Which picture shows the larger flux of blue circles? 1.Left 2.Right 3.Neither

This Week: Global Climate Model Pt. 1 Reading: Chapter 3 Another Problem Set Coming

Towards a Climate Model The energy of a gas is a function of its temperature only (vice versa). Thus, if the atmosphere’s T changes, its energy balance has changed. If we can describe the sources and sinks of energy, we can predict T.

Radiation Absorption, Emission, Temperature - emission - absorption Characteristic of a body’s T --is an energy loss mechanism Induces more atomic/molecular motion  Increases a body’s T --is an energy source

Interactions of Radiation and Matter All processes happen on Earth and are important in considering the energy balance of the planet. 1. Absorption—causes matter to warm 2. Emission—causes matter to cool 3. Transmission—no interaction 4. Scattering—direction of propagation altered like reflection but more general

Earth Energy Balance Model: Take 1 Simplifying assumptions –1. Radiation is sole form of energy transfer –2. Solar radiation is only energy input, constant –3. Everywhere on Earth receives same average energy –4. Atmosphere plays no role –5. Earth is in radiative equilibrium…Energy flow in equals energy flow out

Emission Spectrum “body”Wavelength selector Photon counter wavelength Flux (photons/m 2 /s)

the peak wavelength... …is inversely proportional to the object’s temperature Radiation Flux (W/m 2 ) Blackbody Radiation: Wien’s Law

Radiation Flux (W/m 2 ) Area under curve is the total emission flux  proportional to T 4 Blackbody Radiation: Stefan-Boltzmann

Energy Balance: Halfway Done Energy Flux In = Energy Flux Out F in = F out F in =  T 4 Earth Assume Earth radiates like a blackbody

The sun’s emission spectrum maximizes at a of ~ 0.5  m. The sun’s temperature is 1.~ 1500 K 2.~ 6000 K 3.~ 15,000 K

Announcements Should have received s from me No class Thurs Jan 31  Attend Focus the Nation First exam scheduled for Fri Feb 8 Review session on Thurs Feb 7 in class Any Device ID starting with 0, will be recorded without the 0.

Energy Balance: Halfway Done Energy Flux In = Energy Flux Out F in = F out F in =  T 4 Earth Assume Earth radiates like a blackbody

Earth’s Energy Balance: Towards F IN Need to account for a)Earth-Sun distance (inverse square law), b)Earth intercepts fraction of total solar flux at D SE c)Earth “reflects” some of the intercepted radiation D SE RSRS

The sun emits about 6.3 X 10 7 W/m 2 of radiant energy How are we still here? Solar Emission Flux

Radiant Energy Flux Far From Source vs r obj d1d1 d2d2 Flux decreases as inverse square of distance from source **this picture is a bit misleading **

Spectrum of Solar Radiation Flux Flux Distribution (measured at Earth) Outside of atmosphere Reaching Earth’s surface Perfect blackbody

Earth’s Energy Balance: Towards F IN Need to account for a)Earth-Sun distance (inverse square law), b)Earth intercepts fraction of total solar flux at D SE c)Earth “reflects” some of the intercepted radiation D SE RSRS

Both the sphere and disc have the same radius, which will intercept more radiation? 1.disc 2.sphere 3.both intercept same “Area” =  r 2 “Area” = 2  r 2

Earth’s Energy Balance: Earth Sun Geometry

Earth’s Energy Balance—No Atmosphere F in = F out Same approach for ANY planet!

Earth’s Energy Balance—No Atmosphere Not a very good prediction! What’s wrong with our model? T E ~ 256 K (-17 o C below freezing) Plug in known values for S o, A, and  and predict

Planet S o /4 = 341 Wm -2 (S o /4)A = 96 Wm -2 F IN ~ 245 Wm -2 F out =  T E 4 “Bare rock” Model (i.e. no atmosphere) Predict T E ~ 256 K when atmosphere is neglected Energy Balance Cartoon

Where did we go wrong? 1.Radiation only form of energy 2.Sun only energy source, constant 3.Solar energy deposited uniformly 4.Atmosphere plays no role 5.F in = F out Examine the validity of our assumptions OK for global energy balance Very good for average state OK for global average energy balance Hmmm… Good for global long-term average

The Greenhouse Effect 289 K – 256 K = 33 K T true – T ”bare rock” The atmosphere increases the average surface temperature by about 13% Can we explain the physics and predict the right T?

Announcements Graded Problem Set 1 handed back tomorrow in discussion Problem Set 2 now/soon available, DUE Friday Feb 1 in discussion  SHOW WORK! Reading Chapter 3

Surface T sf S o /4 (S o /4)A F sf IN F sf OUT Atmosphere T atm (1-  ) F sf OUT  F atm OUT Global Climate Model: Take 2 Let’s model the Earth system as a planetary surface with an absorbing atmosphere above the surface.

Global Climate Model: Take 2 1.The atmosphere absorbs only Outgoing Long wave Radiation (no absorption of solar radiation) 2. The atmosphere absorbs the same fraction of OLR at each wavelength. 3. The atmosphere has a uniform temperature. 4. F in = F out for each component and whole system. Simplifying Assumptions

Non-Blackbodies (<100% absorption) The same springs (matter) forced with three different frequencies - emission - absorption

A body will only emit the same wavelengths it absorbs. Radiation Flux Distribution Ideal Blackbody spectrum True spectrum Kirchoff’s Law: Imperfect Blackbody

Surface T sf S o /4 (S o /4)A S o (1-A)/4 Atmosphere T atm (1-  ) F sf OUT  T atm 4 Global Climate Model: Take 2 A planetary surface with an absorbing atmosphere above the surface. (see pg 43 of textbook) F sf OUT =  T sf 4

Global Climate Model: Take 2 Wear it, sleep on it, put it on your cereal box, …

Global Climate Model: Take 2 If  ~ 0.75, then T Earth ~ 289 K

If the atmosphere’s absorptivity, , increases, Earth’s surface T 1.Increases 2.Decreases 3.Stays the same

1. An OLR absorbing atmosphere slows the net energy flow out from surface (relative to no atm). 2. An increase in atmosphere’s absorptivity causes surface T to increase. 3. Radiation reaching space from the Earth is a combination of emission from a warm surface and colder atmosphere. It must be equivalent to 245 W/m 2 at equilibrium. 1-Layer Model Summary