowing down from atm.

We still assume the energy budget is in a steady state: We still assume the energy budget is in a steady state:

IIinin = I = Ioutout

So the component fluxes are:So the component fluxes are:

IIup,up,groundground = I= Iin,in,solarsolar + I+ Idown,down,atmatm

(units are Watts/Area)(units are Watts/Area)

Or,Or,

TT44groundgroundIIsolarsolarTT44

atmatm

TT44groundground

22TT44atmatm

44

Finally, a budget for the Earth overall:Finally, a budget for the Earth overall: Draw a boundary above the atm and figure that if energy Draw a boundary above the atm and figure that if energy

gets across the line in, it’s flowing out at the same rate.gets across the line in, it’s flowing out at the same rate.

IIup,atmup,atm = I = Iin,solarin,solar

The intensities are comprised of The intensities are comprised of

individual fluxes from the Sun and individual fluxes from the Sun and

the atmosphere.the atmosphere.

TT44atm atm = = IIsolarsolar

TT44groundground

In = OutIn = Out

22TT44atmatm

44

Page 25Page 25

Budget for the Earth overall:Budget for the Earth overall:

TT44atm atm = = IIsolarsolar

One unknown is TOne unknown is Tatmatm

If we solve for TIf we solve for Tatm atm we get the we get the

same answer as solving for same answer as solving for

TTearthearth in the in the bare planet modelbare planet model..

This is an important point!This is an important point!

TT44groundground

In = OutIn = Out

22TT44atmatm

44

It tells us that the place in the Earth system where the T is most directly controlled by the rate of incoming solar energy is the T at the location that radiates to space.

This is called the This is called the skin temperature skin temperature of the Earth.of the Earth.

(it’s equal to the outer most T(it’s equal to the outer most Tatmatm))

Now that we know this we can Now that we know this we can plug that into the budget eqn plug that into the budget eqn for the atm.for the atm.

Page 25 - 26Page 25 - 26TT44

groundground

In = OutIn = Out

22TT44atmatm

And see that: (page 26)And see that: (page 26)

22TT44atm = atm = TT44

groundground

Or,Or,

TTgroundground = 2T = 2Tatmatm

This means that the T of the This means that the T of the ground must be warmer than the ground must be warmer than the skin T by a factor of the fourth root skin T by a factor of the fourth root of 2, an irrational number that = of 2, an irrational number that = 1.189. 1.189. (~19%)(~19%)

Fourth root of 2 = ± 1.189207Fourth root of 2 = ± 1.189207

44

Warmer by about 19%Warmer by about 19%

22TT44atmatm

TT44groundground

TTatmatm

Bottom Line!Bottom Line!

In our model where we slide in an In our model where we slide in an atmosphere we have shown that:atmosphere we have shown that:

The T of the ground must be warmer The T of the ground must be warmer than the skin T (at top of atm) than the skin T (at top of atm) by by roughly ~19%.roughly ~19%.

Final points for Chapter 3Final points for Chapter 3

Result from Result from bare rock bare rock model, this model, this

T is more similar to skin T at top T is more similar to skin T at top

of atmof atmRecorded T Recorded T

Data, not from a Data, not from a

modelmodel

Result from layer model Result from layer model

(w/greenhouse(w/greenhouse))

Too cold

Too warm

Pretty close

253 x 1.189 = 300

Atm is not an energy source like a giant heat lamp in the sky.Atm is not an energy source like a giant heat lamp in the sky.

So, how does it change the T of the ground??So, how does it change the T of the ground??AnalogyAnalogy: Equilibrium: Equilibrium water level in a steadily filling/draining water level in a steadily filling/draining sink.sink.

SinkSink

DrainDrain

Water LevelWater Level

1. Water flows in, hangs out awhile, 1. Water flows in, hangs out awhile, drain out.drain out.

energy in = energy outenergy in = energy out

2. Drains faster as the level rises due 2. Drains faster as the level rises due to inc. pressure (weight).to inc. pressure (weight).

energy flows out faster as T energy flows out faster as T risesrises

3. Eventually water level gets to a 3. Eventually water level gets to a point where flow out equals flow in.point where flow out equals flow in.

This is the equlibrium TThis is the equlibrium T

SinkSink

DrainDrain

Water Level RisesWater Level Rises

4.4. Now, constrict the drain with a penny.Now, constrict the drain with a penny.

Water flows out more slowly, Water flows out more slowly, The water level rises until the higher water level pushes The water level rises until the higher water level pushes more water down drain to balance the flow from the faucet more water down drain to balance the flow from the faucet again.again.

Constrict flowConstrict flow

Greenhouse gases are the Greenhouse gases are the ‘penny ‘penny in the drain’.in the drain’.

They make it more difficult for They make it more difficult for heat to heat to escape the Earth, and as a result escape the Earth, and as a result the equilibrium temperature has the equilibrium temperature has to go up until to go up until the fluxes balance each other the fluxes balance each other again.again.

Take Home PointsTake Home Points The outflow of The outflow of IRIR energy from a planet must energy from a planet must

balance heating from the balance heating from the SunSun..

The planet accomplishes this balance by adjusting The planet accomplishes this balance by adjusting its its temperaturetemperature..

Absorption of outgoing Absorption of outgoing IRIR by the atmosphere by the atmosphere warms the surface of the planet, as the planet warms the surface of the planet, as the planet strives to balance its energy budgetstrives to balance its energy budget