Which picture shows the larger flux of blue circles?

Transcription

1 Which picture shows the larger flux of blue circles? 33% 33% 33% 1. Left 2. Right 3. Neither Left Right Neither

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

3 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.

4 Radiation Absorption, Emission, Temperature - emission Characteristic of a body s T --is an energy loss mechanism - absorption Induces more atomic/molecular motion Increases a body s T --is an energy source

5 Interactions of Radiation and Matter 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 All processes happen on Earth and are important in considering the energy balance of the planet.

6 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

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

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

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

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

11 The sun s emission spectrum maximizes at a λ of ~ 0.5 µm. The sun s temperature is 1. ~ 1500 K 2. ~ 6000 K 3. ~ 15,000 K 33% 33% 33% ~ 1500 K ~ 6000 K ~ 15,000 K

12 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.

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

14 Earth s Energy Balance: Towards F IN R S D SE 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

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

16 Radiant Energy Flux Far From Source r obj ** vs d 1 d 2 **this picture is a bit misleading Flux decreases as inverse square of distance from source F d! d " = F * 1 d # $ d 2 1 % 2 & 2

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

18 Earth s Energy Balance: Towards F IN R S D SE 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

19 Both the sphere and disc have the same radius, which will intercept more radiation? Area = πr 2 44% 39% Area = 2πr 2 17% 1. disc 2. sphere 3. both intercept same disc sphere both intercept same

20 Earth s Energy Balance: Earth Sun Geometry

21 Earth s Energy Balance No Atmosphere F in = F out S o ( 1" A) 4 4 =! T E T E = & $ % S o 1 ( 1' A) 4 4( #! " Same approach for ANY planet!

22 Earth s Energy Balance No Atmosphere T E = & $ % Plug in known values for S o, A, and σ and predict S o 1 ( 1' A) 4 4( T E ~ 256 K #! " (-17 o C below freezing) Not a very good prediction! What s wrong with our model?

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

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

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

26 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

27 Global Climate Model: Take 2 Let s model the Earth system as a planetary surface with an absorbing atmosphere above the surface. S o /4 (S o /4)A (1-ε) F sf OUT εf atm OUT Atmosphere T atm F sf IN F sf OUT εf atm OUT Surface T sf

28 Global Climate Model: Take 2 Simplifying Assumptions 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.

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

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

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

32 Global Climate Model: Take 2 ( ) !!!! " # $ $ $ $ % & ' ( ) * +, - - =. / A S T o Wear it, sleep on it, put it on your cereal box,

33 Global Climate Model: Take 2 sf T Earth ~ & $ 247 $ $,. / * 1 - $ % + 2 ) ' ( #!!!! " 1 4 If ε ~ 0.75, then T Earth ~ 289 K

34 If the atmosphere s absorptivity, ε, increases, Earth s surface T 1. Increases 2. Decreases 3. Stays the same 59% 37% sf T Earth ~ & # $ 247! $! $,. ) / 1! $ * - ' % + 2 (! " 1 4 Increases Decreases 4% Stays the same

35 1-Layer Model Summary 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.